Diffusioosmosis of electrolyte solutions along a charged plane wall

The steady diffusioosmotic flow of an electrolyte solution along a dielectric plane wall caused by an imposed tangential concentration gradient is analytically examined. The plane wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by the Poisson-Boltzmann equation. The macroscopic electric field along the tangential direction induced by the imposed electrolyte concentration gradient is obtained as a function of the lateral position. A closed-form formula for the fluid velocity profile is derived as the solution of a modified Navier-Stokes equation. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential of the wall and the properties of the electrolyte solution. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field in the double layer on the diffusioosmotic flow is found to be very significant and cannot be ignored.     

Diffusioosmosis of electrolyte solutions in a fine capillary slit

The steady diffusioosmotic flows of an electrolyte solution along a charged plane wall and in a capillary channel between two identical parallel charged plates generated by an imposed tangential concentration gradient are theoretically investigated. The plane walls may have either a constant surface potential or a constant surface charge density. The electrical double layers adjacent to the charged walls may have an arbitrary thickness and their electrostatic potential distributions are determined by the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the tangential direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the lateral position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field and the relaxation effect in the double layer on the diffusioosmotic flow are found to be very significant.     

Diffusioosmosis of electrolyte solutions in a fine capillary tube

A theoretical study is presented for the steady diffusioosmotic flow of an electrolyte solution in a fine capillary tube generated by a constant concentration gradient imposed in the axial direction. The capillary wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by an analytical approximation to the solution of the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the axial direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the radial position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a prescribed concentration gradient of an electrolyte, the magnitude of fluid velocity at a position in general increases with an increase in its distance from the capillary wall, but there are exceptions. The effect of the radial distribution of the induced tangential electric field and the relaxation effect due to ionic convection in the double layer on the diffusioosmotic flow are found to be very significant.     

Numerical analysis of thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions

Thermophoresis of colloidal particles in aqueous media is more frequently applied in biomedical analysis with processed fluids as biofluids. In this work, a numerical analysis of the thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions is presented. In a particle-fixed reference frame, the flow field of non-Newtonian fluids has been governed by the Cauchy momentum equation and the continuity equation, with the dynamic viscosity following the power-law fluid model. The numerical simulations reveal that the shear-thinning effect of pseudoplastic fluids is advantageous to the thermophoresis, and the shear-thickening effect of dilatant fluids slows down the thermophoresis. Both the shear-thinning and shear-thickening effects of non-Newtonian fluids on a thermodiffusion coefficient are pronounced for the case when the thickness of electric double layer (EDL) surrounding a particle is moderate or thin. Finally, the reciprocal of the dynamic velocity at the particle surface is calculated to approximately estimate the thermophoretic behavior of a charged particle with moderate or thin EDL thickness.     

Diffusioosmosis of electrolyte solutions in a capillary slit with adsorbed polyelectrolyte layers

A theoretical study is presented for the steady diffusioosmotic flow of an electrolyte solution in a fine capillary slit with each of its inside walls coated with a layer of polyelectrolytes generated by an imposed tangential concentration gradient. In this solvent-permeable and ion-penetrable surface charge layer, idealized polyelectrolyte segments are assumed to be distributed at a uniform density. The electric double layer and the surface charge layer may have arbitrary thicknesses relative to the gap width between the slit walls. The Poisson-Boltzmann equation and a modified Navier-Stokes/Brinkman equation are solved numerically to obtain the electrostatic potential, dynamic pressure, tangentially induced electric field, and fluid velocity as functions of the lateral position in the slit in a self-consistent way, with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions. The existence of the surface charge layers can lead to a diffusioosmotic flow quite different from that in a capillary with bare walls. The effect of the lateral distribution of the induced tangential electric field and the relaxation effect due to ionic convection in the slit on the diffusioosmotic flow are found to be very significant in practical situations.     

Diffusioosmotic flows in slit nanochannels

Diffusioosmotic flows of electrolyte solutions in slit nanochannels with homogeneous surface charges induced by electrolyte concentration gradients in the absence of externally applied pressure gradients and potential differences are investigated theoretically. A continuum mathematical model consisting of the strongly coupled Nernst-Planck equations for the ionic species' concentrations, the Poisson equation for the electric potential in the electrolyte solution, and the Navier-Stokes equations for the flow field is numerically solved simultaneously. The induced diffusioosmotic flow through the nanochannel is computed as functions of the externally imposed concentration gradient, the concentration of the electrolyte solution, and the surface charge density along the walls of the nanochannel. With the externally applied electrolyte concentration gradient, a strongly spatially dependent electric field and pressure gradient are induced within the nanochannel that, in turn, generate a spatially dependent diffusioosmotic flow. The diffusioosmotic flow is opposite to the applied concentration gradient for a relatively low bulk electrolyte concentration. However, the electrolyte solution flows from one end of the nanochannel with a higher electrolyte concentration to the other end with a lower electrolyte concentration when the bulk electrolyte concentration is relatively high. There is an optimal concentration gradient under which the flow rate attains the maximum. The induced flow is enhanced with the increase in the fixed surface charge along the wall of the nanochannel for a relatively low bulk electrolyte concentration.     

A multi-domain spectral method for non-Darcian mixed convection flow in a power-law fluid with viscous dissipation

The purpose of this study is to investigate non-Darcian mixed convection flow, heat and mass transfer in a non-Newtonian power-law fluid over a flat plate embedded in porous medium with suction and viscous dissipation and also is to demonstrate the application and utility of a recently developed multi-domain bivariate spectral quasi-linearisation method (MD-BSQLM) in finding the solutions of highly nonlinear differential equations. The flow is subject to, among other source terms, internal heat generation, thermal radiation and partial velocity slip. The coupled system of nonlinear partial differential equations are solved using a MD-BSQLM to find the fluid properties, the skin friction, as well as the heat and mass coefficients. We have presented selected results that give the significance of some system parameters on the fluid properties. This MD-BSQLM has not been used before in the literature to find the nature of the solutions of power-law fluids. Indeed, validation of this numerical method for general fluid flows, heat and mass transfer problems has not yet been done. This study presents the first opportunity to evaluate the accuracy and robustness of the MD-BSQLM in finding solutions of non-Newtonian fluids.     

Magnetic field effects on natural convection flow of a non-Newtonian fluid in an L-shaped enclosure

The effect of magnetic field on natural convection heat transfer in an L-shaped enclosure filled with a non-Newtonian fluid is investigated numerically. The governing equations are solved by finite-volume method using the SIMPLE algorithm. The power-law rheological model is used to characterize the non-Newtonian fluid behavior. It is revealed that heat transfer rate decreases for shear-thinning fluids (of power-law index, n?<?1) and increases for shear-thickening fluids (n?>?1) in comparison with the Newtonian ones. Thermal behavior of shear-thinning and shear-thickening fluids is similar to that of Newtonian fluids for the angle of enclosure α?<?60° and α?>?60°, respectively.     

Mixing of non-Newtonian fluids in wavy serpentine microchannel using electrokinetically driven flow

A numerical investigation is performed into the mixing performance of electrokinetically driven non-Newtonian fluids in a wavy serpentine microchannel. The flow behavior of the non-Newtonian fluids is described using a power-law model. The simulations examine the effects of the flow behavior index, the wave amplitude, the wavy-wall section length, and the applied electric field strength on the mixing performance. The results show that the volumetric flow rate of shear-thinning fluids is higher than that of shear-thickening fluids, and therefore results in a poorer mixing performance. It is shown that for both types of fluid, the mixing performance can be enhanced by increasing the wave amplitude, extending the length of the wavy-wall section, and reducing the strength of the electric field. Thus, although the mixing efficiency of shear-thinning fluids is lower than that of shear-thickening fluids, the mixing performance can be improved through an appropriate specification of the flow and geometry parameters. For example, given a shear-thinning fluid with a flow behavior index of 0.8, a mixing efficiency of 87% can be obtained by specifying the wave amplitude as 0.7, the wavy-wall section length as five times the characteristic length, the nondimensional Debye-Huckel parameter as 100, and the applied electric field strength as 43.5 V/cm.     

Molecular interpretation of electrokinetic potentials

A discussion is given of the electrokinetic, or ζ-potential in terms of the slip process and the composition of the electric double layer. Electrokinetically, only the outer parts of double layers are active. The existence of a stagnant part is generally observed for aqueous solutions adjacent to solid surfaces. It is claimed that this stagnancy is caused by the spontaneous structuring of fluids near solid surfaces. Hence, it is a ubiquitous phenomenon and the thickness of the stagnant layer does not significantly depend on the wettability and the surface charge of the surfaces.     

On Laminar Boundary Layer Flow of Electrically Conducting Liquids Near an Accelerated Vertical Plate

The unsteady hydromagnetic flow of electrically conducting liquids whose Prandtl numbers are different from unity has been considered when the flow takes place near an infinite vertical flat plate subject to uniform heat flux and accelerated motion. A unified exact solution has been derived for the boundary layer velocity and skin friction for the cases of magnetic field being fixed relative to the fluid or to the vertical plate. The solution has been presented in real forms for fluids whose Prandtl numbers are greater than or less than unity. The response of the boundary layer fluid velocity to the variations in magnetic and buoyancy forces has been discussed for two sample fluids corresponding to the different Prandtl number categories. The influence of these forces on the skin friction has also been shown.     

Diffusioosmosis and electroosmosis in a capillary slit with surface charge layers

This study analytically examines the steady diffusioosmotic and electroosmotic flows of an electrolyte solution in a fine capillary slit with each of its inside walls covered by a layer of adsorbed polyelectrolytes. In this solvent-permeable and ion-penetrable surface charge layer, idealized polyelectrolyte segments are assumed to distribute at a uniform density. The electric double layer and the surface charge layer may have arbitrary thicknesses relative to the gap width between the slit walls. The electrostatic potential distribution on a cross section of the slit is obtained by solving the linearized Poisson–Boltzmann equation, which applies to the case of low potentials or low fixed-charge densities. Explicit formulas for the fluid velocity profile due to the imposed electrolyte concentration gradient or electric field through the slit are derived as the solution of a modified Navier–Stokes/Brinkman equation. The results demonstrate that the structure of the surface charge layer can lead to an augmented or a diminished electrokinetic flow (even a reversal in direction of the flow) relative to that in a capillary with bare walls, depending on the characteristics of the capillary, of the surface charge layer, and of the electrolyte solution. For the diffusioosmotic flow with an induced electric field, competition between electroosmosis and chemiosmosis can result in more than one reversal in direction of the flow over a range of the Donnan potential of the adsorbed polyelectrolyte in the capillary.     

Diffusioosmosis and electroosmosis of electrolyte solutions in fibrous porous media

The steady diffusioosmotic and electroosmotic flows of an electrolyte solution in the fibrous porous medium constructed by a homogeneous array of parallel charged circular cylinders are analyzed under conditions of small Peclet and Reynolds numbers. The imposed electrolyte concentration gradient or electric field is constant and can be oriented arbitrarily with respect to the axes of the cylinders. The thickness of the electric double layers surrounding the cylinders is assumed to be small relative to the radius of the cylinders and to the gap width between two neighboring cylinders, but the polarization effect of the diffuse ions in the double layers is incorporated. Through the use of a unit cell model, the appropriate equations of conservation of the electrochemical potential energies of ionic species and the fluid momentum are solved for each cell, in which a cylinder is envisaged to be surrounded by a coaxial shell of the fluid. Analytical expressions for the diffusioosmotic and electroosmotic velocities of the bulk electrolyte solution as functions of the porosity of the ordered array of cylinders are obtained in closed form for various cases. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. In the limit of maximum porosity, these results can be interpreted as the diffusiophoretic and electrophoretic velocities of an isolated circular cylinder caused by the imposed electrolyte concentration gradient or electric field.     

Electroosmotic flow in a water column surrounded by an immiscible liquid

In this paper, we conducted numerical simulation of the electroosmotic flow in a column of an aqueous solution surrounded by an immiscible liquid. While governing equations in this case are the same as that in the electroosmotic flow through a microchannel with solid walls, the main difference is the types of interfacial boundary conditions. The effects of electric double layer (EDL) and surface charge (SC) are considered to apply the most realistic model for the velocity boundary condition at the interface of the two fluids. Effects on the flow field of ?-potential and viscosity ratio of the two fluids were investigated. Similar to the electroosmotic flow in microchannels, an approximately flat velocity profile exists in the aqueous solution. In the immiscible fluid phase, the velocity decreases to zero from the interface toward the immiscible fluid phase. The velocity in both phases increases with ?-potential at the interface of the two fluids. The higher values of ?-potential also increase the slip velocity at the interface of the two fluids. For the same applied electric field and the same ?-potential at the interface of the two fluids, the more viscous immiscible fluid, the slower the system moves. The viscosity of the immiscible fluid phase also affects the flatness of the velocity profile in the aqueous solution.     

Flow and heat transfer in non-Newtonian nanofluids over porous surfaces

In the present study, heat transfer and fluid flow of a pseudo-plastic non-Newtonian nanofluid over permeable surface has been solved in the presence of injection and suction. Similarity solution method is utilized to convert the governing partial differential equations into ordinary differential equations, which then is solved numerically using Runge–Kutta–Fehlberg fourth–fifth order (RKF45) method. The Cu, CuO, TiO₂ and Al₂O₃ nanoparticles are considered in this study along with sodium carboxymethyl cellulose (CMC)/water as base fluid. Validation has been done with former numerical results. The influence of power-law index, volume fraction of nanoparticles, nanoparticles type and permeability parameter on nanofluid flow and heat transfer was investigated. The results of the study illustrated that the flow and heat transfer of non-Newtonian nanofluid in the presence of suction and injection has different behaviors. For injection and the impermeable plate, the non-Newtonian nanofluid shows a better heat transfer performance compared to Newtonian nanofluid. However, changing the type of nanoparticles has a more intense influence on heat transfer process during suction. It was also observed that in injection, contrary to the other two cases, the usage of non-Newtonian nanofluid can decrease heat transfer in all cases.

     

Does macroscopic flow geometry influence wetting dynamic?

The macroscopic flow geometry has long been assumed to have little impact on dynamic wetting behavior of liquids on solid surfaces. This study experimentally studied both spontaneous spreading and forced wetting of several kinds of Newtonian and non-Newtonian fluids to study the effect of the macroscopic flow geometry on dynamic wetting. The relationship between the dynamic contact angle, θ(D), and the velocity of the moving contact line, U, indicates that the macroscopic flow geometry does not influence the advancing dynamic wetting behavior of Newtonian fluids, but does influence the advancing dynamic wetting behavior of non-Newtonian fluids, which had not been discovered before.     

Effect of viscoelasticity on the flow pattern and the volumetric flow rate in electroosmotic flows through a microchannel

Many lab-on-a-chip based microsystems process biofluids such as blood and DNA solutions. These fluids are viscoelastic and show extraordinary flow behaviors, not existing in Newtonian fluids. Adopting appropriate constitutive equations these exotic flow behaviors can be modeled and predicted reasonably using various numerical methods. In the present paper, we investigate viscoelastic electroosmotic flows through a rectangular straight microchannel with and without pressure gradient. It is shown that the volumetric flow rates of viscoelastic fluids are significantly different from those of Newtonian fluids under the same external electric field and pressure gradient. Moreover, when pressure gradient is imposed on the microchannel there appear appreciable secondary flows in the viscoelastic fluids, which is never possible for Newtonian laminar flows through straight microchannels. The retarded or enhanced volumetric flow rates and secondary flows affect dispersion of solutes in the microchannel nontrivially.     

On the Stagnation Point Flow of a Special Class of Non-Newtonian Fluids

Abstract

The two-dimensional boundary layer equations for a class of non-Newtonian fluids, for which the apparent viscosity can be expressed as a polynomial in the second scalar invariant of the rate of strain tensor, have been derived. These equations have been employed to analyse the flow near a stagnation point over a stationary impermeable wall. The non-Newtonian effects on the boundary layer velocity profile and the wall skin friction have been studied, and compared with the corresponding Newtonian fluid. The fluid velocity in the boundary layer has been shown to be retarded by the non-Newtonian effect while the skin friction increases proportionate to it.     

Viscosity of liquid suspensions with fractal aggregates: Magnetic nanoparticles in petroleum colloidal structures

New physical model is presented resulting in a simple formula for the dependence of viscosity η of colloidal liquid solution on the shear rate G applicable to a wide variety of systems including complex natural liquids like petroleum. The principal point of the model is the fractal nature of colloid particle aggregates present in the liquid. Such aggregates are experimentally detected now in non-Newtonian liquids. The model is based on calculation of energy loss on colloidal particle aggregate of fractal structure localized in the flow of liquid with shear rate. We have performed the viscosity measurement experiments which confirmed successfully the developed physical model. Also, we demonstrate experimentally that petroleum colloidal particles and magnetic iron oxide nanoparticles can form composite fractal-like aggregates in natural petroleum materials. Our model can explain both the non-Newtonian properties of petroleum and sensitivity of petroleum viscosity to external magnetic fields.