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Journal articles on the topic 'Non-Newtonian fluid mechanics'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

de Souza Mendes, Paulo R. "Dimensionless non-Newtonian fluid mechanics." Journal of Non-Newtonian Fluid Mechanics 147, no. 1-2 (November 2007): 109–16. http://dx.doi.org/10.1016/j.jnnfm.2007.07.010.

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2

Knight, D. G. "Revisiting Newtonian and non-Newtonian fluid mechanics using computer algebra." International Journal of Mathematical Education in Science and Technology 37, no. 5 (July 15, 2006): 573–92. http://dx.doi.org/10.1080/03091900600712215.

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3

MAYNE, GEORGES. "GEOMETRICAL METHOD IN NON-NEWTONIAN FLUID MECHANICS." Quarterly Journal of Mechanics and Applied Mathematics 42, no. 2 (1989): 239–47. http://dx.doi.org/10.1093/qjmam/42.2.239.

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4

ALBAALBAKI, BASHAR, and ROGER E. KHAYAT. "Pattern selection in the thermal convection of non-Newtonian fluids." Journal of Fluid Mechanics 668 (January 5, 2011): 500–550. http://dx.doi.org/10.1017/s0022112010004775.

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The thermogravitational instability in a fluid layer of a non-Newtonian medium heated from below is investigated. Linear and weakly nonlinear analyses are successively presented. The fluid is assumed to obey the Carreau–Bird model. Although the critical threshold is the same as for a Newtonian fluid, it is found that non-Newtonian fluids can convect in the form of rolls, squares or hexagons, depending on the shear-thinning level. Similar to Newtonian fluids, shear-thickening fluids convect only in the form of rolls. The stability of the convective steady branches is carried out to determine under which specific conditions a pattern is preferred. The influence of the rheological and physical parameters is examined and discussed in detail.

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5

Bullough, W. A., G. E. Cardew, J. Kinsella, and F. E. Boysan. "CFM Self-Teaching in the Fluids Laboratory: Newtonian and Non-Newtonian Flow in Circular Pipes." International Journal of Mechanical Engineering Education 26, no. 3 (July 1998): 167–76. http://dx.doi.org/10.1177/030641909802600301.

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Experiences of a computer fluid mechanics based self-teaching exercise on the flow of Newtonian and non-Newtonian fluids are reported. This was restricted to the steady flow of fluids in circular pipes. The work involved keyboard-literate students in the first year of a mechanical engineering degree course finding the pipe design laws, in terms of the effects of diameter and pressure gradient increase on flow rate. Also, velocity profile plus development length effects, not easily taught via analytical or laboratory classes, were illustrated.

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6

Spodareva, L. A. "Stability of non-newtonian fluid flows." Journal of Applied Mechanics and Technical Physics 41, no. 3 (May 2000): 446–51. http://dx.doi.org/10.1007/bf02465294.

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7

Akbarzadeh, Pooria, Mahmood Norouzi, Reza Ghasemi, and Seyed Zia Daghighi. "Experimental study on the entry of solid spheres into Newtonian and non-Newtonian fluids." Physics of Fluids 34, no. 3 (March 2022): 033111. http://dx.doi.org/10.1063/5.0081002.

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This study experimentally investigates the entry of hydrophobic/hydrophilic spheres into Newtonian and Boger fluids. By considering solution of 82% glycerin and 18% water and solution of 80% glycerin, 20% water and 100 ppm polyacrylamide, Newtonian and Boger fluids are made, respectively. It has been tried that liquids' surface tension, density, and viscosity are almost the same. Thus, all dimensionless numbers are approximately the same at a similar impact velocity except for the elasticity number. A PcoDimaxS highspeed camera captures the spheres' trajectory from the impact to the end of the path. Regarding the range of released height ([Formula: see text]), the impact velocities are approximately in the range of [Formula: see text]. The role of fluid elasticity in combination with the sphere surface wettability on the air cavity formation/evolution/collapse is mainly studied. Also, the kinetics of the sphere motion (velocity, acceleration, and hydrodynamic force coefficient) is studied. The results show that air drawn due to the sphere's impact with the Newtonian liquid is more, and the pinch-off takes place later. Also, shedding bubbles are cusped-shaped in the Boger fluid, while in the Newtonian fluid, they are elliptical. In addition, the most significant impact of surface wettability is observed in the Newtonian fluid. Finally, the results reveal that the sphere in the Newtonian fluid can move faster and travel a longer distance in a specific time interval. The differences observed are closely related to the viscoelastic fluid's elasticity property and extensional viscosity.

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8

Shan, Jie, and Xiaojun Zhou. "The Effect of Bubbles on Particle Migration in Non-Newtonian Fluids." Separations 8, no. 4 (March 24, 2021): 36. http://dx.doi.org/10.3390/separations8040036.

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The movement of the gas–liquid interface caused by the movement of the bubble position will have an impact on the starting conditions for particle migration. This article quantifies the influence of moving bubbles on the starting conditions of particle migration in non-Newtonian fluids, and it aims to better understand the influence of bubbles moving in non-Newtonian fluids on particle migration to achieve more effective control. First, the forces and moments acting on the particles are analyzed; then, fluid dynamics, non-Newtonian fluid mechanics, extended DLVO (Derjaguin Landau Verwey Overbeek theory), surface tension, and friction are applied on the combined effects of particle migration. Then, we reasonably predict the influence of gas–liquid interface movement on particle migration in non-Newtonian fluids. The theoretical results show that the movement of the gas–liquid interface in non-Newtonian fluids will increase the separation force acting on the particles, which will lead to particle migration. Second, we carry out the particle migration experiment of moving bubbles in non-Newtonian fluid. Experiments show that when the solid–liquid two-phase flow is originally stable, particle migration occurs after the bubble movement is added. This phenomenon shows that the non-Newtonian fluid with bubble motion has stronger particle migration ability. Although there are some errors, the experimental results basically support the theoretical data.

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9

Sirivat, A., K. R. Rajagopal, and A. Z. Szeri. "An experimental investigation of the flow of non-Newtonian fluids between rotating disks." Journal of Fluid Mechanics 186 (January 1988): 243–56. http://dx.doi.org/10.1017/s0022112088000126.

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The results of an experimental investigation on the flow of a non-Newtonian fluid between rotating, parallel disks are described in this paper. These results are qualitatively different from those exhibited by linearly viscous fluids in that a narrow layer of exceedingly high velocity gradients appears in the non-Newtonian fluid.

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10

Dai, F., and M. M. Khonsari. "A Theory of Hydrodynamic Lubrication Involving the Mixture of Two Fluids." Journal of Applied Mechanics 61, no. 3 (September 1, 1994): 634–41. http://dx.doi.org/10.1115/1.2901507.

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Based on the principles of continuum mechanics, we drive the governing equations for the hydrodynamic lubrication involving the mixture of two incompressible fluids. The governing equations are general in the sense that they can be applied to the mixture of any simple non-Newtonian fluid with a Newtonian fluid. A mixture thus formed is considered to be nonhomogeneous and non-Newtonian. In the theoretical development, the interaction between the constituents is taken into consideration. It is shown that a number of currently available models are special cases of the theory presented in this paper. As an example, results are presented for journal bearing performance lubricated with a mixture of a power-law fluid mixed with Newtonian oil.

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11

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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12

Hayat, T., S. Asghar, and A. M. Siddiqui. "Periodic unsteady flows of a non-Newtonian fluid." Acta Mechanica 131, no. 3-4 (September 1998): 169–75. http://dx.doi.org/10.1007/bf01177223.

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13

Ramkissoon, H., and K. Rahaman. "Non-Newtonian fluid sphere in a spherical container." Acta Mechanica 149, no. 1-4 (March 2001): 239–45. http://dx.doi.org/10.1007/bf01261675.

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14

Maia, João M. "Numerical and Analytical Methods in Non-Newtonian Fluid Mechanics." Applied Rheology 11, no. 5 (October 1, 2001): 287. http://dx.doi.org/10.1515/arh-2001-0044.

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15

Méndez-Mora, Lourdes, Maria Cabello-Fusarés, Josep Ferré-Torres, Carla Riera-Llobet, Samantha Lopez, Claudia Trejo-Soto, Tomas Alarcón, and Aurora Hernandez-Machado. "Microrheometer for Biofluidic Analysis: Electronic Detection of the Fluid-Front Advancement." Micromachines 12, no. 6 (June 20, 2021): 726. http://dx.doi.org/10.3390/mi12060726.

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The motivation for this study was to develop a microdevice for the precise rheological characterization of biofluids, especially blood. The method presented was based on the principles of rheometry and fluid mechanics at the microscale. Traditional rheometers require a considerable amount of space, are expensive, and require a large volume of sample. A mathematical model was developed that, combined with a proper experimental model, allowed us to characterize the viscosity of Newtonian and non-Newtonian fluids at different shear rates. The technology presented here is the basis of a point-of-care device capable of describing the nonlinear rheology of biofluids by the fluid/air interface front velocity characterization through a microchannel. The proposed microrheometer uses a small amount of sample to deliver fast and accurate results, without needing a large laboratory space. Blood samples from healthy donors at distinct hematocrit percentages were the non-Newtonian fluid selected for the study. Water and plasma were employed as testing Newtonian fluids for validation of the system. The viscosity results obtained for the Newtonian and non-Newtonian fluids were consistent with pertinent studies cited in this paper. In addition, the results achieved using the proposed method allowed distinguishing between blood samples with different characteristics.

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16

Vaidya, Hanumesh, Manjunatha Gudekote, Rajashekhar Choudhari, and Prasad K.V. "Role of slip and heat transfer on peristaltic transport of Herschel-Bulkley fluid through an elastic tube." Multidiscipline Modeling in Materials and Structures 14, no. 5 (December 6, 2018): 940–59. http://dx.doi.org/10.1108/mmms-11-2017-0144.

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Purpose This paper is concerned with the peristaltic transport of an incompressible non-Newtonian fluid in a porous elastic tube. The impacts of slip and heat transfer on the Herschel-Bulkley fluid are considered. The impacts of relevant parameters on flow rate and temperature are examined graphically. The examination incorporates Newtonian, Power-law and Bingham plastic fluids. The paper aims to discuss these issues. Design/methodology/approach The administering equations are solved utilizing long wavelength and low Reynolds number approximations, and exact solutions are acquired for velocity, temperature, flux and stream functions. Findings It is seen that the flow rate in a Newtonian fluid is high when contrasted with the Herschel-Bulkley model, and the inlet elastic radius and outlet elastic radius have opposite effects on the flow rate. Originality/value The analysis carried out in this paper is about the peristaltic transport of an incompressible non-Newtonian fluid in a porous elastic tube. The impact of slip and heat transfer on a Herschel-Bulkley fluid is taken into account. The impacts of relevant parameters on the flow rate and temperature are examined graphically. The examination incorporates Newtonian, Power-law and Bingham plastic fluids.

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17

Hashimoto, H. "Non-Newtonian Effects on the Static Characteristics of One-Dimensional Slider Bearings in the Inertial Flow Regime." Journal of Tribology 116, no. 2 (April 1, 1994): 303–9. http://dx.doi.org/10.1115/1.2927215.

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In this paper, the non-Newtonian effects of lubricants on the static characteristics of one-dimensional, high-speed slider bearings are examined theoretically by considering the fluid inertia effects. In the derivation of the modified Reynolds equation, the fluid inertia term in the momentum equation for the non-Newtonian lubricant films is averaged over the film thickness, and the Rabinowitsch empirical model is used as a constitutive equation for non-Newtonian fluids. Applying the modified Reynolds equation to the one-dimensional slider bearings and solving the equation analytically based on the perturbation technique, the film pressure, load carrying capacity, friction force, and inlet flow rate are obtained under various values of the dimensionless nonlinear factor and film thickness ratio. The combined effects of fluid inertia and non-Newtonian characteristics on these static characteristics of lubricants are discussed.

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18

Sui, P. C., and F. Sadeghi. "Non-Newtonian Thermal Elastohydrodynamic Lubrication." Journal of Tribology 113, no. 2 (April 1, 1991): 390–96. http://dx.doi.org/10.1115/1.2920634.

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A numerical solution to the problem of thermal and non-Newtonian fluid model in elastohydrodynamic lubrication is presented. The generalized Reynolds equation was modified by the Eyring rheology model to incorporate the non-Newtonian effects of the fluid. The simultaneous system of modified Reynolds, elasticity and energy equations were numerically solved for the pressure, temperature and film thickness. Results have been presented for loads ranging from W = 7 × 10−5 to W = 2.3 × 10−4 and the speeds ranging from U* = 2 × 10−11 to U* = 6 × 10−11 at various slip conditions. Comparison between the isothermal and thermal non-Newtonian traction force has also been presented.

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19

Garg, V. K., and K. R. Rajagopal. "Flow of a non-Newtonian fluid past a wedge." Acta Mechanica 88, no. 1-2 (March 1991): 113–23. http://dx.doi.org/10.1007/bf01170596.

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20

Ramkissoon, H. "Lam�-type potentials in a non-Newtonian fluid theory." Acta Mechanica 60, no. 3-4 (July 1986): 135–41. http://dx.doi.org/10.1007/bf01176348.

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21

Labropulu, F. "D'Alembert motions for non-Newtonian second grade fluid." International Journal of Non-Linear Mechanics 38, no. 7 (October 2003): 1027–36. http://dx.doi.org/10.1016/s0020-7462(02)00049-5.

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22

Asghar, S., Masood Khan, and T. Hayat. "Magnetohydrodynamic transient flows of a non-Newtonian fluid." International Journal of Non-Linear Mechanics 40, no. 5 (June 2005): 589–601. http://dx.doi.org/10.1016/j.ijnonlinmec.2004.07.011.

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23

Tarbell, John M. "Influence of Blood Rheology and Vessel Wall Motion on Arterial Fluid Mechanics." Applied Mechanics Reviews 47, no. 6S (June 1, 1994): S291—S295. http://dx.doi.org/10.1115/1.3124426.

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Most model studies of arterial fluid mechanics have assumed that blood is a Newtonian fluid and that vessel wall motion driven by the pressure pulse has a small influence on the local velocity and pressure distributions. This paper provides a brief historical review of arterial flow modeling which emphasizes recent developments in non-Newtonian blood analog fluids and studies of the influence of vessel wall motion on local flow fields. It is pointed out that vessel wall motion can have a dominant effect on mean pressure gradient and a significant effect on mean wall shear stress in the aorta.

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24

VIERU, D., and I. SIDDIQUE. "AXIAL FLOW OF SEVERAL NON-NEWTONIAN FLUIDS THROUGH A CIRCULAR CYLINDER." International Journal of Applied Mechanics 02, no. 03 (September 2010): 543–56. http://dx.doi.org/10.1142/s1758825110000640.

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The velocity field, the longitudinal and the normal tensions corresponding to the axial flow of an Oldroyd-B fluid due to an infinite circular cylinder subject to a longitudinal time-dependent stress are determined by means of the Laplace and finite Hankel transforms. The similar solutions for Maxwell, second grade or Newtonian fluids have been obtained as particular cases of the solutions for Oldroyd-B fluids. Finally, by using dimensionless variables, some characteristics of the motion as well as the influence of the material parameters on the behavior of fluid are shown by graphical illustrations.

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25

V.S., Sampath Kumar, and N. P. Pai. "Suction and injection effect on flow between two plates with reference to Casson fluid model." Multidiscipline Modeling in Materials and Structures 15, no. 3 (May 7, 2019): 559–74. http://dx.doi.org/10.1108/mmms-05-2018-0092.

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Purpose The purpose of this paper is to study the effect of injection and suction on velocity profile, skin friction and pressure distribution of a Casson fluid flow between two parallel infinite rectangular plates approaching or receding from each other with suction or injection at the porous plates. Design/methodology/approach The governing Navier–Stokes equations are reduced to the fourth-order non-linear ordinary differential equation through the similarity transformations. The approximated analytic solution based on the Homotopy perturbation method is given and also compared with the classical finite difference method. Findings From this study, the authors observed that the skin friction is less in non-Newtonian fluids compared to Newtonian fluids. The use of non-Newtonian fluids reduces the pressure in all the cases compared to Newtonian and hence load-carrying capacity will be more. As γ value increases velocity, skin friction and pressure decreases. When γ is fixed, it is observed that skin friction and pressure is minimum for A=0.5 and maximum when A=−0.5. The result of this study also shows that the effect of suction on the velocity profiles, pressure and skin friction is opposite to the effect of injection. Originality/value The present work analyzes the characteristic of non-Newtonian fluid having practical and industrial applications.

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26

Goodyer, Steve. "Advances in Non-Newtonian Fluid Mechanics (INFFM Annual Conference 2013)." Applied Rheology 23, no. 4 (April 1, 2013): 235–36. http://dx.doi.org/10.1515/arh-2013-0021.

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27

Wedgewood, Lewis E. "An objective rotation tensor applied to non-Newtonian fluid mechanics." Rheologica Acta 38, no. 2 (July 2, 1999): 91–99. http://dx.doi.org/10.1007/s003970050159.

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28

R, Keerthi, B. Mahanthesh, and Smita Saklesh Nagouda. "Rayleigh–Bénard convection in a non-Newtonian dielectric fluid with Maxwell–Cattaneo law under the effect of internal heat generation/consumption." Multidiscipline Modeling in Materials and Structures 16, no. 5 (April 17, 2020): 1175–88. http://dx.doi.org/10.1108/mmms-09-2019-0174.

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PurposeThe study of instability due to the effects of Maxwell–Cattaneo law and internal heat source/sink on Casson dielectric fluid horizontal layer is an open question. Therefore, in this paper, the impact of internal heat generation/absorption on Rayleigh–Bénard convection in a non-Newtonian dielectric fluid with Maxwell–Cattaneo heat flux is investigated. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary.Design/methodology/approachThe Casson fluid model is utilized to characterize the non-Newtonian fluid behavior. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary. The governing equations are non-dimensionalized using appropriate dimensionless variables and the subsequent equations are solved for the critical Rayleigh number using the normal mode technique (NMT).FindingsResults are presented for two different cases namely dielectric Newtonian fluid (DNF) and dielectric non-Newtonian Casson fluid (DNCF). The effects of Cattaneo number, Casson fluid parameter, heat source/sink parameter on critical Rayleigh number and wavenumber are analyzed in detail. It is found that the value Rayleigh number for non-Newtonian fluid is higher than that of Newtonian fluid; also the heat source aspect decreases the magnitude of the Rayleigh number.Originality/valueThe effect of Maxwell–Cattaneo heat flux and internal heat source/sink on Rayleigh-Bénard convection in Casson dielectric fluid is investigated for the first time.

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29

Hou, J. S., M. H. Holmes, W. M. Lai, and V. C. Mow. "Boundary Conditions at the Cartilage-Synovial Fluid Interface for Joint Lubrication and Theoretical Verifications." Journal of Biomechanical Engineering 111, no. 1 (February 1, 1989): 78–87. http://dx.doi.org/10.1115/1.3168343.

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The objective of this study is to establish and verify the set of boundary conditions at the interface between a biphasic mixture (articular cartilage) and a Newtonian or non-Newtonian fluid (synovial fluid) such that a set of well-posed mathematical problems may be formulated to investigate joint lubrication problems. A “pseudo-no-slip” kinematic boundary condition is proposed based upon the principle that the conditions at the interface between mixtures or mixtures and fluids must reduce to those boundary conditions in single phase continuum mechanics. From this proposed kinematic boundary condition, and balances of mass, momentum and energy, the boundary conditions at the interface between a biphasic mixture and a Newtonian or non-Newtonian fluid are mathematically derived. Based upon these general results, the appropriate boundary conditions needed in modeling the cartilage-synovial fluid-cartilage lubrication problem are deduced. For two simple cases where a Newtonian viscous fluid is forced to flow (with imposed Couette or Poiseuille flow conditions) over a porous-permeable biphasic material of relatively low permeability, the well known empirical Taylor slip condition may be derived using matched asymptotic analysis of the boundary layer at the interface.

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30

Ramkissoon, H. "Stokes Flow Past a Non-Newtonian Fluid Spheroid." ZAMM 78, no. 1 (January 1998): 61–66. http://dx.doi.org/10.1002/(sici)1521-4001(199801)78:1<61::aid-zamm61>3.0.co;2-o.

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31

Gagnon, D. A., and P. E. Arratia. "The cost of swimming in generalized Newtonian fluids: experiments with C. elegans." Journal of Fluid Mechanics 800 (July 14, 2016): 753–65. http://dx.doi.org/10.1017/jfm.2016.420.

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Numerous natural processes are contingent on microorganisms’ ability to swim through fluids with non-Newtonian rheology. Here, we use the model organism Caenorhabditis elegans and tracking methods to experimentally investigate the dynamics of undulatory swimming in shear-thinning fluids. Theory and simulation have proposed that the cost of swimming, or mechanical power, should be lower in a shear-thinning fluid compared to a Newtonian fluid of the same zero-shear viscosity. We aim to provide an experimental investigation into the cost of swimming in a shear-thinning fluid from (i) an estimate of the mechanical power of the swimmer and (ii) the viscous dissipation rate of the flow field, which should yield equivalent results for a self-propelled low Reynolds number swimmer. We find the cost of swimming in shear-thinning fluids is less than or equal to the cost of swimming in Newtonian fluids of the same zero-shear viscosity; furthermore, the cost of swimming in shear-thinning fluids scales with a fluid’s effective viscosity and can be predicted using fluid rheology and simple swimming kinematics. Our results agree reasonably well with previous theoretical predictions and provide a framework for understanding the cost of swimming in generalized Newtonian fluids.

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32

Gupta, A. S. "Hydromagnetic wake in a non-Newtonian fluid." Mechanics Research Communications 19, no. 3 (May 1992): 237–49. http://dx.doi.org/10.1016/0093-6413(92)90072-i.

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33

Beletsky, Jа S., T. J. Shymko, I. J. Beletsky, and M. V. Senyushkovych. "Thermodynamics of non-Newtonian fluids (drilling mud)." Фізика і хімія твердого тіла 17, no. 2 (June 15, 2016): 286–93. http://dx.doi.org/10.15330/pcss.17.2.286-293.

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Using the method of pressure balance with balance energy forms, calculations are made hidrotermodynamichni mobile hydraulic flow in the well drilling fluids, water-based, which accumulate and transmit energy to other elements. The cases of the flow of liquid upwards (against gravity) and the current flow under gravity down to the bottom hole. The resulting complex equation with specific values that do not depend on the scale of thermodynamics and fluid mechanics processes that occur in the borehole. By combining different similarity criteria can assess the impact of these processes on the performance of any operation in the well during its construction. The dependences can be used dlyautochnennya procedures governing the calculation of regime and technological parameters of the construction of deep wells.

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34

Wolff, R., and A. Kubo. "A Generalized Non-Newtonian Fluid Model Incorporated Into Elastohydrodynamic Lubrication." Journal of Tribology 118, no. 1 (January 1, 1996): 74–82. http://dx.doi.org/10.1115/1.2837095.

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A generalized Reynolds equation for the non-Newtonian fluid, which can incorporate most of the published rheological models, is proposed. The solution of the isothermal EHL line contact lubricated by a non-Newtonian fluid is obtained by applying the Newton-Raphson method. The results of an isothermal non-Newtonian EHL line contact model with different rheological laws and the results of a thermal Newtonian EHL model are presented. Under low load and high rolling velocity conditions, the thermal effects caused by slip have a greater influence on the film shape and pressure distribution than the non-Newtonian effects. For low slip and under heavy load conditions the non-Newtonian behavior of fluid significantly influences the traction coefficient, while thermal effects have a great influence on the traction in case of high slip. The comparison between numerical and experimental results shows that the nonlinear viscous Eyring model overestimates the traction coefficient when high viscosity oil is subjected to a heavy load and low slip conditions. In this case, only the visco-plastic models can predict the traction value. The visco-elastic behavior of the fluid is important at very low slip conditions and it can slightly reduce the traction value.

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35

Najji, B., B. Bou-Said, and D. Berthe. "New Formulation for Lubrication With Non-Newtonian Fluids." Journal of Tribology 111, no. 1 (January 1, 1989): 29–34. http://dx.doi.org/10.1115/1.3261875.

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A global method for the solution of thermohydrodynamic problems is proposed for the analysis of lubricated contacts with non-newtonian fluids. A set of algebraic equations is obtained after introducing the weak form of the energy equation and a modified generalized equation for thin fluid flows. This last equation represents a new formulation for lubrication with non-newtonian fluids. The establishment of this equation is presented below along with several tests including explicit and implicit rheological laws with some comments on the effect of the different parameters which occur in the study.

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36

Pascal, H., and F. Pascal. "Dynamics of non-Newtonian fluid interfaces in a porous medium: Incompressible fluids." International Journal for Numerical Methods in Fluids 8, no. 11 (November 1988): 1389–401. http://dx.doi.org/10.1002/fld.1650081103.

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37

Ryltsev, I. A., O. Yu Frolov, and G. R. Shrager. "NUMERICAL SIMULATION OF A POWERLAW FLUID FLOW IN A CHANNEL WITH DOUBLE CONSTRICTION." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 70 (2021): 76–88. http://dx.doi.org/10.17223/19988621/70/7.

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Flow fields of non-Newtonian fluids in cylindrical channels with obstacles are of great interest for researchers studying the mechanics of fluids. In engineering techniques, such channels represent component parts of heat exchangers and hydraulic systems of various types. In this work, the numerical simulation of a steady non-Newtonian fluid flow in an axisymmetric pipe with two overlaps, whose geometry is described by a cosine function, is carried out. Mathematical formulation of the problem is written in terms of vortex and stream function variables. The Ostwald – de Waele model is used to describe rheological properties of the medium. The solution to a system of differential equations is obtained numerically using the false transient method. To determine the pressure field, the Poisson equation for pressure is solved. Three media are considered in the paper: Newtonian, pseudoplastic, and dilatant fluids. The influence of the Reynolds number, power-law index in the rheological model, and geometric parameters of the channel on the flow characteristics is shown as streamline distributions and functional curves.

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Myllerup, C. M., A. A. Elsharkawy, and B. J. Hamrock. "Couette Dominance Used for Non-Newtonian Elastohydrodynamic Lubrication." Journal of Tribology 116, no. 1 (January 1, 1994): 47–55. http://dx.doi.org/10.1115/1.2927045.

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The perturbational approach that assumes Couette dominance in non-Newtonian elastohydrodynamic lubrication analysis is discussed. The assumption is found valid for non-Newtonian fluid models exhibiting Newtonian properties at low shear strain rate. A general non-Newtonian fluid model which meets that requirement is incorporated into elastohydrodynamic lubrication analysis of line contacts by using the perturbational approach. In the case of a circular fluid model the results obtained from the perturbational approach are in good agreement with those obtained from the direct approach. However, a better convergence and the possibility of avoiding using stress boundary conditions at high shear stress can be achieved by using the perturbational approach. Results are presented for various values of the shape exponent in the general model, and it transpires that this also is an important parameter of the fluid model.

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Асадуллин, Наиль, and Nail Asadullin. "CLASSIFICATION OF FODDER MASSES APPLIED TO ITS HYDRO-MECHANICS." Vestnik of Kazan State Agrarian University 13, no. 2 (August 6, 2018): 71–75. http://dx.doi.org/10.12737/article_5b35058f6bef38.44028308.

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The current stage in the development of agricultural production in livestock is characterized by the extensive use of pipeline transport to move the forage masses, which are related to non-Newtonian fluids. Production experience and scientific work on the study of hydrotransport systems showed that this method of transportation is the most economical and promising, it has high reliability of structural elements, improves sanitary and hygienic working conditions and makes it possible to fully automate the transportation process. The complex nature of the transportation of mixtures has not allowed to create a unified theory of hydrodynamic calculation of their parameters to date, therefore, various models are used for theoretical investigation of the nature of motion. To select a particular model, it is always important to correctly classify viscous semiliquid media with respect to hydrodynamics. Therefore, the article did not set out the specific goal of choosing a method for studying non-Newtonian systems, but solved the problem of their classification by known defining characteristics. The proposed classification does not pretend to be exhaustive in terms of the physical and chemical nature of the fluid, especially their combinations, but it covers almost all the anomalous phenomena that occur in the fluid during its transportation and helps to select a quantitative method for calculating the transporting fluid. The classification of non-Newtonian fluids with respect to their hydromechanics is based on the dependence of the shear stress on the shear gradient. For this dependence, each type of liquid is considered. The developed classification scheme further promotes a more complete account of the rheological properties of high-viscosity liquids during their transportation through pipes and facilitates the development of quantitative calculation methods.

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Kefayati, Gholamreza. "A macroscopic and mesoscopic model of Newtonian and non-Newtonian nanofluids with a two-energy equation method." Physics of Fluids 34, no. 11 (November 2022): 112005. http://dx.doi.org/10.1063/5.0124292.

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We present an updated comprehensive macroscopic model of nanofluids, considering a revisited local thermal non-equilibrium (LTNE) condition to study the temperature difference between carrier fluid and nanoparticles. A new relation for thermal conductivity of solid and liquid phases in the LTNE condition is introduced which considers the possible particle aggregation. This model is thermodynamically consistent and covers the non-Newtonian models of nanofluids, including power-law and viscoplastic ones. A mesoscopic scheme based on the lattice Boltzmann method (LBM) which satisfies the presented macroscopic equations is introduced and derived. This investigation is a further development of our recent studies[G. H. R. Kefayati and A. Bassom, “A lattice Boltzmann method for single and two phase models of nanofluids: Newtonian and non-Newtonian nanofluids,” Phys. Fluids 33, 102008 (2021); G. H. R. Kefayati, “A two- and three-dimensional mesoscopic method for an updated non-homogeneous model of Newtonian and non-Newtonian nanofluids,” Phys. Fluids 34, 032003 (2022).] for simulating and analyzing nanofluids by a two-phase model. To assess the present numerical method, it is studied for a benchmark problem of natural convection in a cavity. The dimensional and non-dimensional macroscopic equations for the mentioned benchmark are defined and the implemented non-dimensional relations of LBM are shown. The present approach is verified with the obtained results of the mixture approach and a previous two-phase model, which demonstrated the accuracy of the presented method. The results including the temperature distributions of the solid and fluid phases, the nanoparticles distributions, and fluid flow behavior as well as the yielded/unyielded sections for the viscoplastic nanofluids are shown and discussed for the defined non-dimensional parameters. It was also demonstrated that the previous proposed thermal conductivity model of nanofluids in the LTNE approach generates a significantly different value compared to experimental results, and the current suggested model produces reliable results to the experimental ones.

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41

Labropulu, F. "Exact solutions of non-Newtonian fluid flows with prescribed vorticity." Acta Mechanica 141, no. 1-2 (March 2000): 11–20. http://dx.doi.org/10.1007/bf01176804.

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Koguchi, Hideo, and Toshio Yada. "The Meniscus Instability in Non-Newtonian Negative Squeeze Films." Journal of Applied Mechanics 57, no. 3 (September 1, 1990): 769–75. http://dx.doi.org/10.1115/1.2897090.

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This paper treats an instability at the free surface of non-Newtonian (power-law) fluid films between two tilted plates in a negative squeeze motion. The meniscus instability in a fluid with the power-law constitutive equation was analyzed on the basis of the linear stability theory. In the analysis, a capillary number for the power-law fluid was newly defined and the relationship between the capillary number and the criterion for the instability of meniscus was theoretically deduced. In the experiment, a water solution of polyacrylamide (separan) whose viscosity obeys a power-law of the strain rate was used as a sample fluid, the meniscus instability in the fluid was examined by using a VTR and the wavelength of disturbances was measured. The theoretical criterion for the instability was in good agreement with experiments and the capillary number could rearrange well the experimental results for the disturbances.

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Ionescu, C. M., I. R. Birs, D. Copot, C. I. Muresan, and R. Caponetto. "Mathematical modelling with experimental validation of viscoelastic properties in non-Newtonian fluids." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2172 (May 11, 2020): 20190284. http://dx.doi.org/10.1098/rsta.2019.0284.

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The paper proposes a mathematical framework for the use of fractional-order impedance models to capture fluid mechanics properties in frequency-domain experimental datasets. An overview of non-Newtonian (NN) fluid classification is given as to motivate the use of fractional-order models as natural solutions to capture fluid dynamics. Four classes of fluids are tested: oil, sugar, detergent and liquid soap. Three nonlinear identification methods are used to fit the model: nonlinear least squares, genetic algorithms and particle swarm optimization. The model identification results obtained from experimental datasets suggest the proposed model is useful to characterize various degree of viscoelasticity in NN fluids. The advantage of the proposed model is that it is compact, while capturing the fluid properties and can be identified in real-time for further use in prediction or control applications. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

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Wei, D. M., and S. Al-Ashhab. "Similarity solutions for non-Newtonian power-law fluid flow." Applied Mathematics and Mechanics 35, no. 9 (July 17, 2014): 1155–66. http://dx.doi.org/10.1007/s10483-014-1854-6.

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45

Min, Shen. "Variational principles in hydrodynamics of a non-Newtonian fluid." Applied Mathematics and Mechanics 19, no. 10 (October 1998): 963–69. http://dx.doi.org/10.1007/bf02457956.

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Sawyer, W. G., and J. A. Tichy. "Non-Newtonian Lubrication With the Second-Order Fluid." Journal of Tribology 120, no. 3 (July 1, 1998): 622–28. http://dx.doi.org/10.1115/1.2834596.

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In certain applications where the lubricant is subjected to rapidly changing conditions along its flowing path (such as an elastohydrodynamic contact), the inherently time dependent nature of the lubricant may be significant. The simplest type of model to correctly account for such time dependence is the second-order fluid, which is a systematic small departure from Newtonian behavior, involving higher order rate-of-rate-of strain tensors. As in a companion paper using the Maxwell model, the formalities of applying such a model to thin film flow are emphasized. Using a regular perturbation in the Deborah number, with the conventional lubrication solution as the leading term, a solution can be obtained. Viscoelasticity may raise or lower pressure depending on the nature of edge boundary conditions.

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Azhdari, Mohsen, Alireza Riasi, and Pedram Tazraei. "Numerical analysis of fluid hammer in helical pipes considering non-Newtonian fluids." International Journal of Pressure Vessels and Piping 181 (March 2020): 104068. http://dx.doi.org/10.1016/j.ijpvp.2020.104068.

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Joseph, Subin P. "New classes of periodic and non-periodic exact solutions for Newtonian and non-Newtonian fluid flows." International Journal of Engineering Science 180 (October 2022): 103740. http://dx.doi.org/10.1016/j.ijengsci.2022.103740.

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Kacou, A., K. R. Rajagopal, and A. Z. Szeri. "Flow of a Fluid of the Differential Type in a Journal Bearing." Journal of Tribology 109, no. 1 (January 1, 1987): 100–107. http://dx.doi.org/10.1115/1.3261298.

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The flow of a homogeneous incompressible non-Newtonian fluid of the differential type between infinite eccentric rotating cylinders is discussed within the context of the lubrication approximation. The problem is studied by means of a perturbation and the effects of the non-Newtonian parameters are delineated. It is found that the load carrying capacity of the bearing can be significantly altered by the non-Newtonian character of the fluid.

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Agarwal, Ravi P., and Donal O'Regan. "Infinite interval problems arising in non-linear mechanics and non-Newtonian fluid flows." International Journal of Non-Linear Mechanics 38, no. 9 (November 2003): 1369–76. http://dx.doi.org/10.1016/s0020-7462(02)00076-8.

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