Journal articles on the topic 'Non-Newtonian fluid flows (incl. rheology)'
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1
KOPLIK, JOEL, and JAYANTH R. BANAVAR. "MOLECULAR DYNAMICS SIMULATIONS OF NON-NEWTONIAN EXTENSIONAL FLUID FLOWS." International Journal of Modern Physics B 17, no. 01n02 (January 20, 2003): 27–32. http://dx.doi.org/10.1142/s0217979203017047.
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We discuss the use of molecular dynamics computer simulations in the extensional flow dynamics of polymeric, non-Newtonian liquids. The molecular model consists of Lennard-Jones monomers bound into linear chains by FENE potentials, a system known to exhibit characteristic non-Newtonian behavior such as shear thinning and normal stress differences. Here, we simulate liquid bridge flows in which cylinders of such liquids are placed between solid plates and extended to the point of rupture. Measurements of the local fluid stress tensor and interface shape provide information on extensional viscosity and rheology, coupled to microscopic information based on the evolution of molecular configurations. The simulations are in good agreement with laboratory data and with the results of macroscopic numerical calculations where available, but provide new and detailed information on the internal dynamics of liquids in extensional flow.
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Roychowdhury, Souradeep, Rajarshi Chattopadhyay, and Sandip Sarkar. "Thermally developed electrokinetic bi-layer flows of Newtonian and non-Newtonian fluids in a microchannel." Physics of Fluids 34, no. 4 (April 2022): 042011. http://dx.doi.org/10.1063/5.0087355.
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In the present study, thermofluidic characteristics of a combined pressure-driven and electrical field mediated thermally fully developed flow of an immiscible Newtonian and a viscoelastic fluid bi-layer in a microchannel have been analyzed. The simplified Phan-Thien–Tanner model with a linear kernel for the stress coefficient function has been utilized to describe the complex fluid rheology for the non-Newtonian fluid. Disparate zeta potentials have been assumed at the interfaces. Accordingly, distinct zeta potential values have been used at the channel walls and interfaces between the fluids to derive the closed-form analytical expressions for the pertinent velocity, stress, and shear viscosity distributions in the fluid layers. For thermally developed flows, the temperature and entropy distributions are obtained along the microchannel for constant wall heat flux boundary conditions. Major findings from our research show that amplification of the viscoelastic parameter designated by the Weissenberg number exhibits an enhancement in the non-dimensional axial velocity, flow rate, and stress magnitudes. Furthermore, the present study indicates that Joule heating and viscous dissipation significantly vary the dimensionless temperature profiles along the fluid bi-layer. The Nusselt number values are found to decrease with the augmentation of the viscoelasticity, Joule heating, and viscous dissipation parameters. The total entropy generation for the fluid layer systems increases with the increasing Joule heating parameter.
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Arzani, Amirhossein. "Accounting for residence-time in blood rheology models: do we really need non-Newtonian blood flow modelling in large arteries?" Journal of The Royal Society Interface 15, no. 146 (September 2018): 20180486. http://dx.doi.org/10.1098/rsif.2018.0486.
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Patient-specific computational fluid dynamics (CFD) is a promising tool that provides highly resolved haemodynamics information. The choice of blood rheology is an assumption in CFD models that has been subject to extensive debate. Blood is known to exhibit shear-thinning behaviour, and non-Newtonian modelling has been recommended for aneurysmal flows. Current non-Newtonian models ignore rouleaux formation, which is the key player in blood's shear-thinning behaviour. Experimental data suggest that red blood cell aggregation and rouleaux formation require notable red blood cell residence-time (RT) in a low shear rate regime. This study proposes a novel hybrid Newtonian and non-Newtonian rheology model where the shear-thinning behaviour is activated in high RT regions based on experimental data. Image-based abdominal aortic and cerebral aneurysm models are considered and highly resolved CFD simulations are performed using a minimally dissipative solver. Lagrangian particle tracking is used to define a backward particle RT measure and detect stagnant regions with increased rouleaux formation likelihood. Our novel RT-based non-Newtonian model shows a significant reduction in shear-thinning effects and provides haemodynamic results qualitatively identical and quantitatively close to the Newtonian model. Our results have important implications in patient-specific CFD modelling and suggest that non-Newtonian models should be revisited in large artery flows.
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Panasenko, G., K. Pileckas, and B. Vernescu. "Steady state non-Newtonian flow in a thin tube structure: equation on the graph." St. Petersburg Mathematical Journal 33, no. 2 (March 4, 2022): 327–40. http://dx.doi.org/10.1090/spmj/1702.
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The dimension reduction for the viscous flows in thin tube structures leads to equations on the graph for the macroscopic pressure with Kirchhoff type junction conditions at the vertices. Nonlinear equations on the graph generated by the non-Newtonian rheology are treated here. The existence and uniqueness of a solution of this problem is proved. This solution describes the leading term of an asymptotic analysis of the stationary non-Newtonian fluid motion in a thin tube structure with no-slip boundary condition on the lateral boundary.
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VERGUET, STÉPHANE, CHUANHUA DUAN, ALBERT LIAU, VEYSEL BERK, JAMIE H. D. CATE, ARUN MAJUMDAR, and ANDREW J. SZERI. "Mechanics of liquid–liquid interfaces and mixing enhancement in microscale flows." Journal of Fluid Mechanics 652 (May 19, 2010): 207–40. http://dx.doi.org/10.1017/s0022112009994113.
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Experimental work on mixing in microfluidic devices has been of growing importance in recent years. Interest in probing reaction kinetics faster than the minute or hour time scale has intensified research in designing microchannel devices that would allow the reactants to be mixed on a time scale faster than that of the reaction. Particular attention has been paid to the design of microchannels in order to enhance the advection phenomena in these devices. Ultimately, in vitro studies of biological reactions can now be performed in conditions that reflect their native intracellular environments. Liau et al. (Anal. Chem., vol. 77, 2005, p. 7618) have demonstrated a droplet-based microfluidic mixer that induces improved chaotic mixing of crowded solutions in milliseconds due to protrusions (‘bumps’) on the microchannel walls. Liau et al. (2005) have shown it to be possible to mix rapidly plugs of highly concentrated protein solutions such as bovine hemoglobin and bovine serum albumin. The present work concerns an analysis of the underlying mechanisms of shear stress transfer at liquid–liquid interfaces and associated enhanced mixing arising from the protrusions along the channel walls. The role of non-Newtonian rheology and surfactants is also considered within the mixing framework developed by Aref, Ottino and Wiggins in several publications. Specifically, we show that proportional thinning of the carrier fluid lubrication layer at the bumps leads to greater advection velocities within the plugs, which enhances mixing. When the fluid within the plugs is Newtonian, mixing will be enhanced by the bumps if they are sufficiently close to one another. Changing either the rheology of the fluid within the plugs (from Newtonian to non-Newtonian) or modifying the mechanics of the carrier fluid-plug interface (by populating it with insoluble surfactants) alters the mixing enhancement.
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MÁLEK, J., M. RŮŽIČKA, and V. V. SHELUKHIN. "HERSCHEL–BULKLEY FLUIDS: EXISTENCE AND REGULARITY OF STEADY FLOWS." Mathematical Models and Methods in Applied Sciences 15, no. 12 (December 2005): 1845–61. http://dx.doi.org/10.1142/s0218202505000996.
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The equations for steady flows of Herschel–Bulkley fluids are considered and the existence of a weak solution is proved for the Dirichlet boundary-value problem. The rheology of such a fluid is defined by a yield stress τ* and a discontinuous constitutive relation between the Cauchy stress and the symmetric part of the velocity gradient. Such a fluid stiffens if its local stresses do not exceed τ*, and it behaves like a non-Newtonian fluid otherwise. We address here a class of nonlinear fluids which includes shear-thinning p-law fluids with 9/5 < p ≤ 2. The flow equations are formulated in the stress-velocity setting (cf. Ref. 25). Our approach is different from that of Duvaut–Lions (cf. Ref. 10) developed for classical Bingham visco-plastic materials. We do not apply the variational inequality but make use of an approximation of the Herschel–Bulkley fluid with a generalized Newtonian fluid with a continuous constitutive law.
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Avazmohammadi, Reza, and Pedro Ponte Castañeda. "The rheology of non-dilute dispersions of highly deformable viscoelastic particles in Newtonian fluids." Journal of Fluid Mechanics 763 (December 17, 2014): 386–432. http://dx.doi.org/10.1017/jfm.2014.687.
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AbstractWe present a model for the rheological behaviour of non-dilute suspensions of initially spherical viscoelastic particles in viscous fluids under uniform Stokes flow conditions. The particles are assumed to be neutrally buoyant Kelvin–Voigt solids undergoing time-dependent finite deformations and exhibiting generalized neo-Hookean behaviour in their purely elastic limit. We investigate the effects of the shape dynamics and constitutive properties of the viscoelastic particles on the macroscopic rheological behaviour of the suspensions. The proposed model makes use of known homogenization estimates for composite material systems consisting of random distributions of aligned ellipsoidal particles with prescribed two-point correlation functions to generate corresponding estimates for the instantaneous (incremental) response of the suspensions, together with appropriate evolution laws for the relevant microstructural variables. To illustrate the essential features of the model, we consider two special cases: (i) extensional flow and (ii) simple shear flow. For each case, we provide the time-dependent response and, when available, the steady-state solution for the average particle shape and orientation, as well as for the effective viscosity and normal stress differences in the suspensions. The results exhibit shear thickening for extensional flows and shear thinning for simple shear flows, and it is found that the volume fraction and constitutive properties of the particles significantly influence the rheology of the suspensions under both types of flows. In particular, for extensional flows, suspensions of particles with finite extensibility constraints are always found to reach a steady state, while this is only the case at sufficiently low strain rates for suspensions of (less realistic) neo-Hookean particles, as originally reported by Roscoe (J. Fluid Mech., vol. 28, 1967, pp. 273–293) and Gao et al. (J. Fluid Mech., vol. 687, 2011, pp. 209–237). For shear flows, viscoelastic particles with high viscosities can experience a damped oscillatory motion of decreasing amplitude before reaching the steady state.
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Almqvist, T., and R. Larsson. "Some Remarks on the Validity of Reynolds Equation in the Modeling of Lubricant Film Flows on the Surface Roughness Scale." Journal of Tribology 126, no. 4 (October 1, 2004): 703–10. http://dx.doi.org/10.1115/1.1760554.
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The objective of this paper is to investigate the flow in a lubricant film on the surface roughness scale and to compare the numerical solutions obtained by two different solution approaches. This is accomplished firstly by the CFD-approach (computational fluid dynamic approach) where the momentum and continuity equations are solved separately, and secondly the Reynolds equation approach, which is a combination and a simplification of the above equations. The rheology is assumed to be both Newtonian and non-Newtonian. An Eyring model is used in the non-Newtonian case. The result shows that discrepancies between the two approaches may occur, primarily due to a singularity which appears in the momentum equations when the stresses in the lubricant attain magnitudes that are common in EHL. This singularity is not represented by the Reynolds equation. If, however, the rheology is shifted to a non-Newtonian Eyring model the deviations between the two solution approaches is removed or reduced. The second source of discrepancies between the two approaches is the film thickness to wavelength scale ω. It will be shown that the Reynolds equation is valid until this ratio is approximately O10−2.
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Maciel, Geraldo de Freitas, Evandro Fernandes da Cunha, Yuri Taglieri Sao, André Luis Toniati, Guilherme Henrique Fiorot, Fabiana de Oliveira Ferreira, Cláudio Kitano, and Vicente de Paula Gonçalves Junior. "Non-intrusive techniques to measure roll waves level evolving in a flume." E3S Web of Conferences 40 (2018): 05049. http://dx.doi.org/10.1051/e3sconf/20184005049.
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An open-channel experimental set-up is presented in this paper as a tool for examining the presence of instabilities on free-surfaces flows of non-Newtonian fluid. When these flows occur in favorable conditions of inclination, discharge and rheological properties, the propagation of instabilities can evolve into a specific type of wave, known as roll waves. The experimental apparatus developed allows study of stabilized roll waves in many scenarios for non-Newtonian rheology fluids, thereby constituting a highly useful tool for the understanding and control of roll waves. The test fluid used in the experiments was carbopol gel which is rheometrically representative of the muddy material from natural disasters, such as mudflows. Two non-intrusive level measurement systems are proposed (ultrasonic transducer and laser-based absorption technique), and the efficiency of each technique is presented and discussed. Both methods presented relatively low-cost implementation, and calibration procedure assured the quality of the results. The results from the experimental set-up were in agreement in shape and amplitude.
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Liu, Tong, Shiming Zhang, and Moran Wang. "Does Rheology of Bingham Fluid Influence Upscaling of Flow through Tight Porous Media?" Energies 14, no. 3 (January 28, 2021): 680. http://dx.doi.org/10.3390/en14030680.
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Non-Newtonian fluids may cause nonlinear seepage even for a single-phase flow. Through digital rock technologies, the upscaling of this non-Darcy flow can be studied; however, the requirements for scanning resolution and sample size need to be clarified very carefully. This work focuses on Bingham fluid flow in tight porous media by a pore-scale simulation on CT-scanned microstructures of tight sandstones. A bi-viscous model is used to depict the Bingham fluid. The results show that when the Bingham fluid flows through a rock sample, the flowrate increases at a parabolic rate when the pressure gradient is small and then increases linearly with the pressure gradient. As a result, an effective permeability and a start-up pressure gradient can be used to characterize this flow behavior. By conducting flow simulations at varying sample sizes, we obtain the representative element volume (REV) for effective permeability and start-up pressure gradient. It is found that the REV size for the effective permeability is almost the same as that for the absolute permeability of Newtonian fluid. The interesting result is that the REV size for the start-up pressure gradient is much smaller than that for the effective permeability. The results imply that the sample size, which is large enough to reach the REV size for Newtonian fluids, can be used to investigate the Bingham fluids flow through porous media as well.
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Dutta, A., and J. M. Tarbell. "Influence of Non-Newtonian Behavior of Blood on Flow in an Elastic Artery Model." Journal of Biomechanical Engineering 118, no. 1 (February 1, 1996): 111–19. http://dx.doi.org/10.1115/1.2795936.
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Two different non-Newtonian models for blood, one a simple power law model exhibiting shear thinning viscosity, and another a generalized Maxwell model displaying both shear thining viscosity and oscillatory flow viscoelasticity, were used along with a Newtonian model to simulate sinusoidal flow of blood in rigid and elastic straight arteries. When the spring elements were removed from the viscoelastic model resulting in a purely viscous shear thinning fluid, the predictions of flow rate and WSS were virtually unaltered. Hence, elasticity of blood does not appear to influence its flow behavior under physiological conditions in large arteries, and a purely viscous shear thinning model should be quite realistic for simulating blood flow under these conditions. When a power law model with a high shear rate Newtonian cutoff was used for sinusoidal flow simulation in elastic arteries, the mean and amplitude of the flow rate were found to be lower for a power law fluid compared to a Newtonian fluid experiencing the same pressure gradient. The wall shear stress was found to be relatively insensitive to fluid rheology but strongly dependent on vessel wall motion for flows driven by the same pressure gradient. The effect of wall motion on wall shear stress could be greatly reduced by matching flow rate rather than pressure gradient. For physiological flow simulation in the aorta, an increase in mean WSS but a reduction in peak WSS were observed for the power law model compared to a Newtonian fluid model for a matched flow rate waveform.
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Plaut, Emmanuel, Nicolas Roland, and Chérif Nouar. "Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology." Journal of Fluid Mechanics 818 (April 5, 2017): 595–622. http://dx.doi.org/10.1017/jfm.2017.149.
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In order to model the transition to turbulence in pipe flow of non-Newtonian fluids, the influence of a strongly shear-thinning rheology on the travelling waves with a threefold rotational symmetry of Faisst & Eckhardt (Phys. Rev. Lett., vol. 91, 2003, 224502) and Wedin & Kerswell (J. Fluid Mech., vol. 508, 2004, pp. 333–371) is analysed. The rheological model is Carreau’s law. Besides the shear-thinning index $n_{C}$, the dimensionless characteristic time $\unicode[STIX]{x1D706}$ of the fluid is considered as the main non-Newtonian control parameter. If $\unicode[STIX]{x1D706}=0$, the fluid is Newtonian. In the relevant limit $\unicode[STIX]{x1D706}\rightarrow +\infty$, the fluid approaches a power-law behaviour. The laminar base flows are first characterized. To compute the nonlinear waves, a Petrov–Galerkin code is used, with continuation methods, starting from the Newtonian case. The axial wavenumber is optimized and the critical waves appearing at minimal values of the Reynolds number $\mathit{Re}_{w}$ based on the mean velocity and wall viscosity are characterized. As $\unicode[STIX]{x1D706}$ increases, these correspond to a constant value of the Reynolds number based on the mean velocity and viscosity. This viscosity, close to the one of the laminar flow, can be estimated analytically. Therefore the experimentally relevant critical Reynolds number $\mathit{Re}_{wc}$ can also be estimated analytically. This Reynolds number may be viewed as a lower estimate of the Reynolds number for the transition to developed turbulence. This demonstrates a quantified stabilizing effect of the shear-thinning rheology. Finally, the increase of the pressure gradient in waves, as compared to the one in the laminar flow with the same mass flux, is calculated, and a kind of ‘drag reduction effect’ is found.
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Slobodian, N. B., and V. Ya Grudz. "The Effect of Physical Properties of Fluids on the Process of Purifying the Main Gas Pipeline from Liquid Pollutants." Prospecting and Development of Oil and Gas Fields, no. 1(74) (March 31, 2020): 89–95. http://dx.doi.org/10.31471/1993-9973-2020-1(74)-89-95.
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The article deals with modern technical methods of improving the efficiency of gas pipelines cleaning. The most effective method of improving the efficiency of a gas pipeline is its periodical cleaning with mechanical treating units. In practice, a large number of cleaning pistons of various technological designs are used. Regardless of the design, none of them can completely remove the fluid accumulations. The reason for the decrease in efficiency is the presence of fluid in the cavity of the pipeline. The fluid can be of two types – high-viscosity resinous deposits and low-viscosity liquid deposits. When moving, they perform the role of local resistance. The type of the main gas pipeline purification process is largely determined by the physical properties of the fluid which is being displaced. The authors specify the functional dependence of the velocity distribution in the pipe cross-section while displacing the Newtonian fluid, as well as the value of the initial pressure of the liquid phase on the cleaning piston. The interaction of a purifying device with fluid accumulations having different physical properties is investigated. The authors develop the algorithm of calculating the volume of the flows over a moving boundary into a back-piston space, in relation to their velocity. The dependence of the volume of fluid flows caused by hydraulic shock for Newtonian and non-Newtonian fluids is composed. Based on the calculations, the authors plot the graphical dependence of the correction coefficient on the ratio of dynamic viscosity to the degree of consistency, as well as the dependence of the total flow rate on the speed of movement of the cleaning unit. The formula for calculating the correction coefficient is obtained. The article presents the results of calculating the value of the correction coefficient which takes into account the rheological properties of the fluid. In relation to the properties and rheology of the non-Newtonian fluid, the authors determine the optimal velocity of a treating unit.
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Busto, Saray, Michael Dumbser, and Laura Río-Martín. "Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows." Mathematics 9, no. 22 (November 21, 2021): 2972. http://dx.doi.org/10.3390/math9222972.
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This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with the k−ε turbulence model. The rheology for calculating the laminar viscosity coefficient under consideration in this work is the one of a non-Newtonian Herschel–Bulkley (power-law) fluid with yield stress, which includes the Bingham fluid and classical Newtonian fluids as special cases. For the spatial discretization, we use edge-based staggered unstructured simplex meshes, as well as staggered non-uniform Cartesian grids. In order to get a simple and computationally efficient algorithm, we apply an operator splitting technique, where the hyperbolic convective terms of the RANS equations are discretized explicitly at the aid of a Godunov-type finite volume scheme, while the viscous parabolic terms, the elliptic pressure terms and the stiff algebraic source terms of the k−ε model are discretized implicitly. For the discretization of the elliptic pressure Poisson equation, we use classical conforming P1 and Q1 finite elements on triangles and rectangles, respectively. The implicit discretization of the viscous terms is mandatory for non-Newtonian fluids, since the apparent viscosity can tend to infinity for fluids with yield stress and certain power-law fluids. It is carried out with P1 finite elements on triangular simplex meshes and with finite volumes on rectangles. For Cartesian grids and more general orthogonal unstructured meshes, we can prove that our new scheme can preserve the positivity of k and ε. This is achieved via a special implicit discretization of the stiff algebraic relaxation source terms, using a suitable combination of the discrete evolution equations for the logarithms of k and ε. The method is applied to some classical academic benchmark problems for non-Newtonian and turbulent flows in two space dimensions, comparing the obtained numerical results with available exact or numerical reference solutions. In all cases, an excellent agreement is observed.
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Kawaguchi, Fukui, Funamoto, Tanaka, Tanaka, Murata, Miyauchi, and Hayase. "Viscosity Estimation of a Suspension with Rigid Spheres in Circular Microchannels Using Particle Tracking Velocimetry." Micromachines 10, no. 10 (October 4, 2019): 675. http://dx.doi.org/10.3390/mi10100675.
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Suspension flows are ubiquitous in industry and nature. Therefore, it is important to understand the rheological properties of a suspension. The key to understanding the mechanism of suspension rheology is considering changes in its microstructure. It is difficult to evaluate the influence of change in the microstructure on the rheological properties affected by the macroscopic flow field for non-colloidal particles. In this study, we propose a new method to evaluate the changes in both the microstructure and rheological properties of a suspension using particle tracking velocimetry (PTV) and a power-law fluid model. Dilute suspension (0.38%) flows with fluorescent particles in a microchannel with a circular cross section were measured under low Reynolds number conditions (Re ≈ 10−4). Furthermore, the distribution of suspended particles in the radial direction was obtained from the measured images. Based on the power-law index and dependence of relative viscosity on the shear rate, we observed that the non-Newtonian properties of the suspension showed shear-thinning. This method will be useful in revealing the relationship between microstructural changes in a suspension and its rheology.
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Tamburrino, Aldo, and Cristóbal Traslaviña. "Condition for the Incipient Motion of Non-Cohesive Particles Due to Laminar Flows of Power-Law Fluids in Closed Conduits." Water 12, no. 5 (May 3, 2020): 1295. http://dx.doi.org/10.3390/w12051295.
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The results of an experimental study on the condition of incipient transport of non-cohesive particles due to the flow of a power-law fluid in a rectangular pipe are presented in this article. The pipe can change its inclination, and experiments were carried out with positive and negative slopes. From a dimensional analysis, the parameters that define the condition of incipient motion were found and validated with experimental data. Thus, the threshold condition is well defined by a particle Reynolds number and a Galileo number, properly modified to take into account the power-law rheology of the fluid. The experimental data are also presented in a standard Shields diagram, including the data obtained in other studies carried out in open-channel laminar flows of Newtonian and power-law fluids.
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Gorthi, Srinivas R., Sanjaya Kumar Meher, Gautam Biswas, and Pranab Kumar Mondal. "Capillary imbibition of non-Newtonian fluids in a microfluidic channel: analysis and experiments." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2242 (October 2020): 20200496. http://dx.doi.org/10.1098/rspa.2020.0496.
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We have presented an experimental analysis on the investigations of capillary filling dynamics of inelastic non-Newtonian fluids in the regime of surface tension dominated flows. We use the Ostwald–de Waele power-law model to describe the rheology of the non-Newtonian fluids. Our analysis primarily focuses on the experimental observations and revisits the theoretical understanding of the capillary dynamics from the perspective of filling kinematics at the interfacial scale. Notably, theoretical predictions of the filling length into the capillary largely endorse our experimental results. We study the effects of the shear-thinning nature of the fluid on the underlying filling phenomenon in the capillary-driven regime through a quantitative analysis. We further show that the dynamics of contact line motion in this regime plays an essential role in advancing the fluid front in the capillary. Our experimental results on the filling in a horizontal capillary re-establish the applicability of the Washburn analysis in predicting the filling characteristics of non-Newtonian fluids in a vertical capillary during early stage of filling (Digilov 2008 Langmuir 24 , 13 663–13 667 ( doi:10.1021/la801807j )). Finally, through a scaling analysis, we suggest that the late stage of filling by the shear-thinning fluids closely follows the variation x ~ t . Such a regime can be called the modified Washburn regime (Washburn 1921 Phys. Rev. 17 , 273–283 ( doi:10.1103/PhysRev.17.273 )).
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Al-Ashhab, Samer, Dongming Wei, Salem A. Alyami, AKM Azad, and Mohammad Ali Moni. "Mutual Interdependence of the Physical Parameters Governing the Boundary-Layer Flow of Non-Newtonian Fluids." Applied Sciences 12, no. 10 (May 23, 2022): 5275. http://dx.doi.org/10.3390/app12105275.
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We consider non-Newtonian boundary-layer fluid flow, governed by a power-law Ostwald-de Waele rheology. Boundary-layer flows of non-Newtonian fluids have far-reaching applications, and are very frequently encountered in physical, as well as, engineering and industrial processes. A similarity transformation results in a BVP consisting of an ODE and some boundary conditions. Our aim is to derive highly accurate analytical relationships between the physical and mathematical parameters associated with the BVP and boundary-layer flow problem. Mathematical analyses are employed, where the results are verified at the numerical computational level, illustrating the accuracy of the derived relations. A set of “Crocco variables” is used to transform the problem, and, where appropriate, techniques are used to deal with the resulting singularities in order to establish an efficient computational setting. The resulting computational setting provides an alternative, which is different from those previously used in the literature. We employ it to carry out our numerical computations.
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Pan, Wenxiao, Alexandre M. Tartakovsky, and Joe J. Monaghan. "A smoothed-particle hydrodynamics model for ice-sheet and ice-shelf dynamics." Journal of Glaciology 58, no. 208 (2012): 216–22. http://dx.doi.org/10.3189/2012jog11j084.
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AbstractMathematical modeling of ice sheets is complicated by the nonlinearity of the governing equations and boundary conditions. Standard grid-based methods require complex front-tracking techniques and have a limited capability to handle large material deformations and abrupt changes in bottom topography. Consequently, numerical methods are usually restricted to shallow ice-sheet and ice-shelf approximations. We propose a new smoothed-particle hydrodynamics (SPH) model for coupled ice-sheet and ice-shelf dynamics. SPH, a fully Lagrangian particle method, is highly scalable and its Lagrangian nature and meshless discretization are well suited to the simulation of free surface flows, large material deformation and material fragmentation. In this paper, we use the SPH model to study ice-sheet/ice-shelf behavior, and the dynamics of the grounding line. The steady-state position of the grounding line obtained from SPH simulations is in good agreement with laboratory observations for a wide range of simulated bedrock slopes and density ratios, similar to those of ice and sea water. The numerical accuracy of the SPH algorithm is verified by simulating the plane-shear flow of two immiscible fluids and the propagation of a highly viscous blob of fluid along a horizontal surface. In the experiment, the ice was represented with a viscous Newtonian fluid. For consistency, in the described SPH model the ice is also modeled as a viscous Newtonian fluid. Typically, ice sheets are modeled as a non-Newtonian fluid, accounting for the changes in the mechanical properties of the ice. Implementation of a non-Newtonian rheology in the SPH model is the subject of our ongoing research.
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Eglit, M. E., and A. E. Yakubenko. "Effect of the bottom material capture and the non-Newtonian rheology on the dynamics of turbulent downslope flows." Fluid Dynamics 51, no. 3 (May 2016): 299–310. http://dx.doi.org/10.1134/s0015462816030017.
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Taheri, Amir, Jan David Ytrehus, Bjørnar Lund, and Malin Torsæter. "Experimental Study of the Use of Tracing Particles for Interface Tracking in Primary Cementing in an Eccentric Hele–Shaw Cell." Energies 14, no. 7 (March 29, 2021): 1884. http://dx.doi.org/10.3390/en14071884.
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We present the results of the displacement flows of different Newtonian and Herschel–Bulkley non-Newtonian fluids in a new-developed eccentric Hele–Shaw cell with dynamic similarly to real field wellbore annulus during primary cementing. The possibility of tracking the interface between the fluids using particles with intermediate or neutral buoyancy is studied. The behaviors and movements of particles with different sizes and densities against the primary vertical flow and strong secondary azimuthal flow in the eccentric Hele–Shaw cell are investigated. The effects of fluid rheology and pumping flow rate on the efficiency of displacement and tracing particles are examined. Moreover, the behavior of pressure gradients in the cell is described and analyzed. Successful results of tracing the interface using particles give us this opportunity to carry out a primary cementing with high quality for the cases that the risk of leakage is high, e.g., primary cementing in wells penetrating a CO2 storage reservoir.
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RAMACHANDRAN, ARUN, and ADITYA S. KHAIR. "The dynamics and rheology of a dilute suspension of hydrodynamically Janus spheres in a linear flow." Journal of Fluid Mechanics 633 (August 25, 2009): 233–69. http://dx.doi.org/10.1017/s0022112009007472.
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The creeping motion of a hydrodynamically ‘Janus’ spherical particle, whose surface is partitioned into two distinct regions, is investigated. On one region, fluid adjacent to the particle obeys the no-slip condition, whereas on the other, fluid slips past the particle. The fore-aft asymmetry of this ‘slip–stick’ sphere (Swan & Khair, J. Fluid Mech., vol. 606, 2008, p. 115) leads to a number of interesting results when it is placed in different flows, which is illustrated by computing the particle motion to first order in the ratio of slip length to particle radius. For example, in a pure straining field the sphere attains an equilibrium orientation either along the compressional or extensional axis of the flow, depending on the ratio of slip-to-stick surface areas. In a simple shear flow, on the other hand, the slip–stick sphere undergoes a periodic rotational motion, or Jeffrey orbit. Moreover, depending on its initial orientation, the particle can either follow a periodic {translational} orbit or undergo a net displacement along the flow direction. Lastly, to first order in the volume fraction of slip–stick spheres, the suspension rheology is non-Newtonian, with non-zero first and second normal stress differences.
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Rusak, Zvi, Nguyen Ly, John A. Tichy, and Shixiao Wang. "Near-critical swirling flow of a viscoelastic fluid in a circular pipe." Journal of Fluid Mechanics 814 (February 6, 2017): 325–60. http://dx.doi.org/10.1017/jfm.2017.16.
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The interaction between flow inertia and elasticity in high-Reynolds-number, axisymmetric and near-critical swirling flows of an incompressible and viscoelastic fluid in an open finite-length straight circular pipe is studied at the limit of low elasticity. The stresses of the viscoelastic fluid are described by the generalized Giesekus constitutive model. This model helps to focus the analysis on low fluid elastic effects with shear thinning of the viscosity. The application of the Giesekus model to columnar streamwise vortices is first investigated. Then, a nonlinear small-disturbance analysis is developed from the governing equations of motion. It reveals the complicated interactions between flow inertia, swirl and fluid rheology. An effective Reynolds number that links between steady states of swirling flows of a viscoelastic fluid and those of a Newtonian fluid is revealed. The effects of the fluid viscosity, relaxation time, retardation time and mobility parameter on the flow development in the pipe and on the critical swirl for the appearance of vortex breakdown are explored. It is found that in vortex flows with either an axial jet or an axial wake profile, increasing the shear thinning by decreasing the ratio of the viscoelastic characteristic times from one (with fixed values of the Weissenberg number and the mobility parameter) increases the critical swirl ratio for breakdown. Increasing the fluid elasticity by increasing the Weissenberg number from zero (with a fixed ratio of the viscoelastic characteristic times and a fixed value of the mobility parameter) or increasing the fluid mobility parameter from zero (with fixed values of the Weissenberg number and the ratio of viscoelastic times) causes a similar effect. The results may explain the trend of changes in the appearance of breakdown zones as a function of swirl level that were observed in the experiments by Stokes et al. (J. Fluid Mech., vol. 429, 2001, pp. 67–115), where Boger fluids were used. This work extends for the first time the theory of vortex breakdown to include effects of non-Newtonian fluids.
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Davoodi, M., K. Zografos, P. J. Oliveira, and R. J. Poole. "On the similarities between the simplified Phan-Thien–Tanner model and the finitely extensible nonlinear elastic dumbbell (Peterlin closure) model in simple and complex flows." Physics of Fluids 34, no. 3 (March 2022): 033110. http://dx.doi.org/10.1063/5.0083717.
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For many commonly used viscoelastic constitutive equations, it is well known that the limiting behavior is that of the Oldroyd-B model. Here, we compare the response of the simplified linear form of the Phan-Thien–Tanner model (“sPTT”) [Phan-Thien and Tanner, “A new constitutive equation derived from network theory,” J. Non-Newtonian Fluid Mech. 2, 353–365 (1977)] and the finitely extensible nonlinear elastic (“FENE”) dumbbell model that follows the Peterlin approximation (“FENE-P”) [Bird et al., “Polymer solution rheology based on a finitely extensible bead—Spring chain model,” J. Non-Newtonian Fluid Mech. 7, 213–235 (1980)]. We show that for steady homogeneous flows such as steady simple shear flow or pure extension, the response of both models is identical under precise conditions ([Formula: see text]). The similarity of the “spring” functions between the two models is shown to help understand this equivalence despite a different molecular origin of the two models. We then use a numerical approach to investigate the response of the two models when the flow is “complex” in a number of different definitions: first, when the applied deformation field is homogeneous in space but transient in time (so-called “start-up” shear and planar extensional flow), then, as an intermediate step, the start-up of the planar channel flow; and finally, “complex” flows (through a range of geometries), which, although being Eulerian steady, are unsteady in a Lagrangian sense. Although there can be significant differences in transient conditions, especially if the extensibility parameter is small [Formula: see text], under the limit that the flows remain Eulerian steady, we once again observe very close agreement between the FENE-P dumbbell and sPTT models in complex geometries.
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Barker, T., D. G. Schaeffer, P. Bohorquez, and J. M. N. T. Gray. "Well-posed and ill-posed behaviour of the -rheology for granular flow." Journal of Fluid Mechanics 779 (August 24, 2015): 794–818. http://dx.doi.org/10.1017/jfm.2015.412.
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In light of the successes of the Navier–Stokes equations in the study of fluid flows, similar continuum treatment of granular materials is a long-standing ambition. This is due to their wide-ranging applications in the pharmaceutical and engineering industries as well as to geophysical phenomena such as avalanches and landslides. Historically this has been attempted through modification of the dissipation terms in the momentum balance equations, effectively introducing pressure and strain-rate dependence into the viscosity. Originally, a popular model for this granular viscosity, the Coulomb rheology, proposed rate-independent plastic behaviour scaled by a constant friction coefficient ${\it\mu}$. Unfortunately, the resultant equations are always ill-posed. Mathematically ill-posed problems suffer from unbounded growth of short-wavelength perturbations, which necessarily leads to grid-dependent numerical results that do not converge as the spatial resolution is enhanced. This is unrealistic as all physical systems are subject to noise and do not blow up catastrophically. It is therefore vital to seek well-posed equations to make realistic predictions. The recent ${\it\mu}(I)$-rheology is a major step forward, which allows granular flows in chutes and shear cells to be predicted. This is achieved by introducing a dependence on the non-dimensional inertial number $I$ in the friction coefficient ${\it\mu}$. In this paper it is shown that the ${\it\mu}(I)$-rheology is well-posed for intermediate values of $I$, but that it is ill-posed for both high and low inertial numbers. This result is not obvious from casual inspection of the equations, and suggests that additional physics, such as enduring force chains and binary collisions, becomes important in these limits. The theoretical results are validated numerically using two implicit schemes for non-Newtonian flows. In particular, it is shown explicitly that at a given resolution a standard numerical scheme used to compute steady-uniform Bagnold flow is stable in the well-posed region of parameter space, but is unstable to small perturbations, which grow exponentially quickly, in the ill-posed domain.
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Castillo-Sánchez, Hugo A., Leandro F. de Souza, and Antonio Castelo. "Numerical Simulation of Rheological Models for Complex Fluids Using Hierarchical Grids." Polymers 14, no. 22 (November 16, 2022): 4958. http://dx.doi.org/10.3390/polym14224958.
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In this work, we implement models that are able to describe complex rheological behaviour (such as shear-banding and elastoviscoplasticity) in the HiGTree/HiGFlow system, which is a recently developed Computational Fluid Dynamics (CFD) software that can simulate Newtonian, Generalised-Newtonian and viscoelastic flows using finite differences in hierarchical grids. The system uses a moving least squares (MLS) meshless interpolation technique, allowing for more complex mesh configurations while still keeping the overall order of accuracy. The selected models are the Vasquez-Cook-McKinley (VCM) model for shear-banding micellar solutions and the Saramito model for viscoelastic fluids with yield stress. Development of solvers and numerical simulations of inertial flows of these models in 2D channels and planar-contraction 4:1 are carried out in the HiGTree/HiGFlow system. Our results are compared with those predicted by two other methodologies: the OpenFOAM-based software RheoTool that uses the Finite-Volume-Method and an in-house code that uses the Vorticity-Velocity-Formulation (VVF). We found an excellent agreement between the numerical results obtained by these three different methods. A mesh convergence analysis using uniform and refined meshes is also carried out, where we show that great convergence results in tree-based grids are obtained thanks to the finite difference method and the meshless interpolation scheme used by the HiGFlow software. More importantly, we show that our methodology implemented in the HiGTreee/HiGFlow system can successfully reproduce rheological behaviour of high interest by the rheology community, such as non-monotonic flow curves of micellar solutions and plug-flow velocity profiles of yield-stress viscoelastic fluids.
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Spanjaards, Michelle, Nick Jaensson, Martien Hulsen, and Patrick Anderson. "A Numerical Study of Particle Migration and Sedimentation in Viscoelastic Couette Flow." Fluids 4, no. 1 (February 11, 2019): 25. http://dx.doi.org/10.3390/fluids4010025.
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In this work, a systematic investigation of the migration of sedimenting particles in a viscoelastic Couette flow is presented, using finite element 3D simulations. To this end, a novel computational approach is presented, which allows us to simulate a periodic configuration of rigid spherical particles accurately and efficiently. To study the different contributions to the particle migration, we first investigate the migration of particles sedimenting near the inner wall, without an externally-imposed Couette flow, followed by the migration of non-sedimenting particles in an externally-imposed Couette flow. Then, both flows are combined, i.e., sedimenting particles with an externally-imposed Couette flow, which was found to increase the migration velocity significantly, yielding migration velocities that are higher than the sum of the combined flows. It was also found that the trace of the conformation tensor becomes asymmetric with respect to the particle center when the particle is initially placed close to the inner cylinder. We conclude by investigating the sedimentation velocity with an imposed orthogonal shear flow. It is found that the sedimentation velocity can be both higher or lower then the Newtonian case, depending on the rheology of the suspending fluid. Specifically, a shear-thinning viscosity is shown to play an important role, which is in-line with previously-published results.
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Schippa, Leonardo, Ferruccio Doghieri, Anna Pellegrino, and Elisa Pavesi. "Thixotropic Behavior of Reconstituted Debris-Flow Mixture." Water 13, no. 2 (January 11, 2021): 153. http://dx.doi.org/10.3390/w13020153.
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Time-dependent rheological properties and thixotropy of reconstituted debris-flows samples taken from channel bank deposits are examined using a commercial rheometer equipped with a vane rotor geometric system. Sweep tests and creep tests were carried out involving mixtures having different grain concentrations ranging between 50% and 58%. Different initial conditions of the mixtures were considered in order to analyze the effects of aging and rejuvenation (thixotropy) over a short period of time and long period of time. Tested slurries show viscosity bifurcation, yield stress and time-dependent behavior. According to the experimental results, three different regimes were identified: a lower shear rate regime, corresponding to a shear rate lower than the critical value; an intermediate banding shear rate regime characterized by static and dynamic yield stress level; and a higher shear rate regime where the flowing debris behaves as a non-Newtonian fluid characterized by a constant steady state ultimate apparent viscosity. In any case, the initial state of the mixture and the sediment concentration affects the ultimate steady state rheology and the time-dependent (thixotropy) slurries’ behavior.
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Schippa, Leonardo, Ferruccio Doghieri, Anna Maria Pellegrino, and Elisa Pavesi. "Thixotropic Behavior of Reconstituted Debris-Flow Mixture." Water 13, no. 2 (January 11, 2021): 153. http://dx.doi.org/10.3390/w13020153.
Full textAbstract:
Time-dependent rheological properties and thixotropy of reconstituted debris-flows samples taken from channel bank deposits are examined using a commercial rheometer equipped with a vane rotor geometric system. Sweep tests and creep tests were carried out involving mixtures having different grain concentrations ranging between 50% and 58%. Different initial conditions of the mixtures were considered in order to analyze the effects of aging and rejuvenation (thixotropy) over a short period of time and long period of time. Tested slurries show viscosity bifurcation, yield stress and time-dependent behavior. According to the experimental results, three different regimes were identified: a lower shear rate regime, corresponding to a shear rate lower than the critical value; an intermediate banding shear rate regime characterized by static and dynamic yield stress level; and a higher shear rate regime where the flowing debris behaves as a non-Newtonian fluid characterized by a constant steady state ultimate apparent viscosity. In any case, the initial state of the mixture and the sediment concentration affects the ultimate steady state rheology and the time-dependent (thixotropy) slurries’ behavior.
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Manenti, Wang, Domínguez, Li, Amicarelli, and Albano. "SPH Modeling of Water-Related Natural Hazards." Water 11, no. 9 (September 9, 2019): 1875. http://dx.doi.org/10.3390/w11091875.
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This paper collects some recent smoothed particle hydrodynamic (SPH) applications in the field of natural hazards connected to rapidly varied flows of both water and dense granular mixtures including sediment erosion and bed load transport. The paper gathers together and outlines the basic aspects of some relevant works dealing with flooding on complex topography, sediment scouring, fast landslide dynamics, and induced surge wave. Additionally, the preliminary results of a new study regarding the post-failure dynamics of rainfall-induced shallow landslide are presented. The paper also shows the latest advances in the use of high performance computing (HPC) techniques to accelerate computational fluid dynamic (CFD) codes through the efficient use of current computational resources. This aspect is extremely important when simulating complex three-dimensional problems that require a high computational cost and are generally involved in the modeling of water-related natural hazards of practical interest. The paper provides an overview of some widespread SPH free open source software (FOSS) codes applied to multiphase problems of theoretical and practical interest in the field of hydraulic engineering. The paper aims to provide insight into the SPH modeling of some relevant physical aspects involved in water-related natural hazards (e.g., sediment erosion and non-Newtonian rheology). The future perspectives of SPH in this application field are finally pointed out.
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Lavigne, Frank, and Jean-Claude Thouret. "Les lahars; depots, origines et dynamique." Bulletin de la Société Géologique de France 171, no. 5 (September 1, 2000): 545–57. http://dx.doi.org/10.2113/171.5.545.
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Abstract A lahar is a flowing mixture of rock debris and water (other than normal streamflow) from a volcano, which encompasses a continuum from debris flows (sediment concentration > or =60% per volume) to hyperconcentrated streamflows (sediment concentration from 20 to 60% per volume). Debris flow deposits are poorly sorted and massive with abundant clasts. Lahars can be either syn-eruptive, post-eruptive or have a non-eruptive origin. Four types of lahars can be generated during an eruption, based on distinct sources of water (i.e. ice, snow, crater lake, river, and rain) that allow the sediments to be removed and incorporated in the lahar (e.g., Mount St.-Helens in 1980, Nevado del Ruiz in 1985). Post-eruptive lahars, which are rain-triggered, occur during several years after an eruption (e.g., still occurring at Pinatubo). Non-eruptive lahars are flows generated on volcanoes without eruptive activity, particularly in the case of a debris avalanche or a lake outburst (e.g., Kelud or Ruapehu). Lahars flow as pulses, whose velocity and discharge are much higher than those of streamflows, including catchments similar in size. Sediment transport capacity of lahars is exceptional, owing to buoyancy, dispersive pressure, and to the amount of cohesive clay and silt. However, the finding of recent experimental works indicates that even clay-rich lahar mixtures have little true cohesion. Therefore, the typical classification of lahars into "cohesive" and "non cohesive" seems to be inappropriate at present. Besides, past work on lahar mechanics used models based on the Bagnold's or the Bingham's theories. Recent advances in experimentation show that a lahar has specific rheological properties: it moves as a surge or series of surges, driven by gravity, by porosity fluctuation, and by pore fluid pressures, in accordance with the Coulomb grain flow model. Grain size distribution and sorting control pore pressure distribution. Lahar mechanics depend on much more than steady-state rheology, because lahars are highly unsteady and typically heterogeneous flows. Lahar can show a succession of debris flow phases, hyperconcentrated flow phases, and sometimes transient streamflow phases. Therefore, some fluids-mechanics concepts and terminology, such as "viscous", "laminar" or "non-Newtonian" are inappropriate to describe the mechanical properties of lahars. Processes of deposition are complex and poorly known. Interpretation of massive and unsorted lahar deposits commonly ascribe the deposition regime to a freezing en masse process. However, recent laboratory experiments highlight that debris-flow deposits may result from incremental deposition processes.
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Nedolujko, A. I., and A. A. Kotesova. "Accelerating flows of pseudo-plastic and dilatant non-newtonian fluids in straight pipelines." Vestnik Mashinostroeniya, May 2020, 57–61. http://dx.doi.org/10.36652/0042-4633-2020-5-57-61.
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The accelerated flows of non-Newtonian fluids are studied, the viscosity-strength properties of which are described by the equation τ = kΥn. Dependencies are obtained for calculating the velocity field and the time it takes to reach the stationary flow for liquids with arbitrary rheological parameters. Keywords technical fluid, non-Newtonian medium, rheology, viscometer, model, acceleration flow, pipeline. a.kotesova@mail.ru
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Rashidi, Masoud, Ahmad Sedaghat, Biltayib Misbah, Mohammad Sabati, and Koshy Vaidyan. "Use of SiO2 Nanoparticles in Water-Based Drilling Fluids for Improved Energy Consumption and Rheology: A Laboratory Study." SPE Journal, March 1, 2021, 1–15. http://dx.doi.org/10.2118/205361-pa.
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Summary In wellbore drilling, it is appreciable to devise methods to study the rheology of high-speed annulus fluid flows. In this paper, a high-speedTaylor-Couette system (TCS) was devised to explore non-Newtonian fluid flow behavior appraised by SiO2 nanoparticles toward friction reduction, power saving, and rheology modeling of nanofluids. Water-based mud (WBM) as an environmentally friendly drilling fluid is investigated by adding SiO2 nanoparticles at four low-volume concentrations of 0.05, 0.1, 0.5, and 1% at speeds from 0 to 1,600 rev/min with 200 rev/min intervals in the TCS. Five rheology models based on the Herschel-Bulkley-Extended (HBE) model and a generalized Reynolds number were optimized to fit with the experimental data. All models except the Newtonian model have fitted all nanofluids with high accuracy, especially Bingham and HBE models. Negative deviation from Darcy friction was avoided for power-law (PL) and Herschel-Bulkley (HB) models using the modification to the generalized Reynolds number. Higher energy saving and enhanced rheology is reported particularly at lower volume concentrations of SiO2 WBM nanofluids. The Darcy friction factor deviated from laminar flow at the generalized Reynolds number beyond 2,000 into turbulent, which is a good indicator for the flow condition of complex non-Newtonian nanofluids in real-lifeapplication.
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Guazzelli, Élisabeth, and Olivier Pouliquen. "Rheology of dense granular suspensions." Journal of Fluid Mechanics 852 (August 14, 2018). http://dx.doi.org/10.1017/jfm.2018.548.
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Suspensions are composed of mixtures of particles and fluid and are omnipresent in natural phenomena and in industrial processes. The present paper addresses the rheology of concentrated suspensions of non-colloidal particles. While hydrodynamic interactions or lubrication forces between the particles are important in the dilute regime, they become of lesser significance when the concentration is increased, and direct particle contacts become dominant in the rheological response of concentrated suspensions, particularly those close to the maximum volume fraction where the suspension ceases to flow. The rheology of these dense suspensions can be approached via a diversity of approaches that the paper introduces successively. The mixture of particles and fluid can be seen as a fluid with effective rheological properties but also as a two-phase system wherein the fluid and particles can experience relative motion. Rheometry can be undertaken at an imposed volume fraction but also at imposed values of particle normal stress, which is particularly suited to yield examination of the rheology close to the jamming transition. The response of suspensions to unsteady or transient flows provides access to different features of the suspension rheology. Finally, beyond the problem of suspension of rigid, non-colloidal spheres in a Newtonian fluid, there are a great variety of complex mixtures of particles and fluid that remain relatively unexplored.
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Ramirez, M. G., D. O. A. Cruz, F. Nikfarjam, and H. R. Anbarlooei. "A Mechanistic Model for the Two-Phase Slug Flow of the Purely Viscous Non-Newtonian Liquids through Pipes." SPE Production & Operations, November 1, 2022, 1–14. http://dx.doi.org/10.2118/212838-pa.
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Summary Mechanistic slug models generally depend on several empirical correlations. This work presents an extended model, which incorporates a recently theoretically developed family of friction equations for purely viscous non-Newtonian fluids to reduce this dependency. In contrast to other models where a fixed transition Reynolds number is used, a proper rheology-dependent laminar-to-turbulent transition criteria has been adopted. Finally, to fully specify the characteristics of the slug flow, a new model is introduced for the slug frequency, by balancing the pressure forces and the drag over the gas bubble. The resulting model requires just one empirical coefficient, drag coefficient of the bubble, which depends on the rheology of the fluids and diameter of the pipe. The developed models have been extensively verified with the experimental data, for the two-phase flows with Newtonian and non-Newtonian (power law and Bingham) liquid phase. Our mechanistic model predicts the pressure drop of the experimental data within ±20% error range, while it does not introduce any new empirical coefficient for the non-Newtonian case. This model, besides its simplicity and accuracy, successfully captures the physical trends in experimental data where other available models fail. The frequency model with calibrated drag coefficient reproduces the experiments with less than 30% error, while one can find a universal drag coefficient which can reproduce most of the experimental observations within the same error range. To summarize, the proposed models can fully characterize two-phase slug flows in presence of a non-Newtonian purely viscous fluid phase.
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Savorana, Giovanni, Steffen Geisel, Tianyu Cen, Yuya Ling, Roman Stocker, Roberto Rusconi, and Eleonora Secchi. "Transport of Pseudomonas aeruginosa in Polymer Solutions." Frontiers in Physics 10 (June 30, 2022). http://dx.doi.org/10.3389/fphy.2022.910882.
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Bacteria often live surrounded by polymer solutions, such as in animal respiratory, gastrointestinal, and reproductive tracts. In these systems, polymer solutions are often exposed to fluid flow, and their complex rheology can affect the transport of chemical compounds and microorganisms. Recent studies have focused on the effect of polymer solutions on the motility of bacteria in the absence of fluid flow. However, flow can be a game-changer on bacterial transport, as demonstrated by the depletion of motile bacteria from the low-shear regions and trapping in the high-shear regions in simple fluids, even for flows as simple as the Poiseuille one. Despite the relevance of polymer solutions in many bacterial habitats, the effect of their complex rheology on shear-induced trapping and bacterial transport in flow has remained unexplored. Using microfluidic experiments and numerical modeling, we studied how the shear rate and the rheological behavior of Newtonian and non-Newtonian polymer solutions affect the transport of motile, wild-type Pseudomonas aeruginosa in a Poiseuille flow. Our results show that, in Newtonian solutions, an increase in viscosity reduces bacterial depletion in the low-shear regions at the microchannel center, due to a reduction in the bacterial swimming velocity. Conversely, in the non-Newtonian solution, we observed a depletion comparable to the buffer case, despite its zero-shear viscosity being two orders of magnitude higher. In both cases, bacterial swimming and polymer fluid rheology control the magnitude of bacterial depletion and its shear-rate dependence. Our observations underscore the importance of the rheological behavior of the carrier fluid in controlling bacterial transport, in particular, close to surfaces giving rise to velocity gradients, with potential consequences on surface colonization and biofilm formation in many naturally relevant microbial habitats.
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Subedi, J., S. Rajendran, and R. M. Manglik. "Laminar Forced Convection in Viscous Shear-Thinning Liquid Flows Inside Circular Pipes: Case for a Modified Power-Law Rheology." Journal of Heat Transfer 142, no. 12 (September 22, 2020). http://dx.doi.org/10.1115/1.4048092.
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Abstract Laminar forced convection in viscous, non-Newtonian polymeric liquids that exhibit pseudoplastic or shear-thinning behavior is characterized. The fluid rheology is characterized by a new asymptotic power-law (APL) model, which appropriately represents extensive data for apparent viscosity variation with shear rate—from the low-shear constant-viscosity plateau to shear thinning at high shear rates. This is contrasted with the traditional Ostwald-de-Waele or power-law (PL) model that invariably over-extends the pseudoplasticity in the very low shear-rate region. The latter's limitations are demonstrated by computationally obtaining frictional loss and convective heat transfer results for fully developed laminar flows in a circular pipe maintained at uniform heat flux. The Fanning friction factor and Nusselt number, as would be anticipated from the rheology map of pseudoplastic fluids, are functions of flow rate with the APL model unlike the Newtonian-like constant value obtained with the PL model. Comparisons of the two sets of results highlight the extent of errors inherent in the PL rheology model, which range from 23% to 68% for frictional loss and 3.8% to 13.7% for heat transfer. The new APL rheology model is thus shown to be the more precise characterization of viscous shear-thinning fluids for their thermal processing applications with convective heat transfer.
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Oliveira, Iago L., Gabriel B. Santos, José L. Gasche, Julio Militzer, and Carlos E. Baccin. "Non-Newtonian Blood Modeling in Intracranial Aneurysm Hemodynamics: Impact on the Wall Shear Stress and Oscillatory Shear Index Metrics for Ruptured and Unruptured Cases." Journal of Biomechanical Engineering 143, no. 7 (April 5, 2021). http://dx.doi.org/10.1115/1.4050539.
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Abstract When simulating blood flow in intracranial aneurysms (IAs), the Newtonian model seems to be ubiquitous. However, analyzing the results from the few studies on this subject, the doubt remains on whether it is necessary to use non-Newtonian models in computational fluid dynamics (CFD) simulations of cerebral vascular flows. The objective of this study is to investigate whether different rheology models would influence the hemodynamic parameters related to the wall shear stress (WSS) for ruptured and unruptured IA cases, especially because ruptured aneurysms normally have morphological features, such as lobular regions and blebs, that could trigger non-Newtonian phenomena in the blood flow due to low shear rates. Using CFD in an open-source framework, we simulated four ruptured and four unruptured patient-specific aneurysms to assess the influence of the blood modeling on the main hemodynamic variables associated with aneurysm formation, growth, and rupture. Results for WSS and oscillatory shear index (OSI) and their metrics were obtained using Casson and Carreau–Yasuda non-Newtonian models and were compared with those obtained using the Newtonian model. We found that all differences between non-Newtonian and the Newtonian models were consistent among all cases irrespective of their rupture status. We further found that the WSS at peak systole is overestimated by more than 50% by using the non-Newtonian models, but its metrics based on time and surface averaged values are less affected—the maximum relative difference among the cases is 7% for the Casson model. On the other hand, the surface-averaged OSI is underestimated by more than 30% by the non-Newtonian models. These results suggest that it is recommended to investigate different blood rheology models in IAs simulations when specific parameters to characterize the flow are needed, such as peak-systole WSS and OSI.
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Lovato, Stefano, Serge Toxopeus, Just Settels, and Geert Keetels. "Application of a maritime CFD code to a benchmark problem for non-Newtonian fluids: the flow around a sphere." International Shipbuilding Progress, July 11, 2022, 1–25. http://dx.doi.org/10.3233/isp-220002.
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The ship’s resistance and manoeuvrability in shallow waters can be adversely influenced by the presence of fluid mud layers on the seabed of ports and waterways. Fluid mud exhibits a complex non-Newtonian rheology that is often described using the Herschel–Bulkley model. The latter has been recently implemented in a maritime finite-volume CFD code to study the manoeuvrability of ships in the presence of muddy seabeds. In this paper, we explore the accuracy and robustness of the CFD code in simulating the flow of Herschel–Bulkley fluids, including power-law, Bingham and Newtonian fluids as particular cases. As a stepping stone towards the final maritime applications, the study is carried out on a classic benchmark problem in non-Newtonian fluid mechanics: the laminar flow around a sphere. The aim is to test the performance of the non-Newtonian solver before applying it to the more complex scenarios. Present results could also be used as reference data for future testing. Flow simulations are carried out at low Reynolds numbers in order to compare our results with an extensive collection of data from the literature. Results agree both qualitatively and quantitatively with literature. Difficulties in the convergence of the iterative solver emerged when simulating Bingham and Herschel–Bulkley flows. A simple change in the interpolation of the apparent viscosity has mitigated such difficulties. The results of this work, combined with our previous code verification exercises, suggest that the non-Newtonian solver works as intended and it can be thus employed on more complex applications.
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Roy, Manideep, Pritam Chakraborty, Pranab Kumar Mondal, and Somchai Wongwises. "Leveraging spreadsheet analysis tool for electrically actuated start-up flow of non-Newtonian fluid in small-scale systems." Scientific Reports 12, no. 1 (November 21, 2022). http://dx.doi.org/10.1038/s41598-022-24287-2.
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AbstractIn this article, we demonstrate the solution methodology of start-up electrokinetic flow of non-Newtonian fluids in a microfluidic channel having square cross-section using Spreadsheet analysis tool. In order to incorporate the rheology of the non-Newtonian fluids, we take into consideration the Ostwald-de Waele power law model. By making a comprehensive discussion on the implementation details of the discretized form of the transport equations in Spreadsheet analysis tool, and establishing the analytical solution for a special case of the start-up flow, we compare the results both during initial transience as well as in case of steady-state scenario. Also, to substantiate the efficacy of the proposed spreadsheet analysis in addressing the detailed flow physics of rheological fluids, we verify the results for several cases with the corresponding numerical results. It is found that the solution obtained from the Spreadsheet analysis is in good agreement with the numerical results—a finding supporting spreadsheet analysis's suitability for capturing the fine details of microscale flows. We strongly believe that our analysis study will open up a new research scope in simulating microscale transport process of non-Newtonian fluids in the framework of cost-effective and non-time consuming manner.
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Shakhawath Hossain, Md, and Nihad E. Daidzic. "The Shear-Driven Fluid Motion Using Oscillating Boundaries." Journal of Fluids Engineering 134, no. 5 (May 1, 2012). http://dx.doi.org/10.1115/1.4006362.
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A classical Stokes’ second problem has been known for a long time and represents one of the few exact solutions of nonlinear Navier-Stokes equations. However, oscillatory flow in a semi-infinite domain of Newtonian fluid under harmonic boundary excitation only leads to fluid wind-milling back and forth in close wall vicinity. In this study, we are presenting the mathematical model and the numerical simulations of the Newtonian fluid and the shear-thinning non-Newtonian blood-mimicking fluid flow. Positive flow rates were obtained by periodic yet nonharmonic oscillatory motion of one or two infinite boundary flat walls. The oscillatory flows in semi-infinite or finite 2D geometry with sawtooth or periodic rectified-sine boundary conditions are presented. Rheological human blood models used were: Power-Law, Sisko, Carreau, and Herschel-Bulkley. A one-dimensional time-dependent nonlinear coupled conservative diffusion-type boundary layer equations for mass, linear momentum, and energy were solved using the finite-differences method with finite-volume discretization. It was possible to test the accuracy of the in-house developed computational programs with the few isothermal flow analytical solutions and with the celebrated classical Stokes’ first and second problems. Positive flow rates were achieved in various configurations and in absence of the adverse pressure gradients. Body forces, such as gravity, were neglected. The calculations utilizing in-phase sawtooth and rectified-sine wall excitations resulted in respectable net flow which stabilizes and becomes quasi-steady, starting from rest, after three to ten periods depending on the fluid rheology. It was assumed that rapid return stroke of the wall actuator resulted in total wall slip while forward wall motion existed with no-slip boundary condition. Shear “driving” and “driven” fluid regions were identified. The shear-thinning fluid rheology delivered many interesting results, such as pluglike flow. Constructive interference of diffusive penetration layers from multiple flat surfaces could be used as practical pumping mechanism in micro-scales.
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Zhou, Jian, and Ian Papautsky. "Viscoelastic microfluidics: progress and challanges." Microsystems & Nanoengineering 6, no. 1 (December 2020). http://dx.doi.org/10.1038/s41378-020-00218-x.
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AbstractThe manipulation of cells and particles suspended in viscoelastic fluids in microchannels has drawn increasing attention, in part due to the ability for single-stream three-dimensional focusing in simple channel geometries. Improvement in the understanding of non-Newtonian effects on particle dynamics has led to expanding exploration of focusing and sorting particles and cells using viscoelastic microfluidics. Multiple factors, such as the driving forces arising from fluid elasticity and inertia, the effect of fluid rheology, the physical properties of particles and cells, and channel geometry, actively interact and compete together to govern the intricate migration behavior of particles and cells in microchannels. Here, we review the viscoelastic fluid physics and the hydrodynamic forces in such flows and identify three pairs of competing forces/effects that collectively govern viscoelastic migration. We discuss migration dynamics, focusing positions, numerical simulations, and recent progress in viscoelastic microfluidic applications as well as the remaining challenges. Finally, we hope that an improved understanding of viscoelastic flows in microfluidics can lead to increased sophistication of microfluidic platforms in clinical diagnostics and biomedical research.
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Uthe, Brian, John E. Sader, and Matthew Pelton. "Optical measurement of the picosecond fluid mechanics in simple liquids generated by vibrating nanoparticles: A review." Reports on Progress in Physics, September 1, 2022. http://dx.doi.org/10.1088/1361-6633/ac8e82.
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Abstract Standard continuum assumptions commonly used to describe the fluid mechanics of simple liquids have the potential to break down when considering flows at the nanometer scale. Two common assumptions for simple molecular liquids are that (1) they exhibit a Newtonian response, where the viscosity uniquely specifies the linear relationship between the stress and strain rate, and (2) the liquid moves in tandem with the solid at any solid-liquid interface, known as the no-slip condition. However, even simple molecular liquids can exhibit a non-Newtonian, viscoelastic response at the picosecond time scales that are characteristic of the motion of many nanoscale objects; this viscoelasticity arises because these time scales can be comparable to those of molecular relaxation in the liquid. In addition, even liquids that wet solid surfaces can exhibit nanometer-scale slip at those surfaces. It has recently become possible to interrogate the viscoelastic response of simple liquids and associated nanoscale slip using optical measurements of the mechanical vibrations of metal nanoparticles. Plasmon resonances in metal nanoparticles provide strong optical signals that can be accessed by several spectroscopies, most notably ultrafast transient-absorption spectroscopy. These spectroscopies have been used to measure the frequency and damping rate of acoustic oscillations in the nanoparticles, providing quantitative information about mechanical coupling and exchange of mechanical energy between the solid particle and its surrounding liquid. This information, in turn, has been used to elucidate the rheology of viscoelastic simple liquids at the nanoscale in terms of their constitutive relations, taking into account separate viscoelastic responses for both shear and compressible flows. The nanoparticle vibrations have also been used to provide quantitative measurements of slip lengths on the single-nanometer scale. Viscoelasticity has been shown to amplify nanoscale slip, illustrating the interplay between different aspects of the unconventional fluid dynamics of simple liquids at nanometer length scales and picosecond time scales.
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Banerjee, Debanjan, Sukumar Pati, and Pankaj Biswas. "Analysis of electroviscous effect and heat transfer for flow of non-Newtonian fluids in a microchannel with surface charge-dependent slip at high zeta potentials." Physics of Fluids, October 24, 2022. http://dx.doi.org/10.1063/5.0123964.
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Hydrophobic surfaces in pressure-driven flows induce electrokinetic flow retardation, where the slip length decreases due to the surface charge. In the current work, we investigate the thermal transport and fluid flow behavior of a pressure-driven flow of shear-thinning fluid with an electroviscous effect, accounting for the influence of surface charge on the slip. The electrical potential field induced in the electrical double layer (EDL), velocity, streaming potential, and temperature are obtained after solving the Poisson-Boltzmann equation, mass, momentum and energy conservation equations without invoking the Debye-Hückel linearization. Results are presented for a broad range of dimensionless parameters, such as surface charge-independent slip length, Debye-Hückel parameter, zeta potential, heat flux and flow consistency index ( n). The flow velocity decreases after considering the effect of surface charge on slip and such decrement is more for lower values of n, higher magnitude of zeta potential and thicker EDL. Moreover, for lower values of n, the alteration of the Nusselt number with the surface charge is non-monotonic, whereas, it increases with the surface charge for higher values of n. Further, for lower values of n (1/3), the Nusselt number enhances by the surface charge effect on the slip, whereas, for higher values of n (1/2), the trend is the opposite. Also, there is a strong interplay of the rheology of the fluid and EDL thickness in dictating the variation of the Nusselt number.
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Lacassagne, Tom, Adrien Lyon, Serge Simoëns, Mahmoud El Hajem, and Jean-Yves Champagne. "Flow around an oscillating grid in water and shear-thinning polymer solution at low Reynolds number." Experiments in Fluids 61, no. 1 (December 3, 2019). http://dx.doi.org/10.1007/s00348-019-2840-0.
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Abstract The study of turbulence in complex fluids is of great interest in many environmental and industrial applications, in which the interactions between liquid phase rheology, turbulence, and other phenomena such as mixing or heat and mass transfer have to be understood. Oscillating grid stirred tanks have been used for many purposes in research involving turbulence. However, the mechanisms of turbulence production by the oscillating grid itself have never been studied, and oscillating grid turbulence (OGT) remained undescribed in non-Newtonian, shear-thinning, dilute polymer solutions until recently (Lacassagne et al., in Phys Fluids 31(8):083,102, 2019). The aim of this paper is to study the influence of the shear-thinning property of dilute polymer solutions (DPS), such as xanthan gum (XG), on mean flow, oscillatory flows, and turbulence around an oscillating grid. Liquid phase velocity is measured by particle image velocimetry (PIV) in a vertical plane above the central grid bar. Mean, oscillatory and turbulent components of the velocity fields are deduced by triple Hussain–Reynolds decomposition based on grid phase-resolved measurements. Outside of the grid swept region, the amplitude of oscillatory fluctuations quickly become negligible compared to that of turbulent fluctuations, and the triple and classical Reynolds decomposition become equivalent. Oscillatory jets and wakes behind the grid and their interactions are visualized. Turbulent (Reynolds) and oscillatory stresses are used to evidence a modification of oscillatory flow and turbulence intensity repartition in and around the grid swept region. Energy transfer terms between mean, oscillatory and turbulent flows are estimated and used to describe turbulence production in the grid swept region. Energy is injected by the grid into the oscillatory component. In water, it is transferred to turbulence mostly inside the grid swept region. In DPS, oscillatory flow persists outside of the grid swept zone. Energy is transferred not only to turbulence , in the grid swept region, and far from the tank’s walls, but also to the mean flow, leading to an enhancement of the latter. Mean flow production and enhancement mechanisms are explainable by oscillatory jet variable symmetry and intensity, and by time- and space-variable viscosity. Backward transfer from turbulence to oscillatory flow is also evidenced in DPS. Finally, using phased root mean square (rms) values of turbulent velocity fluctuations, it is shown that in water, the decay of turbulence intensity behind an oscillating grid can be related to the decay of fixed grid turbulence for specific grid positions, a result no longer valid in DPS. Graphic abstract