Hydrodynamic Slip Conditions Research Articles

Effect of the Surface Charge-Dependent Boundary Slip on the Electrophoresis of a Hydrophobic Polarizable Rigid Colloid.

The electrophoresis of a hydrophobic charged rigid colloid is studied by considering the lateral movement of the adsorbed surface charge. The slip velocity condition at the hydrophobic surface is modified to take into account the impact of the frictional and electric forces created by the adsorbed laterally mobile surface charge. Though the dependency of the surface charge on the slip velocity in the context of electrophoresis has been addressed before, the effect of the laterally mobile adsorbed surface charge on the electrophoresis of hydrophobic colloids has not been studied. The dielectric colloid is considered to polarize and create an induced immobile surface charge when subjected to an imposed electric field. The impact of the mobile surface charge along with the immobile induced surface charge on electrophoresis of a hydrophobic colloid is elucidated by numerically solving the governing electrokinetic equations in their full form. We have also developed a simplified model under a weak applied field consideration, which can be further reduced to a closed-form analytic expression for the mobility under the Debye-Hückel approximation. This analytic model for mobility is in excellent agreement with the exact numerical solution for an entire range of the Debye length when the ζ-potential is in the order of the thermal potential. One of the notable features of this closed-form mobility expression is that it accounts for the mobile adsorbed surface charge on the hydrodynamic slip condition and the dielectric polarization of the particle. We find that the mobility of the surface charge decreases the electrophoretic mobility of the hydrophobic dielectric colloid. However, the mobile surface charge enhances the mobility of a conducting hydrophobic colloid.

Power-law fluid annular flows between concentric rotating spheres subject to hydrodynamic slip

ABSTRACT We report analytical solutions to the problem of non-Newtonian power-law fluid flows in the annular space between a pair of concentric spherical surfaces rotating at distinct angular velocities with the inner and outer wall boundaries subject to general asymmetric hydrodynamic slip conditions. Analytical solutions are possible because of assuming constant valued apparent hydrodynamic slip lengths in the linearized kinematic slip conditions, and our solutions can be validated against the limiting results of Newtonian fluids, no-slip conditions or a single rotating sphere reported in previous literature. Comprehensive systematic parametric studies show that (additional to the power-law fluid flow behavior index) the degree of hydrodynamic slip at the inner surface is the dominant factor that determines the limiting values of the viscous torque exerted on the inner sphere as the outer-to-inner radius ratio assumes significantly large values. Nonetheless, the flow behavior index and outer slip length prove to be the crucial key parameters responsible for a variety of torque responses, which can be categorized by a compact analytical expression, as the outer-to-inner radius ratio is increased in the small to moderate regime. We propose a criteria which identifies the proper slip length and outer-to-inner radius ratio combinations for a given power-law flow behavior index such that the hydrodynamic slip wall effects of the outer surface can be minimized or eliminated. A simple method is also presented to characterize and quantify the apparent hydrodynamic slip effects by use of the concentric rotating spheres viscometer.

Start-Up Multilayer Electro-Osmotic Flow of Maxwell Fluids through an Annular Microchannel under Hydrodynamic Slip Conditions

The present investigation analyzes the transient multilayer electro-osmotic flow through an annular microchannel with hydrophobic walls. The fluids are considered immiscible and viscoelastic, following the Maxwell rheological model. In the problem examined, the linearized Poisson–Boltzmann and Cauchy momentum equations are used to determine the electric potential distribution and the flow field, respectively. Here, different interfacial phenomena are studied through the imposed boundary conditions, such as the hydrodynamic slip and specified zeta potentials at solid–liquid interfaces, the velocity continuity, the electroviscous stresses balance, the potential difference, and the continuity of electrical displacements at the interfaces between fluids. The semi-analytic solution uses the Laplace transform theory. In the results, the velocity profiles and velocity tracking show the oscillatory behavior of flow, which strongly depends on the dimensionless relaxation time. Furthermore, the hydrodynamic slip on the channel walls contributes to the release of energy stored in the fluids due to elastic effects at the start-up of the flow. Similarly, other dimensionless parameters are also investigated. This research aims to predict the parallel flow behavior in microfluidic devices under electro-osmotic effects.

Upscaling Reactive Transport Under Hydrodynamic Slip Conditions in Homogeneous Porous Media

AbstractReactive transport of a dilute species in a Newtonian fluid saturating a homogeneous porous medium for slip flow is analyzed in this work. Incompressible Newtonian flow with a first‐order (Navier) slip boundary condition is considered together with a first‐order heterogeneous reaction. Kinetic numbers range up to unity while Knudsen numbers, characteristic of slip‐flow, are smaller than approximately 0.1. The pore‐scale problem is upscaled, using the volume averaging method, to obtain a macroscopic transport equation (referred to as the complete upscaled model) operating at the Darcy scale. Using order of magnitude estimates and an expansion in terms of the Kinetic number, simplifications in the expressions of the effective coefficients are explored. The conditions under which the effective convective velocity and the total dispersion tensor are independent of reaction are derived. Under such conditions, a simplified version of the macroscopic transport equation is obtained. This is referred to as the simplified model. Numerical results for a simple structure indicate that the longitudinal dispersion coefficient decreases with decreasing Knudsen number, while the opposite holds for the transverse component of the total dispersion tensor, the effective convective velocity, and the effective reaction rate coefficient. These effects are more evident when the Péclet number increases (i.e., in the convective‐favored regime) and when slip effects are more pronounced. Results predicted by the simplified and the complete versions of the upscaled model are validated with direct numerical simulations of the pore‐scale problem on a two‐dimensional model structure.

Analysis of the Effects of Joule Heating and Viscous Dissipation on Combined Pressure-Driven and Electrokinetic Flows in a Two-Parallel Plate Channel with Unequal Constant Temperatures

In this article, we perform an entropy generation analysis for the micro channel heat sink applications where the flow of fluid is actuated by combined influences of applied pressure gradient and electric field under electrical double layer phenomenon. The upper and lower walls of the channels are kept at different constant temperatures. The temperature-dependent viscosity of the fluid is considered and hence the momentum equation and energy equations are coupled in this study. Also, a hydrodynamic slip condition is employed on the viscous dissipation. For complete analysis of the entropy generation, we use a perturbation approach with lubrication approximation. In this study, we discuss the results depicting variations in the velocity and temperature distributions and their effect on local entropy generation rate and Bejan number in the system. It can be summarized from this analysis that the enhanced velocity gradients in the flow field due to combined effect of temperature-dependent viscosity and Joule heating and viscous dissipative effects, leads to an enhancement in the local entropy generation rate in the system.

HEAT TRANSFER IN VISCOPLASTIC BOUNDARY-LAYER FLOW FROM A VERTICAL PERMEABLE CONE WITH MOMENTUM AND THERMAL WALL SLIP: NUMERICAL STUDY

A mathematical model is presented for the laminar free convection boundary layer flow of Casson viscoplastic non-Newtonian fluid external to a vertical penetrable circular cone in the presence of thermal and hydrodynamic slip conditions. The cone surface is maintained at non-uniform surface temperature. The boundary layer conservation equations, which are parabolic in nature, are transformed into non-dimensional form via appropriate similarity variables, and the emerging boundary value problem is solved computationally with the second order accurate implicit Keller-box finite-difference scheme. The influence of velocity (momentum) slip, thermal slip and Casson non-Newtonian parameter on velocity, temperature, skin friction and Nusselt number are illustrated graphically. Validation of solutions with earlier published work is included. The computations show that the flow near the cone surface is strongly decelerated with increasing momentum slip whereas the temperature and thermal boundary layer thickness are increased. Increasing Casson parameter generally decelerates the flow and also decreases temperatures. Both velocity and thermal boundary layer thickness are reduced with greater Prandtl number. The study is relevant to petro-chemical engineering (polymer) processing systems.

Computational Analysis of Magnetohydrodynamic Free Convection Flow and Heat Transfer of Non-Newtonian Tangent Hyperbolic Fluid from a Horizontal Circular Cylinder with Partial Slip

An analysis is presented for the nonlinear steady boundary layer flow and heat transfer of an incompressible tangent hyperbolic non-Newtonian fluid from horizontal circular cylinder in the presence of thermal and hydrodynamic slip condition. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely Weissenberg number $$(W_{e})$$ , power law index $$(n)$$ , velocity slip parameter $$(\hbox {S}_\mathrm{f})$$ , thermal jump parameter $$(\hbox {S}_\mathrm{T})$$ , Prandtl number (Pr), magnetic parameter $$(M)$$ and dimensionless tangential coordinate $$(\xi )$$ on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is observed that velocity, skin friction and heat transfer rate are reduced with increasing Weissenberg number ( $$W_{e}$$ ), whereas, temperature increases slightly. Increasing power law index ( $$n$$ ) increases velocity and heat transfer rate but decreases temperature and skin friction. An increase in $$S_{f}$$ , is observed to enhance velocity and heat transfer rate but decreases temperature and local skin friction. Whereas, increasing $$S_{T}$$ , is found to decrease velocity, temperature, skin friction and Nusselt number. The study is relevant to chemical materials processing applications.

Free Convection Flow and Heat Transfer of Non-Newtonian Tangent Hyperbolic Fluid from an Isothermal Sphere with Partial Slip

An analysis is presented for the nonlinear steady boundary layer flow and heat transfer of an incompressible Tangent Hyperbolic non-Newtonian fluid from an isothermal sphere in the presence of thermal and hydrodynamic slip condition. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite difference Keller-box technique. The numerical code is validated with previous studies. The influence of a number of emerging non-dimensional parameters, namely the Weissenberg number (We), the power law index (n), Velocity slip (Sf), thermal jump (ST), Prandtl number (Pr) and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented and excellent correlation achieved. It is observed that velocity, skin friction and the Nusselt number (heat transfer rate) are reduced with increasing (We), whereas the temperature is enhanced. Increasing power (n) enhances velocity and Nusselt number (heat transfer rate) but reduces temperature and skin friction. An increase in Sf, is observed to enhance velocity and Nusselt number but reduces temperature and local skin friction. Whereas increasing ST is found to decrease velocity, temperature, skin friction and Nusselt number. The study is relevant to chemical materials processing applications.

Slip Flow of Casson Rheological Fluid Under Variable Thermal Conductivity with Radiation Effects

This paper investigates the radiation and chemical reaction effects on Casson non-Newtonian fluid towards a porous stretching surface in the presence of thermal and hydrodynamic slip conditions. The governing boundary layer conservation equations are normalized into nonsimilar form using similarity transformations. A numerical approach is applied to the resultant equations. The behavior of the velocity, temperature, concentration, as well as the skin friction coefficient, Nusselt number, and Sherwood number for various governing physical are discussed. Increasing the radiation parameter decreases the temperature. An increase in the rheological parameter (Casson parameter) induces an elevation in the skin friction coefficient, the heat and mass transfer rates. The larger the β values the closer the fluid is in behavior to a Newtonian fluid and further departs from plastic flow. Temperature of the fluid was found to decrease with increasing values of the Casson rheological parameter. The most important non-Newtonian fluid possessing a yield value is the rheological Casson fluid, which finds significant applications in polymer processing industries, biomechanics, and chocolate food processing.

Heat Transfer in a Casson Rheological Fluid from a Semi-infinite Vertical Plate with Partial Slip

The laminar boundary layer flow and heat transfer of Casson non-Newtonian fluid from a semi-infinite vertical plate in the presence of thermal and hydrodynamic slip conditions is analyzed. The plate surface is maintained at a constant temperature. Increasing velocity slip induces acceleration in the flow near the plate surface and the reverse effect further from the surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in the Casson rheological parameter acts to elevate considerably the skin friction (non-dimensional wall shear stress) and this effect is pronounced at higher values of tangential coordinate. Temperatures, however, are very slightly decreased with increasing values of Casson rheological parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21115

Modelling laminar transport phenomena in a Casson rheological fluid from a horizontal circular cylinder with partial slip

The laminar boundary layer flow and heat transfer of Casson non-Newtonian fluid from a permeable horizontal cylinder in the presence of thermal and hydrodynamic slip conditions is analysed. The cylinder surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalised into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. Increasing velocity slip induces acceleration in the flow near the cylinder surface and the reverse effect further from the surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in Casson rheological parameter acts to elevate considerably the skin friction (non-dimensional wall shear stress) and this effect is pronounced at higher values of tangential coordinate. Temperatures are however very slightly decreased with increasing values of Casson rheological parameter. Increasing mass flow injection (blowing) at the cylinder surface causes a strong acceleration, whereas increasing suction is found to induce the opposite effect. The study finds applications in rheological chocolate food processing.

MHD duct flows under hydrodynamic “slip” condition

Three classic MHD problems are revisited assuming hydrodynamic slip condition at the interface between the electrically conducting fluid and the insulating wall: (1) Hartmann flow; (2) fully developed flow in a rectangular duct; and (3) quasi-two-dimensional (Q2D) turbulent flow. The first two problems have been solved analytically. Additionally to the Hartmann number (Ha), a new dimensionless parameter S, the ratio of the slip length to the thickness of the Hartmann layer, has been identified. One of the most important conclusions of the paper is that the duct flows with the slip still exhibit Hartmann layers, whose thickness scales as 1/Ha, while the thickness of the side layers is a function of both Ha and S. In the case of Q2D flows, a new expression for the Hartmann braking time has been derived showing its increase at Ha >> 1 by factor (1+ S). Numerical simulations performed for a flow with the “M-shaped” velocity profile show that in the presence of the slip, a Q2D flow becomes more irregular as vortical structures experience less Joule and viscous dissipation in the Hartmann layers.