Non-uniform Zeta Potential Distribution Research Articles

Physics Informed Neural Network application on mixing and heat transfer in combined electroosmotic-pressure driven flow

In the current research, different architectures of physics-informed neural networks (PINNs) are implemented to investigate the mixed electroosmotic pressure driven (EOF/PD) flow in microchannels with non-uniform zeta-potential distribution on the walls. Through performing a detailed numerical simulation and PINN solutions based on Poisson-Boltzmann, Laplace, Navier-Stokes, concentration, and energy equations, we predict the non-uniformly distributed zeta-potential on the fluid dynamic, and heat transfer characteristics. It is observed that there is a good agreement between the Finite Volume Method (FVM) and segregated PINN approach. Comparing the PINN results with the numerical simulation, we show that amalgamating losses in all governing equations and applying a single PINN leads to higher training loss when compared to the multi-structured PINN, where a PINN is separately trained for each governing equation. Specifically, the normalized mean absolute percentage errors in the velocity prediction of the single and segregated PINNs are 20.17% and 9.2% respectively. In addition to the structure of the PINN, we also examine the effect of grid point distribution on PINNs. We demonstrate that using boundary layer collocation points can drastically improve the training efficiency and reduce the total loss for EOF/PD flow.

Mixing control in a continuous-flow microreactor using electro-osmotic flow

In recent years, pharmaceutical production has been stimulating the gradual miniaturization of continuous-flow chemical reactors. This process eventually resulted in the emergence of a new generation of microreactors. The advantages of these new reactor types are the flexible production that allows us to quickly reconfigure the scheme, small reactant quantities used for the synthesis, the control of the main reaction parameters with high accuracy. Nevertheless, a decrease in the thickness of the channels where the species contact and react forces us to search for new non-mechanical mechanisms for mixing. This problem is relevant for the slow reaction occurring in a slot where diffusion alone cannot provide mixing at reasonable distances from the entrance. It is also true for the fast reaction that takes place in a frontal manner. In this work, we consider the efficiency of mixing the reactants induced by electro-osmotic flow in a Hele-Shaw configuration with non-uniform zeta potential distribution. As a test reaction, we take the neutralization reaction with simple albeit non-linear kinetics. The reaction occurs between two miscible solutions, which are initially separated in space and come into contact in a continuous-flow microreactor. The reaction proceeds frontally, which prevents the efficient mixing of the reactants due to diffusion. Using direct numerical simulations of 2D and 3D flows, we demonstrate that the zeta potential applied to boundaries can effectively control the mixing rate of fluids by lengthening the front of the reaction. This approach makes it possible to increase the yield of the reaction product.

Analytical study of AC electroosmotic mixing in 2-dimensional microchannel with time periodic surface potential.

This work reported an analytic study of AC electroosmotic flows with a view to control the degree of mixing in a rectangular microchannel. Only with spatially non-uniform zeta potential distribution, fluid particles travel back and forth along a vortical flow field developed inside a microchannel. Although complex patterns of electroosmotic vortical flows can be obtained by various types of non-uniform zeta potential distributions, fluid particles always follow regular paths due to a laminar flow limit. To further facilitate the mixing of sample fluid, we propose a scheme that the zeta potential distribution was temporally non-uniform as well. General solutions for both the double layer potential distribution and the AC electroosmotic flow field are analytically determined by solving the unsteady Stokes equation with an electrostatic body force. As an illustrative example, we consider a case where two different types of non-uniform zeta potential distributions alternate with each other and the effects of both the AC frequency and the frequency of the alternation of the two zeta potential distributions on flow characteristics are examined using the Poincaré sections. Conclusively, one can either enhance or prevent mixing compared to a static electroosmotic flow, which is in line with previously demonstrated experimental works. Thus, the results presented would be an effective mean for controllable electroosmotic flow in a microfluidic platform.

Flow patterning in Hele-Shaw configurations using non-uniform electro-osmotic slip

We present an analytical study of electro-osmotic flow in a Hele-Shaw configuration with non-uniform zeta potential distribution. Applying the lubrication approximation and assuming thin electric double layer, we obtain a pair of uncoupled Poisson equations for the pressure and depth-averaged stream function, and show that the inhomogeneous parts in these equations are governed by gradients in zeta potential parallel and perpendicular to the applied electric field, respectively. We obtain a solution for the case of a disk-shaped region with uniform zeta potential and show that the flow field created is an exact dipole, even in the immediate vicinity of the disk. In addition, we study the inverse problem where the desired flow field is known and solve for the zeta potential distribution required in order to establish it. Finally, we demonstrate that such inverse problem solutions can be used to create directional flows confined within narrow regions, without physical walls. Such solutions are equivalent to flow within channels and we show that these can be assembled to create complex microfluidic networks, composed of intersecting channels and turns, which are basic building blocks in microfluidic devices.

Macroscale description of electrokinetic flows at large zeta potentials: Nonlinear surface conduction

For highly charged dielectric surfaces, the asymptotic structure underlying electrokinetic phenomena in the thin-double-layer limit reshuffles. The large counterion concentration near the surface, associated with the Boltzmann distribution in the diffuse layer, supports appreciable tangential fluxes appearing as effective surface currents in a macroscale description. Their inevitable nonuniformity gives rise in turn to comparable transverse currents, which, for logarithmically large zeta potentials, modify the electrokinetic transport in the electroneutral bulk. To date, this mechanism has been studied only using a weak-field linearization. We present here a generic thin-double-layer analysis of the electrokinetic transport about highly charged dielectric solids, which is not restricted to weak fields. We identify the counterion concentration amplification with the emergence of an internal boundary layer--within the diffuse part of the double layer--characterized by distinct scaling of ionic concentrations and electric field. In this multiscale description, surface conduction is conveniently localized within the internal layer. Our systematic scheme thus avoids the cumbersome procedure of retaining small asymptotic terms which change their magnitude at large zeta potentials. The electrokinetic transport predicted by the resulting macroscale model is inherently accompanied by bulk concentration polarization, which in turn results in nonlinear bulk transport. A novel fundamental subtlety associated with this intrinsic feature, overlooked in the weak-field approximation, has to do with the ambiguity of the "particle zeta potential" concept: In general, even uniformly charged surfaces are characterized by a nonuniform zeta-potential distribution. This impairs the need for a careful identification of the dimensionless number representing the transition to large zeta potentials.

Dielectric-solid polarization at strong fields: Breakdown of Smoluchowski's electrophoresis formula

We investigate the thin-double-layer electrophoretic drift of a uniformly charged dielectric particle, driven by an intense electric field comparable to the transverse Debye-layer field. Under these circumstances, solid polarization affects the leading-order electrokinetic transport in the fluid by inducing a nonuniform zeta-potential distribution. The resulting expression for the particle velocity is accordingly nonlinear in the applied field. The electrophoretic “mobility”—the ratio of this velocity and the applied field—depends upon two parameters, the first quantifying the surface-charge density, and the second constituting the product of the solid-to-liquid permittivity ratio and the scaled applied-field magnitude. At weak values of this product, solid polarization results in field-cubed deviations from Smoluchowski's velocity; at large values of it, the particle velocity is a slowly increasing function of the applied field, essentially varying with its logarithm. The transition between these two limits features a shift from zeta-potential proportionality to a charge-density proportionality. For all values of the two governing parameters solid polarization acts so as to reduce the electrophoretic velocity relative to the Smoluchowski limit.

Electrophoresis of a Cylindrical Particle with a Nonuniform Zeta Potential Distribution Parallel to a Charged Plane Wall

An analytical study is presented for the steady, transverse electrophoretic motion of a circular cylindrical particle with an arbitrary angular distribution of its surface potential parallel to a plane wall prescribed with the potential distribution consistent with the applied electric field. The electric double layers adjacent to the solid surfaces are assumed to be very thin with respect to the particle radius and spacing between the surfaces. The two-dimensional electrostatic and hydrodynamic governing equations are solved using cylindrical bipolar coordinates, and the typical electric field line, equipotential line, and streamline patterns are exhibited. The explicit formulas for the electrophoretic and angular velocities of the particle are obtained with the contribution from the electroosmotic flow produced by the interaction between the applied electric field and the thin double layer adjacent to the plane wall. To apply these formulas, one only has to calculate the leading multipole moments of the...

Micromixing using induced-charge electrokinetic flow

The mixing effect of induced-charge electrokinetic flow (ICEKF) in a rectangular microchannel with embedded conducting hurdles is investigated in this paper. A correction method is suggested to estimate numerically the induced zeta potential on the conducting surface. Two-dimensional pressure-linked Navier–Stokes equation is used to model the flow field in the channel. The numerical results show flow circulations generated from the induced non-uniform zeta potential distribution along the conducting hurdle surfaces. It is demonstrated that the local flow circulations provide effective means to enhance the flow mixing between different solutions. The mixing enhancement effect is experimentally validated using PDMS based microchannels with embedded platinum hurdles. The dependence of the degree of mixing enhancement on the hurdle geometries and hurdle numbers is also predicted. The mixing using ICEKF described in this paper can be used in various microfluidics and lab-on-a-chip applications.

Mixing and flow regulating by induced-charge electrokinetic flow in a microchannel with a pair of conducting triangle hurdles

The induced-charge electrokinetic flow (ICEKF) in a rectangular micorchannel with a pair of conducting triangle hurdles embedded in the middle is investigated in this paper. A correction method is suggested to numerically estimate the induced zeta potential on the conducting surface. Two-dimensional pressure-linked Navier-–Stokes equation is used to model the flow field in the channel. The numerical results show flow circulations generated from the induced non-uniform zeta potential distribution along the conducting hurdle surfaces. It is demonstrated numerically that the local flow circulations provide effective means to enhance the flow mixing between different solutions; by adjusting the electric field applied through the microchannel with a non-symmetric triangle hurdle pair, an electrokinetic flow regulating effect can be obtained and this effect depends on the dimensions of the conducting converging–diverging section. The mixing and flow regulating using ICEKF described in this paper can be used in various microfluidics and lab-on-a-chip (LOC) applications.

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.

Effects of surface heterogeneity on flow circulation in electroosmotic flow in microchannels

The characteristics of electroosmotic flow in a cylindrical microchannel with non-uniform zeta potential distribution are investigated in this paper. Two-dimensional full Navier–Stokes equation is used to model the flow field and the pressure field. The numerical results show the distorted electroosmotic velocity profiles and various kinds of flow circulation resulting from the axial variation of the zeta potential. The influences of heterogeneous patterns of zeta potential on the velocity profile, the induced pressure distribution and the volumetric flow rate are discussed in this paper. This work shows that using either heterogeneous patterns of zeta potential or a combination of a heterogeneous zeta potential distribution and an applied pressure difference over the channel can generate local flow circulations and hence provide effective means to improve the mixing between different solutions in microchannels.

Electrophoretic Motion of a Slightly Deformed Sphere with a Nonuniform Zeta Potential Distribution

Electrophoretic motion is analyzed for a rigid, slightly deformed sphere with a nonuniform zeta potential distribution. Hydrodynamics and electrostatics solutions for the deformed sphere with an arbitrary double-layer thickness are determined by using the domain perturbation method. The surface shape and the zeta potential distribution for the deformed sphere are expressed by using the multipole expansion representation. In terms of monopole, dipole, and quadrupole moments of the surface shape and the zeta potential distribution, explicit expressions are obtained for the translational and rotational electrophoretic mobility tensors. The ensemble average for the mobility of the deformed sphere with a uniform orientation distribution is also derived. The utility of the general mobility expression is demonstrated by studying the electrophoretic motion of axisymmetric and ellipsoidal particles. The translational and rotational mobilities of axisymmetric particles are both affected by the monopole, dipole, and quadrupole moments of the zeta potential. For ellipsoidal particles, however, the dipole moment of the zeta potential does not affect the translational mobility, while the rotational mobility depends only on the dipole moment. The mobility of the deformed sphere with either a thick or a thin double layer is also derived.