Pressure-driven Microchannel Flow Research Articles

Inertial migration of rigid particles in shear-thinning fluids under asymmetric wall slip conditions

The determination of flow-induced equilibrium positions in pressure-driven flows in microchannels is of great practical importance in particle manipulation. In the computational analysis presented in this paper, the inertial ordering of neutrally buoyant rigid spheres in shear-thinning fluid flow through a hydrophobic microchannel is investigated. The combined effect of the viscosity index n of a power-law fluid and fluid slippage at the wall on the lateral focusing of microspheres is examined in detail. Using the finite element method, the Eulerian flow field between partially slipping parallel walls is simulated, and the Lagrangian movement of particles is continuously tracked. The Navier slip model is used to ensure a finite fluid velocity at the wall, and it is tuned by modifying the slip-length. It is observed that inertial particles concentrate at a standard equilibrium position of 0.6 times the channel half-width H, irrespective of fluid slip due to the symmetry of the flow field. However, this equilibrium position shifts closer to the walls as the viscosity index increases; for instance, when n = 0.5, particles stabilize at 0.75H. As a consequence of asymmetry in hydrodynamic behavior due to different fluid slippages at the upper and lower walls, the particle migration path is altered. In a channel with a no-slip upper wall and a partially slipping lower wall (β/H = 0.4), particles settle closer to the lower wall at 0.8H. Most importantly, the lateral movement of a particle released at a given vertical position can be altered by tailoring the wall hydrophobicity and viscosity index, thus enabling multiple equilibrium locations to be achieved.

Combined electromagnetohydrodynamic flow in microchannels with consideration of the surface charge-dependent slip

In microscale systems, hydrodynamic slip is considered to significantly influence the fluid flow field. Existing theories of electromagnetohydrodynamic flow in hydrophobic microchannels have postulated a constant slip length and ignored the effect of the surface charge on slip. In this study, we extended prior models by considering a combined pressure-driven and electromagnetohydrodynamic flow in microchannels with consideration of surface charge-dependent slip. An analytical solution for this simple model was derived. After a detailed discussion of the obtained results, we demonstrate that the more realistic surface-charge-dependent case has smaller velocities and flow rates than the surface-charge-independent slip case. Considering the effect of the surface charge on slip, the flow rate can be reduced by up to 7% in the currently selected parameter range. Our results are useful for optimizing electromagnetohydrodynamic flow models in microchannels.

Hydrodynamic drag reduction of shear-thinning liquids in superhydrophobic textured microchannels

Super-hydrophobic textured surfaces reduce hydrodynamic drag in pressure-driven laminar flows in micro-channels. However, despite the wide usage of non-Newtonian liquids in microfluidic devices, the flow behaviour of such liquids was rarely examined so far in the context of friction reduction in textured super-hydrophobic micro-channels. Thus, we have investigated the influence of topologically different rough surfaces on friction reduction of shear-thinning liquids in micro-channels. First, the friction factor ratio (a ratio of friction factor on a textured surface to a plain surface) on generic surface textures, such as posts, holes, longitudinal and transverse ribs, was estimated numerically over a range of Carreau number as a function of microchannel constriction ratio, gas fraction and power-law exponent. Resembling the flow behaviour of Newtonian liquids, the longitudinal ribs and posts have exhibited significantly less flow friction than the transverse ribs and holes while the friction factor ratios of all textures has exhibited non-monotonic variation with the Carreau number. While the minima of the friction factor ratio were noticed at a constant Carreau number irrespective of the microchannel constriction ratio, the minima have shifted to a higher Carreau number with an increase in the power-law index and gas fraction. Experiments were also conducted with aqueous Xanthan Gum liquids in micro-channels. The flow enhancement (the flow rate with super-hydrophobic textures with respect to a smooth surface) exhibited a non-monotonic behaviour and attenuated with an increase in power-law index tantamount to simulations. The results will serve as a guide to design frictionless micro-channels when employing non-Newtonian liquids.

An Analytical Modeling on Flow and Heat Transfer for a Pressure-Driven Electroosmotic Flow in Microchannel Considering First Order Slip Model

An analytical solution to study fundamental behaviors of a pressure-driven electroosmotic flow in a parallel plate microchannel is presented in the present work. A thermally fully developed flow of a Newtonian liquid is considered. The fluid motion is assumed to be caused with a pressure gradient applied externally and an electrostatic potential field. The electrical potential field is determined by solving the Poisson–Boltzmann equation. The Debye–Huckel approximation is not considered for higher accuracy of results. A modified form of the Navier–Stokes equation with slip boundary conditions is considered to evaluate velocity field and skin friction coefficient, whereas the energy equation is simplified to obtain temperature profile as well as Nusselt number. Homotopy perturbation method (HPM) is applied to solve the Poisson–Boltzmann equation, whereas the momentum and the energy equations has been solved analytically to achieve the velocity and temperature profiles, respectively. The predicted results are compared with existing work and show a good harmony. Results obtained for electric potential, velocity and temperature fields have been shown graphically varying wall zeta potential, slip coefficient and pressure gradient. Subsequently, a parametric study is presented for skin friction coefficient and the Nusselt number. Finally, an effort is made to determine local volumetric entropy generation and global entropy generation. The proposed results exhibit both the influence of the Brinkman number and pressure gradient on the entropy generation.

Pressure-Driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls

Gas flow and heat transfer in confined geometries at micro-and nanoscales differ considerably from those at macro-scales, mainly due to nonequilibrium effects such as velocity slip and temperature jump. Nonequilibrium effects increase with a decrease in the characteristic length-scale of the fluid flow or the gas density, leading to the failure of the standard Navier–Stokes–Fourier (NSF) equations in predicting thermal and fluid flow fields. The direct simulation Monte Carlo (DSMC) method is employed in the present work to investigate pressure-driven nitrogen flow in divergent microchannels with various divergence angles and isothermal walls. The thermal fields obtained from numerical simulations are analysed for different inlet-to-outlet pressure ratios (1.5≤Π≤2.5), tangential momentum accommodation coefficients, and Knudsen numbers (0.05≤Kn≤12.5), covering slip to free-molecular rarefaction regimes. The thermal field in the microchannel is predicted, heat-lines are visualised, and the physics of heat transfer in the microchannel is discussed. Due to the rarefaction effects, the direction of heat flow is largely opposite to that of the mass flow. However, the interplay between thermal and pressure gradients, which are affected by geometrical configurations of the microchannel and the applied boundary conditions, determines the net heat flow direction. Additionally, the occurrence of thermal separation and cold-to-hot heat transfer (also known as anti-Fourier heat transfer) in divergent microchannels is explained.

A study on mixed electro-osmotic/pressure-driven microchannel flows of a generalised Phan-Thien–Tanner fluid

This work presents new semi-analytical solutions for the combined fully developed electro-osmotic pressure-driven flow in microchannels of viscoelastic fluids, described by the generalised Phan-Thien–Tanner model (gPTT) recently proposed by Ferras et al. (Journal of Non-Newtonian Fluid Mechanics, 269:88–99, 2019). This generalised version of the PTT model presents a new function for the trace of the stress tensor—the Mittag–Leffler function—where one or two new fitting constants are considered in order to obtain additional fitting flexibility. The semi-analytical solution is obtained under sufficiently weak electric potential that allows the Debye–Huckel approximation for the electrokinetic fields and for thin electric double layers. Based on the solution, the effects of the various relevant dimensionless numbers are assessed and discussed, such as the influence of $$\varepsilon Wi^2$$ , of the parameters $$\alpha $$ and $$\beta $$ of the gPTT model, and also of $${\bar{\kappa }}$$ , the dimensionless Debye–Huckel parameter. We conclude that the new model characteristics enhance the effects of both $$\varepsilon Wi^2$$ and $${\bar{\kappa }}$$ on the velocity distribution across the microchannels. The effects of a high zeta potential and of the finite size of ions are also studied numerically.

Numerical investigation on pressure-driven electro osmatic flow and mixing in a constricted micro channel by triangular obstacle

Purpose The characteristics of fluid motions in micro-channel are strong fluid-wall surface interactions, high surface to volume ratio, extremely low Reynolds number laminar flow, surface roughness and wall surface or zeta potential. Due to zeta potential, an electrical double layer (EDL) is formed in the vicinity of the wall surface, namely, the stern layer (layer of immobile ions) and diffuse layer (layer of mobile ions). Hence, its competent designs demand more efficient micro-scale mixing mechanisms. This paper aims to therefore carry out numerical investigations of electro osmotic flow and mixing in a constricted microchannel by modifying the existing immersed boundary method. Design/methodology/approach The numerical solution of electro-osmotic flow is obtained by linking Navier–Stokes equation with Poisson and Nernst–Planck equation for electric field and transportation of ion, respectively. Fluids with different concentrations enter the microchannel and its mixing along its way is simulated by solving the governing equation specified for the concentration field. Both the electro-osmotic effects and channel constriction constitute a hybrid mixing technique, a combination of passive and active methods. In microchannels, the chief factors affecting the mixing efficiency were studied efficiently from results obtained numerically. Findings The results indicate that the mixing efficiency is influenced with a change in zeta potential (ζ), number of triangular obstacles, EDL thickness (λ). Mixing efficiency decreases with an increment in external electric field strength (Ex), Peclet number (Pe) and Reynolds number (Re). Mixing efficiency is increased from 28.2 to 50.2% with an increase in the number of triangular obstacles from 1 to 5. As the value of Re and Pe is decreased, the overall percentage increase in the mixing efficiency is 56.4% for the case of a mixing micro-channel constricted with five triangular obstacles. It is also vivid that as the EDL overlaps in the micro-channel, the mixing efficiency is 52.7% for the given zeta potential, Re and Pe values. The findings of this study may be useful in biomedical, biotechnological, drug delivery applications, cooling of microchips and deoxyribonucleic acid hybridization. Originality/value The process of mixing in microchannels is widely studied due to its application in various microfluidic devices like micro electromechanical systems and lab-on-a-chip devices. Hence, its competent designs demand more efficient micro-scale mixing mechanisms. The present study carries out numerical investigations by modifying the existing immersed boundary method, on pressure-driven electro osmotic flow and mixing in a constricted microchannel using the varied number of triangular obstacles by using a modified immersed boundary method. In microchannels, the theory of EDL combined with pressure-driven flow elucidates the electro-osmotic flow.

On the Enhancement of Heat Transfer and Reduction of Entropy Generation by Asymmetric Slip in Pressure-Driven Non-Newtonian Microflows

We study hydrodynamics, heat transfer, and entropy generation in pressure-driven microchannel flow of a power-law fluid. Specifically, we address the effect of asymmetry in the slip boundary condition at the channel walls. Constant, uniform but unequal heat fluxes are imposed at the walls in this thermally developed flow. The effect of asymmetric slip on the velocity profile, on the wall shear stress, on the temperature distribution, on the Bejan number profiles, and on the average entropy generation and the Nusselt number are established through the numerical evaluation of exact analytical expressions derived. Specifically, due to asymmetric slip, the fluid momentum flux and thermal energy flux are enhanced along the wall with larger slip, which, in turn, shifts the location of the velocity's maximum to an off-center location closer to the said wall. Asymmetric slip is also shown to redistribute the peaks and plateaus of the Bejan number profile across the microchannel, showing a sharp transition between entropy generation due to heat transfer and due to fluid flow at an off-center-line location. In the presence of asymmetric slip, the difference in the imposed heat fluxes leads to starkly different Bejan number profiles depending on which wall is hotter, and whether the fluid is shear-thinning or shear-thickening. Overall, slip is shown to promote uniformity in both the velocity field and the temperature field, thereby reducing irreversibility in this flow.

Graetz problem for combined pressure-driven and electroosmotic flow in microchannels with distributed wall heat flux

There has been a growing interest in the development of microchannel heat sinks deploying electrically modulated fluid flow in recent years. The efficient design of such devices requires heat transfer models that can account for complex distributions of heat generation in microelectronics. In this paper, expressions are obtained for temperature distribution and Nusselt number of thermally developing mixed electroosmotic and pressure-driven flow through circular/slit microchannels of axially non-uniform wall heat flux. The heating section is considered to be of a finite length in order to simulate a physically more realistic situation. Both the Joule heating and axial conduction effects are considered in the model. By comparing the results for linear, sinusoidal, and exponential distributions of the wall heat flux with the predictions of full numerical simulations, it is shown that the analytical solutions presented are accurate up to a Péclet number of 10. This threshold is demonstrated to be larger than the maximum Péclet number encountered in practical applications involving electroosmotic pumping mechanisms. After justification of the model, a parametric analysis is executed, revealing that the average Nusselt number is a decreasing function of the EDL thickness and pressure-driven velocity, irrespective of the wall heat flux distribution. Moreover, whereas a higher Joule heating rate is accompanied by a smaller value of the average Nusselt number for pure electroosmotic and pressure-assisted flows, the opposite is true in the presence of a significant back pressure.

A simplified model for unsteady pressure driven flows in circular microchannels of variable cross-section

• A fast model for unsteady flows in circular channels is presented. • Channels have a small aspect ratio but can have large diameter variations. • The simplified model is up to 2 orders of magnitude faster than CFD. • It accounts for some inertia with no restrictions on forcing frequency or shape. • The model can be applied to a wide spectrum of problems in MEMS and bio-mechanics. In this paper, we present a fast and accurate model for unsteady pressure-driven flows in circular microchannels of variable cross-section. The model is developed for channels of small diameter to length ratio, but allows for large variations in the channel’s diameter along the axis. A key feature of the model is that it puts no restriction on the time dependence of the forcing, in terms of shape and frequency. The only condition on the forcing is such that the advective component of the inertia term is small. This is a major departure from many previous expositions which assume harmonic forcing. The model is based on an extended and unsteady lubrication approximation in the aspect ratio of the channel. The resulting equations for each order are solved analytically using a finite Hankel transform, except for the implicit pressure profile, which is solved numerically with a recursive time scheme. Compared to classical CFD simulations, the reduced order semi-analytic method is two orders of magnitude faster, owing in part to the fact that the number of modes required for the convergence of these expressions is not too large. The numerical simulations reveal that the model is accurate for a large class of channels and a fairly wide range of Reynolds numbers. This, combined with the fact that it imposes no conditions on the shape and frequency of the unsteady forcing, renders the model a valuable tool for rapidly simulating large fluidic circuits (as in lab-on-a-chip, μ TAS and the human body), thereby allowing significant reduction in the design parameters space.

Numerical study of enhanced mixing in pressure-driven flows in microchannels using a spatially periodic electric field.

We propose an innovative mechanism for enhancing mixing in steady pressure driven flow of an electrolytic solution in a straight rectangular microchannel. A transverse electric field is used to generate an electroosmotic flow across the cross-section. The resulting flow field consists of a pair of helical vortices that transport fluid elements along the channel. We show, through numerical simulations, that chaotic advection may be induced by periodically varying the direction of the applied electric field along the channel length. This periodic electric field generates a longitudinally varying, three-dimensional steady flow, such that the streamlines in the first half of the repeating unit cell intersect those in the second half, when projected onto the cross-section. Mixing is qualitatively characterized by tracking passive particles and obtaining Poincaré maps. For quantification of the extent of mixing, Shannon entropy is calculated using particle advection of a binary mixture. The convection diffusion equation is also used to track the evolution of a scalar species and quantify the mixing efficiency as a function of the Péclet number.

Advective superdiffusion in superhydrophobic microchannels.

We consider pressure-driven flows in wide microchannels, and discuss how a transverse shear, generated by misaligned superhydrophobic walls, impacts cross-sectional spreading of Brownian particles. We show that such a transverse shear can induce an advective superdiffusion, which strongly enhances dispersion of particles compared to a normal diffusion, and that maximal cross-sectional spreading corresponds to a crossover between its subballistic and superballistic regimes. This allows us to argue that an advective superdiffusion can be used for boosting dispersion of particles at smaller Péclet numbers compared to known concepts of passive microfluidic mixing. This implies that our superdiffusion scenario allows one efficient mixing of much smaller particles or using much thinner microchannels than methods, which are currently being exploited.

Self-Organized Velocity Pulses of Dense Colloidal Suspensions in Microchannel Flow.

We present a numerical study of dense colloidal suspensions in a pressure-driven microchannel flow in two dimensions. The colloids are modeled as elastic and frictional spheres suspended in a Newtonian fluid, which we simulate using the method of multiparticle collision dynamics. The model reproduces periodic velocity and density pulse trains, traveling upstream in the microchannel, which are found in experiments conducted by Isa etal. [Phys. Rev. Lett. 102, 058302 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.058302]. We show that colloid-wall friction and the resultant force chains are crucial for the formation of these pulses. With an increasing colloid density, first solitary jams occur, which become periodic pulse trains at intermediate densities and unstable solitary pulses at high densities. We formulate a phenomenological continuum model and show how these spatiotemporal flow and density profiles can be understood as homoclinic and periodic orbits in traveling-wave equations.

Velocity amplification in pressure-driven flows between superhydrophobic gratings of small solid fraction.

With diminishing fraction of their solid portion, compound gas-solid superhydrophobic surfaces exhibit a large amount of slip which allows for appreciable velocity amplification in pressure-driven microchannel flows. We address this small solid-fraction limit in the context of a grating-like configuration, where superhydrophobicity is provided by a periodic array of flat-meniscus bubbles which are trapped in a Cassie state within the grooved channel walls. Asymptotic analysis for both longitudinal and transverse flows reveals a logarithmic scaling of the effective slip length in the solid fraction of the compound boundaries, thus refuting earlier claims of an algebraic singularity. The logarithmic scaling in the longitudinal problem is explained using an analogy between the unidirectional velocity and the velocity potential in two-dimensional irrotational flows. In the transverse problem it has to do with the Stokes paradox. The mechanisms identified herein explain the absence of slip-length singularity in the comparable asymmetric configuration, where only one of the channel walls is superhydrophobic.

KNUDSEN'S PERMEABILITY CORRECTION FOR GAS FLOW IN TIGHT POROUS MEDIA USING THE R26 MOMENT METHOD

Gas in microchannels and tight porous media is often in a nonequilibrium state. The conventional thermodynamic models for fluid flow and heat transfer fail, i.e., the classical Navier-Stokes-Fourier equations, are no longer accurate or valid. In this situation, the pressure-driven gas flows in parallel microchannels, circular micropipes, and tight porous media are solved based on the regularized 26 moment equations in this paper. A higher-order approximation of more general correlation for rarefied gas flow called higher-order Knudsen's permeability is presented in both microchannels and tight porous media. In addition, the Klinkenberg's first- and second-order equations are proposed according to Taylor series' expansion of higher-order Knudsen's permeability. The comparisons are implemented between the present model and available experimental data.

The coupling of surface charge and boundary slip at the solid–liquid interface and their combined effect on fluid drag: A review

Fluid drag of micro/nano fluidic systems has inspired wide scientific interest. Surface charge and boundary slip at the solid–liquid interface are believed to affect fluid drag. This review summarizes the recent studies on the coupling of surface charge and slip, and their combined effect on fluid drag at micro/nano scale. The effect of pH on surface charge of borosilicate glass and silica surfaces in deionized (DI) water and saline solution is discussed using a method based on colloidal probe atomic force microscopy (AFM). The boundary slip of various oil–solid interfaces are discussed for samples with different degrees of oleophobicity prepared by nanoparticle-binder system. By changing the pH of solution or applying an electric field, effect of surface charge on slip of a smooth hydrophobic octadecyltrichlorosilane (OTS) in DI water and saline solution is studied. A theoretical model incorporating the coupling relationship between surface charge and slip is used to discuss the combined effect of surface charge-induced electric double layer (EDL) and slip on fluid drag of pressure-driven flow in a one-dimensional parallel-plates microchannel. A theoretical method is used to reduce the fluid drag. The studies show that the increasing magnitude of surface charge density leads to a decrease in slip length. The surface charge results in a larger fluid drag, and the coupling of surface charge and slip can further increase the fluid drag. Surface charge-induced EDLs with asymmetric zeta potentials can effectively reduce the fluid drag.

DSMC Study of Pressure-Driven Slip Flow through Microchannel at Non-Uniform Wall Temperature

ABSTRACTThe present study is to investigate the pressure-driven gas flow in microchannel at no-uniform wall temperature. DSMC is employed to generate the flow field details which are then used in analysis of the slip flow characteristics. The major concern is the influences of thermal creep effect on the pressure-driven slip flow. Thermal creep is resulted from tangential wall temperature gradient. In this work, two kinds of thermal boundary condition are considered. One is the linearly varied temperature (LVT) applied to both walls, the other is that has the bottom wall at a thermal condition combined LVT and adiabatic (AD) wall, i.e. LVT-AD-LVT condition. The present DSMC results reveal that the fluid slip is weakened (enhanced) in the case with a negative (positive) wall temperature gradient. Relatively, thermal creep effect on fluid slip over the adiabatic wall is more pronounced in the presence of negative wall temperature gradient. The mass flowrate is a strong function of the wall temperature gradient. However, there is only little difference between the mass flowrates predicted under the two kinds of thermal conditions studied in the present work.

Combined effects of streaming potential and wall slip on flow and heat transfer in microchannels

In this study, the effects of wall slip and streaming potential on liquid flow and heat transfer in planar microchannels with imposed heat flux are numerically investigated. Electrical potential of the electrical double layer, liquid flow and thermal characteristics is determined using the Poisson-Boltzmann, the modified Navier–Stokes and the energy equations, respectively. The analytical solution for pressure-driven electrokinetic flows in microchannels is obtained without introducing the Debye–Huckel approximation. The results reveal that the streaming potential effect retards the liquid flow and leads to an increase in the temperature of electrolyte solution, thereby decreasing the heat transfer rate. On the contrary, the wall slip effect tends to increase the flow velocity and hence enhances the heat transfer. When the above two effects appear in microchannels simultaneously, the wall slip assists the streaming potential to retard the flow. Furthermore, they counteract each other when the zeta potential is large enough.

Solitary and transitional waves in pressure-driven two-layer microchannel flow

Similar to the case of the gravity-driven flow (Sisoev and Bennett 2013 Fluid Dyn. Res. 45 015503) we use the integral method to derive evolution equations modeling a pressure-driven two-layer flow of immiscible viscous fluids in a plane microchannel. It is shown that the system possesses a vast set of steady-traveling solitary and transitional waves. Analysis of the phase trajectories of the relevant dynamical system indicates the existence of families of steady-traveling periodic waves.

Filter-matrix lattice Boltzmann model for microchannel gas flows

The lattice Boltzmann method has been shown to be successful for microscale gas flows, and it has attracted significant research interest. In this paper, the recently proposed filter-matrix lattice Boltzmann (FMLB) model is first applied to study the microchannel gas flows, in which a Bosanquet-type effective viscosity is used to capture the flow behaviors in the transition regime. A kinetic boundary condition, the combined bounce-back and specular-reflection scheme with the second-order slip scheme, is also designed for the FMLB model. By analyzing a unidirectional flow, the slip velocity and the discrete effects related to the boundary condition are derived within the FMLB model, and a revised scheme is presented to overcome such effects, which have also been validated through numerical simulations. To gain an accurate simulation in a wide range of Knudsen numbers, covering the slip and the entire transition flow regimes, a set of slip coefficients with an introduced fitting function is adopted in the revised second-order slip boundary condition. The periodic and pressure-driven microchannel flows have been investigated by the present model in this study. The numerical results, including the velocity profile and the mass flow rate, as well as the nonlinear pressure distribution along the channel, agree fairly well with the solutions of the linearized Boltzmann equation, the direct simulation Monte Carlo results, the experimental data, and the previous results of the multiple effective relaxation lattice Boltzmann model. Also, the present results of the velocity profile and the mass flow rate show that the present model with the fitting function can yield improved predictions for the microchannel gas flow with higher Knudsen numbers in the transition flow regime.