Electroviscous Forces on a Charged Cylinder Moving Near a Charged Wall

The refined theory of the electroviscous lift forces is presented for the case when the separation distance between the particle and the wall is larger than the double-layer thickness. The theory is based on the lubrication approximation for motion of a long cylinder near a solid wall in creeping flow. The approximate analytical formula for the lift force valid for Pe相似文献   

Electroviscous cylinder-wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged cylindrical particle and a charged plane boundary wall when the particle translates parallel to the wall and rotates around its axis in a symmetric electrolyte solution at rest. The electroviscous effects, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, derived from R.G. Cox's general theory [J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential, and electroviscous flow field. It is assumed a priori that the double layer thickness surrounding each charged surface is much smaller than the length scale of the problem. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the cylinder are explicitly determined analytically for small particle-wall distances for low and intermediate Peclet numbers. It is found that the tangential force usually increases the drag above the purely hydrodynamic drag, although for certain conditions the drag can be reduced. Similarly the normal force is usually repulsive, i.e., it is an electrokinetic lift force, but under certain conditions the normal force can be attractive.     

DC-electrokinetic motion of colloidal cylinder(s) in the vicinity of a conducting wall

The boundary effects on DC-electrokinetic behavior of colloidal cylinder(s) in the vicinity of a conducting wall is investigated through a computational model. The contribution of the hydrodynamic drag, gravity, electrokinetic (i.e., electrophoretic and dielectrophoretic), and colloidal forces (i.e., forces due to the electrical double layer and van der Waals interactions) are incorporated in the model. The contribution of electrokinetic and colloidal forces are included by introducing the resulting forces as an external force acting on the particle(s). The colloidal forces are implemented with the prescribed expressions from the literature, and the electrokinetic force is obtained by integrating the corresponding Maxwell stress tensor over the particles' surfaces. The electrokinetic slip-velocity together with the thin electrical double layer assumption is applied on the surfaces. The position and velocity of the particles and the resulting electric and flow fields are obtained and the physical insight for the behavior of the colloidal cylinders are discussed in conjunction with the experimental observations in the literature.     

Effect of direct current dielectrophoresis on the trajectory of a non-conducting colloidal sphere in a bent pore

Dielectrophoresis has shown a wide range of applications in microfluidic devices. Force approximations utilizing the point-dipole method in dielectrophoresis have provided convenient predictions for particle motion by neglecting interactions between the particle and its surrounding electric and flow fields. The validity of this approach, however, is unclear when the particle size is comparable to the characteristic length of the channel and when the particle is in close proximity to the channel wall. To address this issue, we apply an accurate numerical approach based on the boundary-element method (BEM) to solve the coupled electric field, flow, and particle motion. This method can handle much closer particle-wall distances than the other numerical approaches such as the finite-element method. Using the BEM and integrating the Maxwell stress tensor, we simulate an electrokinetic, spherical particle moving within a bent cylindrical pore to investigate how the dielectrophoretic force affects the particle's trajectory. In the simulation, both the particle and the channel wall are non-conducting, and the electric double layers adjacent to the solid surfaces are assumed to be thin with respect to the particle radius and particle-wall gap. The results show that as the particle comes close to the wall, its finite size has an increasingly important effect on its own transient motion and the point-dipole approximation may lead to significant error.     

Sedimentation of a charged colloidal sphere in a charged cavity

An analytical study is presented for the quasisteady sedimentation of a charged spherical particle located at the center of a charged spherical cavity. The overlap of the electric double layers is allowed, and the polarization (relaxation) effect in the double layers is considered. The electrokinetic equations that govern the ionic concentration distributions, electric potential profile, and fluid flow field in the electrolyte solution are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetric electrolyte with the surface charge densities of the particle and cavity as the small perturbation parameters. An analytical expression for the settling velocity of the charged sphere is obtained from a balance among the gravitational, electrostatic, and hydrodynamic forces acting on it. Our results indicate that the presence of the particle charge reduces the magnitude of the sedimentation velocity of the particle in an uncharged cavity and the presence of the fixed charge at the cavity surface increases the magnitude of the sedimentation velocity of an uncharged particle in a charged cavity. For the case of a charged sphere settling in a charged cavity with equivalent surface charge densities, the net effect of the fixed charges will increase the sedimentation velocity of the particle. For the case of a charged sphere settling in a charged cavity with their surface charge densities in opposite signs, the net effect of the fixed charges in general reduces/increases the sedimentation velocity of the particle if the surface charge density of the particle has a greater/smaller magnitude than that of the cavity. The effect of the surface charge at the cavity wall on the sedimentation of a colloidal particle is found to increase with a decrease in the particle-to-cavity size ratio and can be significant in appropriate situations.     

Revisit of wall‐induced lateral migration in particle electrophoresis through a straight rectangular microchannel: Effects of particle zeta potential

Previous studies have reported a lateral migration in particle electrophoresis through a straight rectangular microchannel. This phenomenon arises from the inherent wall‐induced electrical lift that can be exploited to focus and separate particles for microfluidic applications. Such a dielectrophoretic‐like force has been recently found to vary with the buffer concentration. We demonstrate in this work that the particle zeta potential also has a significant effect on the wall‐induced electrical lift. We perform an experimental study of the lateral migration of equal‐sized polystyrene particles with varying surface charges under identical electrokinetic flow conditions. Surprisingly, an enhanced focusing is observed for particles with a faster electrokinetic motion, which indicates a substantially larger electrical lift for particles with a smaller zeta potential. We speculate this phenomenon may be correlated with the particle surface conduction that is a strong function of particle and fluid properties.     

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.     

On the effect of induced electro-osmosis on a cylindrical particle next to a surface

The effect of induced electro-osmosis on a cylindrical particle positioned next to a planar surface (wall) is studied theoretically both under the thin double layer approximation utilizing the Smoluchowski slip velocity approximation and under thick electric double layer conditions by solving the Poisson-Nernst-Planck (PNP) equations. The imposed, undisturbed electric field is parallel to the planar surface. The induced hydrodynamic and electrostatic forces are calculated as functions of the particle's and the medium's dielectric constants and the distance between the particle and the surface. The resultant force acting on the particle is directed normal to and away from the wall. The presence of such a repulsive force may adversely affect the interactions between macromolecules suspended in solution and wall-immobilized molecules and may be significant to near-wall particle imaging velocimetry (PIV) in electrokinetic flows.     

Electrokinetic transport of charged solutes in micro- and nanochannels: the influence of transverse electromigration

The accurate prediction of electrokinetic migration velocity and dispersion is crucial to separating electrophoretically charged solutes in micro- or nanochannels. In this paper, we investigate numerically the influence of transverse electromigration (TEM) on the solute electrokinetic transport in a series of micro- and nanochannels. The TEM, often ignored in previous studies, is demonstrated to significantly affect the solute migration velocity in nanochannels and the electrokinetic dispersion in microchannels. This is because the TEM can force either positively charged solutes into or negatively charged solutes out of the electrical double layer that forms adjacent to the negatively charged channel wall and contains the velocity gradients. Analytical solutions are also derived for characterizing the electrokinetic transport of charged solutes in nanochannels, which has been validated to be in good agreement with the numerical simulation. Moreover, we demonstrate that the proposed analytical formula for the solute migration velocity actually applies to channels of any size.     

Nonlinear effects on electrokinetics of a highly charged porous sphere

The motivation of the present study is to provide a correct estimate of the electrophoretic mobility of a charged porous particle for wide-range electrokinetic parameters, such as particle charge density, permeability, and Debye length. Based on the Nernst–Planck equation, which takes into account the external electric field and fluid convection on ion transport, we have estimated the mobility of the particle by establishing a force balance. We have validated our results with the linear model due to Hermans and Fujita (K Nederl Akad Wet Proc Ser B 58:182–187, 1955) and the computed solution based on perturbation of the Poisson–Boltzmann model as obtained by Hsu and Lee (J Colloid Interface Sci 390:85–95, 2013). For the case of thin double layer, our computed results agree with the linear model even for large values of charge density of the particle. The linear model overpredicts our computed solution for mobility when the thick Debye layer is considered. However, a large discrepancy of the present model from the results based on the perturbation of the Boltzmann model is observed for all the cases considered. We have analyzed the double-layer polarization and counterion condensation through the distribution of counterions, net charge density, and the effective charge density of the particle.     

Electrophoresis of a colloidal sphere in a spherical cavity with arbitrary zeta potential distributions

An analytical study is presented for the quasi-steady electrophoretic motion of a dielectric sphere situated at the center of a spherical cavity when the surface potentials are arbitrarily nonuniform. The applied electric field is constant, and the electric double layers adjacent to the solid surfaces are assumed to be much thinner than the particle radius and the gap width between the surfaces. The presence of the cavity wall causes three basic effects on the particle velocity: (1) the local electric field on the particle surface is enhanced or reduced by the wall; (2) the wall increases the viscous retardation of the moving particle; and (3) a circulating electroosmotic flow of the suspending fluid exists because of the interaction between the electric field and the charged wall. The Laplace and Stokes equations are solved analytically for the electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the electrophoretic and angular velocities of the particle are obtained. To apply these formulas, one has to calculate only the monopole, dipole, and quadrupole moments of the zeta-potential distributions at the particle and cavity surfaces. It is found that the contribution from the electroosmotic flow developing from the interaction of the imposed electric field with the thin double layer adjacent to the cavity wall and the contribution from the wall-corrected electrophoretic driving force to the particle velocities can be superimposed as a result of the linearity of the problem.     

Boundary effects on electrophoresis of a colloidal cylinder with a nonuniform zeta potential distribution

The electrophoretic motion of a long dielectric circular cylinder with a general angular distribution of its surface potential under a transversely imposed electric field in the vicinity of a large plane wall parallel to its axis is analyzed. The thickness of the electric double layers adjacent to the solid surfaces is assumed to be much smaller than the particle radius and the gap width between the surfaces, but the applied electric field can be either perpendicular or parallel to the plane wall. The presence of the confining wall causes three basic effects on the particle velocity: (1) the local electric field on the particle surface is enhanced or reduced by the wall; (2) the wall increases viscous retardation of the moving particle; (3) an electroosmotic flow of the suspending fluid may exist due to the interaction between the charged wall and the tangentially imposed electric field. Through the use of cylindrical bipolar coordinates, the Laplace and Stokes equations are solved analytically for the two-dimensional electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the quasisteady electrophoretic and angular velocities of the cylindrical particle are obtained. To apply these formulas, one has only to calculate the multipole moments of the zeta potential distribution at the particle surface. It is found that the existence of a plane wall near a nonuniformly charged particle can cause its translation or rotation which does not occur in an unbounded fluid with the same applied electric field.     

Electrophoretic motion of a charged porous sphere within micro- and nanochannels

Electrophoretic motion of a charged porous sphere within micro- and nanochannels is investigated theoretically. The Brinkman model and the full non-linear Poisson-Boltzmann equation are adopted to model the system, with the charged porous sphere resembling polyelectrolytes like proteins and DNA. General electrokinetic equations are employed and solved with a pseudo-spectral method. Key parameters of electrokinetic interest are examined for their respective effect as well as overall impact on the particle motion. We found, among other things, that the confinement effect of the channel can be so drastic that 75% reduction of particle mobility is observed in some situations for a poorly permeable particle. However, only 15% for the corresponding highly permeable particle due to the allowance of fluid penetration which alleviates the retarding shear stress significantly. In particular, an intriguing phenomenon is observed for the highly permeable particle: the narrower the channel is, the faster the particle moves! This was experimentally observed as well in the literature on DNA electrophoresis within nanostructures. The reason behind it is thoroughly explained here. Moreover, charged channels can exert electroosmosis flow so dominant that sometimes it may even reverse the direction of the particle motion. Comparison with experimental data available in the literature for some polyelectrolytes is excellent, indicating the reliability of this analysis. The results of this study provide fundamental knowledge necessary to interpret experimental data correctly in various microfluidic and nanofluidic operations involving bio-macromolecules, such as in biosensors and Lab-on-a-chip devices.     

Electrokinetic diffusioosmotic flow of Ostwald-de Waele fluids near a charged flat plate in the thin double layer limit

Electrokinetic diffusioosmotic flow of Ostwald-de Waele, or power-law, fluids near a large charged flat plate is theoretically investigated for very thin double layers. Solutions to the flow velocity both up-close and far from the flat plate as well as the effective viscosity are presented for general values of the flow behavior index. Results show that given a wall zeta potential, ζ, diffusivity difference parameter, β, and constant imposed solute concentration gradient, both the near and far field diffusioosmotic flow velocities obtained for the respective dilatant and pseudoplastic liquids considerably deviate from those obtained for Newtonian liquids as found in previous literature. This likely suggests that the electrokinetic diffusioosmosis and its complementary effect of diffusiophoresis depend sensitively not only on the ζ-β parametric pair, but also on the possible non-Newtonian characteristics of the electrolytic liquid phase of the system. The theory presented herein can also be readily modified to model or describe electrodiffusioosmosis in power-law fluids, which is likely found in flow situations where the fluid non-Newtonian response, imposed solute concentration gradient, and an additional externally applied electric current density (or electric field) are of equal importance.     

Electrokinetic boundary condition compatible with the Onsager reciprocal relation in the thin double layer approximation

The boundary condition, which has been used in the conventional electrokinetic calculation in the thin double layer approximation, has a flaw that it does not give the Onsager reciprocal relation for the sedimentation of charged particle. We propose a new boundary condition, which satisfies the reciprocal relation, and derive a general form for the mobility matrix for the motion of a charged particle under the action of external force, torque, and electric field. We then calculate the mobility matrix explicitly for homogeneously charged spherical particle and discuss the effect of the surface slippage and the surface conductivity on the particle mobility and electric conductivity.     

Controlled protein adsorption on a silica microparticle

In the present study, controlled protein adsorption on a rigid silica microparticle is investigated numerically using classical Langmuir and two-state models under electrokinetic flow conditions. The instantaneous particle locations are simulated along a straight microchannel using an arbitrary Lagrangian−Eulerian framework in the finite element method for the electrophoretic motion of the charged particle. Within the scope of the parametric study, the strength of the external electric field (E), particle diameter (D_p), the zeta potential of the particle (ζ_p), and the location of the microparticle away from the channel wall (H) are systematically varied. The results are also compared to the data of pressure-driven flow having a parabolic flow profile at the inlet whose maximum magnitude is set to the particle's electrophoretic velocity magnitude. The validation studies reveal that the code developed for the particle motion in the present simulations agrees well with the experimental results. It is observed that protein adsorption can be controlled using electrokinetic phenomena. The plug-like flow profile in electrokinetics is beneficial for a microparticle at every spatial location in the microchannel, whereas it is not valid for the pressure-driven flow. The electric field strength and the zeta potential of the particle accelerate the protein adsorption. The wall shear stress and shear rate are good indicators to predict the adsorption process for electrokinetic flow.     

ac electroosmosis in rectangular microchannels

Motivated by the growing interest in ac electroosmosis as a reliable no moving parts strategy to control fluid motion in microfluidic devices for biomedical applications, such as lab-on-a-chip, we study transient and steady-state electrokinetic phenomena (electroosmosis and streaming currents) in infinitely extended rectangular charged microchannels. With the aid of Fourier series and Laplace transforms we provide a general formal solution of the problem, which is used to study the time-dependent response to sudden ac applied voltage differences in case of finite electric double layer. The Debye-Huckel approximation has been adopted to allow for an algebraic solution of the Poisson-Boltzmann problem in Fourier space. We obtain the expressions of flow velocity profiles, flow rates, streaming currents, as well as expressions of the complex hydraulic and electrokinetic conductances. We analyze in detail the dependence of the electrokinetic conductance on the extension of linear dimensions relative to the Debye length, with an eye on finite electric double layer effects.     

Electrophoresis of a charge-regulated sphere at an arbitrary position in a charged spherical cavity

The electrophoresis of a charge-regulated spherical particle at an arbitrary position in a charged spherical cavity is modeled under conditions of low surface potential (<25 mV) and weak applied electric field (<25 kV/m). The charged cavity allows us to simulate the effect of electroosmotic flow, and the charge-regulated nature of the particle permits us to model various types of surface. The problem studied previously is reanalyzed based on a more rigorous electric force formula. In particular, the influences of various types of charged conditions on the electrophoretic behavior of a particle and the roles of all the relevant forces acting on the particle are examined in detail. Several new results are found. For instance, the mobility of a particle has a local minimum as the thickness of a double layer varies, which is not seen in the cases where the surface of a particle is maintained at a constant potential and at a constant charge density.     

Diffusiophoresis of a highly charged soft particle normal to a conducting plane

Diffusiophoresis of a soft particle in electrolyte solutions normal to a conducting solid plane is investigated theoretically in this study, focusing on the highly charged particle in particular. A pseudo-spectral method based on Chebyshev polynomial is adopted to solve the resultant governing electrokinetic equations. It was found, among other things, that the closer the soft particle is to the plane, the faster it moves in general, provided only the chemiphoresis component of the diffusiophoresis is involved, i.e., no diffusion potential is present. The presence of the conducting plane is found to have three effects upon the particle motion nearby: the geometric boundary confinement effect, the electrostatic mirror-image force analog effect, and the hydrodynamic retarding effect. The enhancement of the double layer polarization by the first two effects leads to the seeming intriguing observation mentioned above. The particle always moves away from the plane in chemiphoresis. If a diffusion potential is present, however, then it is possible to drive the particle toward the plane. The results have potential applications in drug delivery.     

Density functional theory and the contact condition for an electrolyte near a charged wall

The density functional theory is used to derive and extend the “contact condition” of the density profile of an electrolyte near a charged wall. This approach complements the one which is commonly used starting from the hydrostatic equilibrium equation and the stress tensor. Extensions to other systems like the Donnan membrane are discussed.