Academic literature on the topic 'Micro-inertia Driven Flow Rule'

In this paper, we have studied the effects of retardation time of non-Newtonian Oldroyd-B type fluid driven by Helmholtz-Smoluchowski velocity in a micro-channel. The potential electric field is applied along the length of the micro-channel describing by the Poisson–Boltzmann equation. The governing model equation was solved analytically using the classical method of partial differential equations. Analytical solution was simulated with the help of MATHEMATICA software and the graphical results for various physical flow parameters were analyzed. Results shows that for larger values of retardation time of a viscoelastic fluid the higher the viscoelastic effect of the fluid and this makes it to need more time for the stress to respond to deformation. Also, the electrokinetic width of micro-channel play a vital rule on the performance of velocity distribution.

It is well known that an increased viscosity slows down fluid dynamics. Here we show that this intuitive rule is not general and can fail for liquids flowing in confined liquid-repellent systems. A gravity-driven, highly viscous glycerol droplet inside a sealed superhydrophobic capillary is moving more than 10 times faster than a water droplet with three-orders-of-magnitude lower viscosity. Using tracer particles, we show that the low-viscosity droplets are rapidly rotating internally, with flow velocities greatly exceeding the center-of-mass velocity. This is in stark contrast to the faster moving high-viscosity droplets with nearly vanishing internal flows. The anomalous viscosity-enhanced flow is caused by a viscosity-suppressed deformation of the droplet-air interface and a hydro- and aerodynamic coupling between the droplet and the air trapped within the micro/nanostructures (plastron). Our work demonstrates the unexpected role of the plastron in controlling fluid flow beyond the mere reduction in contact area and friction.

Viscous liquid flow in micro-channels is typically laminar because of the low Reynolds number constraint. However, by introducing elasticity into the fluids, the flow behavior could change drastically to become turbulent; this elasticity can be realized by dissolving small quantities of polymer molecules into an aqueous solvent. Our recent investigation has directly visualized the extension and relaxation of these polymer molecules in an aqueous solution. This elastic-driven phenomenon is known as ‘elastic turbulence’. Hitherto, existing studies on elastic flow instability are mostly limited to single-stream flows, and a comprehensive statistical analysis of a multi-stream elastic turbulent micro-channel flow is needed to provide additional physical understanding. Here, we investigate the flow field characteristics of elastic turbulence in a 3-stream contraction-expansion micro-channel flow. By applying statistical analyses and flow visualization tools, we show that the flow field bares many similarities to that of inertia-driven turbulence. More interestingly, we observed regions with two different types of power-law dependence in the velocity power spectra at high frequencies. This is a typical characteristic of two-dimensional turbulence and has hitherto not been reported for elastic turbulent micro-channel flows.

Fluid flows through nano-scale channels depend sensitively on the physical and chemical properties of the walls that surround them. The sub-micron dimensions of such channels, however, are impossible to resolve optically, which rules out most methods for flow visualization. Classic calculations by Squire (Q. J. Mech. Appl. Maths, vol. IV, 1951, pp. 321–329) and Landau & Lifshitz (Fluid Mechanics, vol. 6, 1959, Pergamon) showed that the laminar flow driven outside a capillary, by fluid emerging from the end of the capillary, is identical to the flow driven by a point force proportional to the average velocity in the capillary. Secchi et al. (J. Fluid Mech. 826, R3) analyze the dispersion of a solute that is injected along with the fluid, whose concentration decays slowly with distance but with a strong angular dependence that encodes the intra-capillary velocity. Fluorescence micrographs of the concentration profile emerging from the nanocapillary can be related directly to the average fluid velocity within the nanocapillary. Beyond their remarkable capacity for nano-velocimetry, Landau–Squire plumes will likely appear throughout micro- and nano-fluidic systems.

PurposeThe purpose of this paper is to discuss the 3D micropolar hybrid (Ag-CuO/H2O) nanofluid past rapid moving surface, where porous medium has been considered.Design/methodology/approachThe model of problem was represented by highly partial differential equations which were deduced by using suitable approximations (boundary layer). Then, the governing model was converted into five combined ordinary differential equations applying proper similarity transformations. Therefore, the eminent iterative Runge–Kutta–Fehlberg method (RKF45) has been applied to solve the resulting equations.FindingsHigher values of vortex viscosity, spin gradient viscosity and micro-inertia density parameters are reduced in horizontal direction, whereas opposite behaviour is noticed for vertical direction.Originality/valueThe work has not been done in the area of hybrid micropolar nanofluid. Hence, this article culminates to probe how to improve the thermal conduction and fluid flow in 3D boundary layer flow of micropolar mixture of nanoparticles driven by rapidly moving plate with convective boundary condition.

A constitutive model is proposed for simulations of hot forming processes. Dominant mechanisms in hot forming including inter-granular deformation, grain boundary sliding and grain boundary diffusion are considered in the constitutive model. A Taylor type polycrystalline model is used to predict inter-granular deformation. Previous works on grain boundary sliding and grain boundary diffusion are extended to drive three dimensional macro stress-strain rate relationships for each mechanism. In these relationships, the effect of grain size is also taken into account. It is shown that for grain boundary diffusion, stress-strain rate relationship obeys the Prandtl-Reuss flow rule. The proposed model is used to simulate step strain rate tests and the results are compared with experimental data. It is concluded that the model can be used to predict flow stress for various grain sizes and strain rates. The proposed model can be directly used in simulation of hot forming processes and as an example the bulge forming process is simulated and the results are compared with experimental data.

Advection by ocean currents modifies phytoplankton size structure at small scales (1–10 cm) by aggregating cells in different regions of the flow depending on their size. This effect is caused by the inertia of the cells relative to the displaced fluid. It is considered that, at larger scales (greater than or equal to 1 km), biological processes regulate the heterogeneity in size structure. Here, we provide observational evidence of heterogeneity in phytoplankton size structure driven by ocean currents at relatively large scales (1–10 km). Our results reveal changes in the phytoplankton size distribution associated with the coastal circulation patterns. A numerical model that incorporates the inertial properties of phytoplankton confirms the role of advection on the distribution of phytoplankton according to their size except in areas with enhanced nutrient inputs where phytoplankton dynamics is ruled by other processes. The observed preferential concentration mechanism has important ecological consequences that range from the phytoplankton level to the whole ecosystem.

This paper presents aspects of the concept and design of prostheses for the upper limb. The objective of this research is that of prototyping a customized prosthesis, with EMG signals that initiate the motion. The prosthesis’ fingers’ motions (as well as that of its hand and forearm parts) are driven by micro-motors, and assisted by the individualized command and control system. The software and hardware tandem concept of this mechatronic system enables complex motion (in the horizontal and vertical plane) with accurate trajectory and different set rules (gripping pressure, object temperature, acceleration towards the object). One important idea is regarding customization via reverse engineering techniques. Due to this, the dimensions and appearance (geometric characteristics) of the prosthesis would look like the human hand itself. The trajectories and motions of the fingers, thumbs, and joints have been studied by kinematic analysis with the matrix–vector method aided by Matlab. The concept and design of the mechanical parts allow for complex finger motion—rotational motion in two planes. The command and control system is embedded, and data received from the sensors are processed by a micro-controller for managing micro-motor control. Preliminary testing of the sensors and micro-motors on a small platform, Arduino, was performed. Prototyping of the mechanical components has been a challenge because of the high accuracy needed for the geometric precision of the parts. Several techniques of rapid prototyping were considered, but only DLP (digital light processing) proved to be the right one.

Cilia are micro-scale hair-like organelles. They can exhibit self-sustained oscillations which play crucial roles in flow transport or locomotion. Recent studies have shown that these oscillations can spontaneously emerge from dynamic instability triggered by internal stresses via a Hopf bifurcation. However, the flow transport induced by an instability-driven cilium still remains unclear, especially when the fluid is non-Newtonian. This study aims at bridging these gaps. Specifically, the cilium is modelled as an elastic filament, and its internal actuation is represented by a constant follower force imposed at its tip. Three generalized Newtonian behaviours are considered, i.e. the shear-thinning, Newtonian and shear-thickening behaviours. Effects of four key factors, including the filament zero-stress shape, Reynolds number ( $Re$ ), follower-force magnitude and fluid rheology, on the filament dynamics, fluid dynamics and flow transport are explored through direct numerical simulation at $Re$ of 0.04 to 5 and through a scaling analysis at $Re \approx 0$ . The results reveal that even though it is expected that inertia vanishes at $Re \ll 1$ , inertial forces do alter the filament dynamics and deteriorate the flow transport at $Re\ge 0.04$ . Regardless of $Re$ , the flow transport can be improved when the flow is shear thinning or when the follower force increases. Furthermore, a linear stability analysis is performed, and the variation of the filament beating frequency, which is closely correlated with the filament dynamics and flow transport, can be predicted.

Modelling highly non-linear, strongly temperature- and rate-dependent visco-plastic behaviour of poly-crystalline solids (e.g., metals and metallic alloys) is one of the most challenging topics of contemporary research interest, mainly owing to the increasing use of metallic structures in engineering applications. Numerous classical models have been developed to model the visco-plastic behaviour of poly-crystalline solids. However, limitations of classical visco-plasticity models have been realized mainly in two cases: in problems at the scale of mesoscopic length (typically in the range of a tenth of a micron to a few tens of micron) or lower, and in impact problems under high-strain loading with varying temperature. As a remedy of the first case, several length scale dependent non-local visco-plasticity models have been developed in the last few decades. Unfortunately, a rationally grounded continuum model with the capability of reproducing visco-plastic response in accord with the experimental observations under high strain-rates and varying temperatures remains elusive and attempts in this direction are often mired in controversies. With the understanding of metal visco-plasticity as a macroscopic manifestation of the underlying dislocation motion, there are attempts to develop phenomenological as well as physics-based continuum models that could be applied across different regimes of temperature and strain rate. Yet, none of these continuum visco-plasticity models accurately capture the experimentally observed oscillations in the stress-strain response of metals (e.g. molybdenum, tantalum etc.) under high strain rates and such phenomena are sometimes even dismissed as mere experimental artefacts. The question arises as to whether the existing models have consistently overlooked any important mechanism related to dislocation motion which could be very important at high strain-rate loading and possibly responsible for oscillations in the stress-strain response. In the search for an answer to this question, one observes that the existing macro-scale continuum visco-plasticity models do not account for the effects of dislocation inertia which is identified in this thesis as a dominating factor in the visco-plastic response under high strain rates. Incorporating the effect of dislocation inertia in the continuum response, a visco-plasticity model is developed. Here the ow rule is derived based on an additional balance law, the micro-force balance, for the forces arising from (and maintaining) the plastic flow. The micro-force balance together with the classical momentum balance equations thus describes the visco-plastic response of isotropic poly-crystalline materials. The model is thermodynamically consistent as the constitutive relations for the fluxes are determined on satisfying the laws of thermodynamics. The model includes consistent derivation of temperature evolution, thus replaces the empirical route. Partial differential equations (PDEs) describing the visco-plastic behaviour in the present model is highly non-linear and solving them requires the employment of numerical techniques. Had the interest been limited only to problems with nicely behaved continuous field variables, the finite element method (FEM) could have been a natural choice for solving the governing PDEs. Keeping in mind the limitations of the FEM in discretizing such large deformation problems and in handling discontinuities, a smooth particle hydrodynamics (SPH) formulation for the micro-inertia driven visco-plasticity model is undertaken in this thesis. The visco-plasticity model is then exploited to simulate ductile damage by suitably coupling the discretized SPH equations with an existing damage model. The current scheme does not necessitate the introduction of a yield or damage surface in evolving the plastic strain/ damage parameters and thus the numerical implementation avoids a computationally intensive return mapping. Our current approach therefore provides for an efficient numerical route to simulating impact dynamics problems. However, implementation of the SPH equations demands some additional terms such as artificial viscosity to arrive at a numerically stable solution. Using such stabilizing terms is however bereft of a rational or physical basis. The choice of artificial viscosity parameters is ad-hoc -an inappropriate choice leading to unphysical solutions. In order to circumvent this, the micro-inertia driven visco-plasticity model is reformulated using peri dynamics (PD), a more efficacious scheme to treat shock waves/discontinuities within a continuum model. Remarkably, the PD model naturally accounts for the localization residual terms in the local balances for internal energy and entropy, originally conceived of by Edelen and co-workers nearly half a century ago as a source of non-local interaction. Exploiting the present model, we also explore the determination of conservation laws based on a variational formulation for dissipative visco-plastic solids wherein the system variables are appropriately augmented with those describing the time-reversed dynamics. This in turn enables us to undertake symmetry analyses on the resulting Lagrangian to assess, for instance, material resistance to crack propagation. Specifically, our results confirm that materials with higher rate sensitivity tend to offer higher resistance to fracture. Moreover, it is found that the kinetic energy of the inertial forces contributes to increased plastic flow thereby reducing the available free energy for crack propagation. This part of the work potentially opens a model-based route to the design of micro-defect structures for optimal fracture resistance.

Understanding and controlling stirring in micro-systems is necessary for the design of efficient passive micro-mixer. In this study, we focus on the dispersion of passive tracers injected in flows in between two rough surfaces under weak inertia influence (small but non-zero Reynolds number). The flow is induced by a constant applied pressure gradient between two cross-sections of the channel and the velocity field is calculated thanks to an extension of the lubrication approximation taking into account the first order inertial corrections. Tracers trajectories are obtained by integrating numerically the quasi-analytic velocity field. Our purpose is to examine the flow structure for various surface patterns and various Reynolds number. We focus on a simplified aperture field which is a smooth periodic function. This study puts forward interesting behavior of streamlines and show the dispersion of passive tracers in various geometries.

Abstract Design and analysis of a meso-scale rotary Wankel compressor is presented here. The compressor is primarily designed for a hand-held power generation system, based on a modified Brayton cycle and capable of producing 20 W with a specific energy of 2400 to 3800 W-hr/kg for usage duration of 72 to 240 hours. The small size of the overall system makes the conventional design rules and concepts inappropriate, thus requiring new design concepts for the compressor and other components. In the current design, the major axis of the epitrochoid is 14 mm. The three-lobed rotor is driven by a drive shaft through an internal gear system such that each revolution of the rotor corresponds to 3 revolutions of the drive shaft and 6 compression “strokes”. There are two intake ports and two discharge ports. The valves within these ports operate to limit the pressure ratio to 2.5, the target of the design. Rotor thickness is 9.1 mm and at a rotational speed of 5000 rpm, the compressor can provide a flow rate of 0.138 g/s air, as needed by the power generation system. The pressure ratio of the compressor is a function of geometry (not rotor speed), and hence this design is well-suited for load following in a variable load application. Its drive shaft can be de-coupled from other system components of the power generation system. This mechanical isolation can lead to thermal isolation, which is essential for miniature power generation devices. Micro-stereo lithography and micro-EDM appear to be the best methods to fabricate the necessary components of the compressor. Micro-stereo lithography, in particular, can provide a seamlessly integrated compressor, thus reducing the integration and assembly cost. Micro-EDM is more suited for production of large batch sizes because of the relatively high initial cost. More sophisticated micro-fabrication methods such as LIGA, UV-LIGA and lithography SU-8 can also be used. However, since the device thickness is rather large compared to what is typically done with these methods, multiple layers need to be bonded in both of these approaches because of the large thickness of the proposed design.

Abstract Design and analysis of a meso-scale rotary Wankel compressor is presented here. The compressor is primarily designed for a hand-held power generation system, based on a modified Brayton cycle and capable of producing 20 W with a specific energy of 2400 to 3800 W-hr/kg for usage duration of 72 to 240 hours. The small size of the overall system makes the conventional design rules and concepts inappropriate, thus requiring new design concepts for the compressor and other components. In the current design, the major axis of the epitrochoid is 14 mm. The three-lobed rotor is driven by a drive shaft through an internal gear system such that each revolution of the rotor corresponds to 3 revolutions of the drive shaft and 6 compression “strokes”. There are two intake ports and two discharge ports. The valves within these ports operate to limit the pressure ratio to 2.5, the target of the design. Rotor thickness is 9.1 mm and at a rotational speed of 5000 rpm, the compressor can provide a flow rate of 0.138 g/s air, as needed by the power generation system. The pressure ratio of the compressor is a function of geometry (not rotor speed), and hence this design is well-suited for load following in a variable load application. Its drive shaft can be de-coupled from other system components of the power generation system. This mechanical isolation can lead to thermal isolation, which is essential for miniature power generation devices. Micro-stereo lithography and micro-EDM appear to be the best methods to fabricate the necessary components of the compressor. Micro-stereo lithography, in particular, can provide a seamlessly integrated compressor, thus reducing the integration and assembly cost. Micro-EDM is more suited for production of large batch sizes because of the relatively high initial cost. More sophisticated micro-fabrication methods such as LIGA, UV-LIGA and lithography SU-8 can also be used. However, since the device thickness is rather large compared to what is typically done with these methods, multiple layers need to be bonded in both of these approaches because of the large thickness of the proposed design.

Microchannel networks can be efficiently used for several applications. For example, they can be the main elements of micro chemical reactors or micro heat exchangers for cooling electronic chips. In such networks, the flow of liquid can be generated either by a pressure difference, by electro-osmosis or by both of them. The design of the network can be optimized in order to deliver a maximum flowrate. In this paper, an analytical study of a pressure driven and electro-osmotic flow in tree-shaped microchannel network is developed. The network is built with a series of rectangular microchannels with high aspect ratio. Each bifurcation connects a parent microchannel to a couple of twin child microchannels. The objective of this work is to determine the geometrical configuration which offers the highest flowrate. The efficiency of the tree-shaped network is compared to the efficiency of a series of parallel microchannels, for the same inlet and outlet values of electric potential and pressure and for the same network volume. Focusing on one bifurcation, the influence of the thickness of the electrical double layer is discussed. The optimal geometric dimensions, such as the ratio of the child over parent microchannel widths and the ratio of the parent over total microchannel lengths, are calculated. The influence of the number of bifurcations is also analyzed and optimal design rules are proposed.

Achieving the fast mixing requirements posed by the chemical, biological, and life science community for confined microchannel flows remains an engineering challenge. The viscous and surface tension forces that dominate conventional micro-flows undermine fast, efficient mixing. By increasing the collisional velocity of reagent droplets, inertia can be exploited to increase mixing rates. This paper experimentally investigates inertial droplet mixing in micro flows. A high speed, gaseous flow is used to detach, transport, and collide droplets of nanoliter-size volumes in standard T and Y-junction microchannel geometries. Mixing rates are quantified using differential fluorescent optical diagnostics. Measured droplet mixing times are compared to the characteristic time scales for mass and viscous diffusion and bulk convection. Results show that mixing times are decreased as the droplet inertia is increased, indicating the potential benefit of inertia-driven mixing.

In this paper, a simply-designed reciprocating-type micropump is presented. We also report the coupling effects between the valve motion and the flow behaviors, which were studied using a micro-PIV technique. The fluids were easily driven by a PZT plate and net flow was directed toward the outlet after rectification by two planar passive valves. The results revealed that good pumping performance was obtained even at a low excitation voltage of 10V. The optimum flow rate was measured at a frequency of 0.8kHz and the maximum flow rate was 275μl/min at 30V. The micropump was uniquely characterized by the existence of a linear relationship between the flow rate and the driving frequency, which enabled this micropump to be easily operated and controlled. The experimental results showed that the micropump was reliable in terms of the high linearity and repeatability, which is very favorable for portable microfluidic systems. The micro-PIV measurements of the transient motions of the valve and the flow behaviors clearly revealed that the valve efficiency depended on the mass inertia of the moving part, excitation frequency, and voltage. The present results are useful for the optimum design of this planar passive valve to improve the pumping efficiency.

This paper develops criteria for the prediction of two distinct instabilities in microflows, one isothermal, the other with heat transfer. The engineering objective is to transport droplets that act as micro-reactors and are carried through various processes in a carrier fluid to prepare sample reactants or complete a chemical reaction. The requirement is that the carrier fluid flow be stable so that droplet trajectories can be accurately controlled. The popular two-dimensional microfluidic geometry of three streamlines merging at a junction is chosen for this analysis. A dimensional analysis of the governing flow-field and boundary conditions is undertaken to derive the non-dimensional groups upon which the flow characteristics of the junction are dependent. The emerging parameters are the Grasshof number (Gr) and Reynolds numbers (Re) of both inlet streams. Experimental flow visualisation images are used to determine the relationship between these scaling groups for both isothermal flow and buoyancy opposing mixed convection. The experimental range of inlet Re’s is from 1 to 100. It is found that the ratio of the inlet Re’s is sufficient to describe isothermal flows and that a parameter referred to as W* (the product of the Richardson number (Ri) and Re of the centreline stream) provides a good correlation for buoyancy opposing mixed convection. Inertia dominated flow regimes are seen to exist for W* values below approximately 2 and re-circulation zones are observed when W* is increased above this value. It was also observed that buckling flow was attainable at a critical Re of 65 for isothermal flow and that this critical Re is significantly reduced as W* is increased. An analogy is drawn from the results between the flow studied in this paper and that of cross flow over bluff objects such as a cylinder. Finally, based on the results of this work a design envelope is developed for predicting the stability of scaled models of the fluidic junction.

Capturing particles, mainly bio-particles, such as viruses and spores, from the air into a liquid is critical for air purification and analysis of the sampling systems. In the conventional impinger sampling systems, the air bubbles carrying the particles are injected into a liquid column. The particles are captured from the air into the liquid as the bubbles travel to the surface due to the buoyancy forces. This paper focuses on the numerical simulation of a newly developed microfluidic air sampling system. In this system, a microscale liquid column, equipped with an array of microchannels as pressure controlled gas injection points, is used for gas bubbling process for air sampling purpose. The air bubbles containing the particles are injected into the bottom of the microscale column filled with a liquid (such as water). As the microscale bubbles (of about 250∼500 microns) travel to the surface, a shear driven flow will develop within the bubbles and the airborne particles will follow the flow toward the boundary of the bubble. The inertia force of particles will result in the departure of particles from the flow into the liquid. The fraction of the particles departed from air bubble and trapped in the liquid represents the collection efficiency of the air sampler. For tracking the liquid/gas interface, the Volume-of-Fluid (VOF) method along with Youngs’ algorithm for geometric reconstruction of the free surface is used. The particle trajectories are predicted by integrating the force balance on each particle, which is based on a Lagrangian frame of reference. It is found that in addition to the particle departure during the bubble rising, a considerable amount of particles are trapped in the liquid during the air injection and bubble formation which may be due to the high velocity of the injected air and oscillation of the bubble interface. It is worth noting that this is the first time that the numerical simulation is performed to understand the whole air sampling process which was never addressed in the past. As a comparison, an experimental study was conducted to measure the collection efficiency. The fluorescent polystyrene latex particles with different diameters (diameters: 0.5, 1, 2 microns) were used in the experiment. The experimental results were compared with that of numerical simulation. Both the experiments and computations revealed that a collection efficiency of 90% can be achieved by the microfluidics based impinger, which is much higher than that of conventional, macro-scale, impinger systems. In addition to verifying the existing experimental work, this numerical simulation method provides a valuable tool to design and improve new generations of air sampling systems.