Cunlu Zhao

Analysis of electroosmotic flow of power-law fluids in a slit microchannel.

Electroosmotic flow of power-law fluids in a slit channel is analyzed. The governing equations including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, and the continuity equation are solved to seek analytical expressions for the shear stress, dynamic viscosity, and velocity distribution. Specifically, exact solutions of the velocity distributions are explicitly found for several special values of the flow behavior index. Furthermore, with the implementation of an approximate scheme for the hyperbolic cosine function, approximate solutions of the velocity distributions are obtained. In addition, a generalized Smoluchowski velocity is introduced by taking into account contributions due to the finite thickness of the electric double layer and the flow behavior index of power-law fluids. Calculations are performed to examine the effects of kappaH, flow behavior index, double layer thickness, and applied electric field on the shear stress, dynamic viscosity, velocity distribution, and average velocity/flow rate of the electroosmotic flow of power-law fluids.

Electrokinetics of non-Newtonian fluids: a review.

This work presents a comprehensive review of electrokinetics pertaining to non-Newtonian fluids. The topic covers a broad range of non-Newtonian effects in electrokinetics, including electroosmosis of non-Newtonian fluids, electrophoresis of particles in non-Newtonian fluids, streaming potential effect of non-Newtonian fluids and other related non-Newtonian effects in electrokinetics. Generally, the coupling between non-Newtonian hydrodynamics and electrostatics not only complicates the electrokinetics but also causes the fluid/particle velocity to be nonlinearly dependent on the strength of external electric field and/or the zeta potential. Shear-thinning nature of liquids tends to enhance electrokinetic phenomena, while shear-thickening nature of liquids leads to the reduction of electrokinetic effects. In addition, directions for the future studies are suggested and several theoretical issues in non-Newtonian electrokinetics are highlighted.

Nonlinear Smoluchowski velocity for electroosmosis of Power-law fluids over a surface with arbitrary zeta potentials

Electroosmotic flow of Power‐law fluids over a surface with arbitrary zeta potentials is analyzed. The governing equations including the nonlinear Poisson–Boltzmann equation, the Cauchy momentum equation and the continuity equation are solved to seek exact solutions for the electroosmotic velocity, shear stress, and dynamic viscosity distributions inside the electric double layer. Specifically, an expression for the general Smoluchowski velocity is obtained for electroosmosis of Power‐law fluids in a fashion similar to the classic Smoluchowski velocity for Newtonian fluids. The existing Smoluchowski slip velocities under two special cases, (i) for Newtonian fluids with arbitrary zeta potentials and (ii) for Power‐law fluids with small zeta potentials, can be recovered from our derived formula. It is interesting to note that the general Smoluchowski velocity for non‐Newtonian Power‐law fluids is a nonlinear function of the electric field strength and surface zeta potentials; this is due to the coupling electrostatics and non‐Newtonian fluid behavior, which is different from its counterpart for Newtonian fluids. This general Smoluchowski velocity is of practical significance in determining the flow rates in microfluidic devices involving non‐Newtonian Power‐law fluids.

Exact solutions for electro-osmotic flow of viscoelastic fluids in rectangular micro-channels

Transient electro-osmotic flow of viscoelastic fluids in rectangular micro-channels is investigated. The general twofold series solution for the velocity distribution of electro-osmotic flow of viscoelastic fluids with generalized fractional Oldroyd-B constitutive model is obtained by using finite Fourier and Laplace transforms. Under three limiting cases, the generalized Oldroyd-B model simplifies to Newtonian model, fractional Maxwell model and generalized second grade model, where all the explicit exact solutions for velocity distribution are found through the discrete Laplace transform of the sequential fractional derivatives. These exact solutions may be able to predict the flow behavior of viscoelastic biological fluids in BioMEMS and Lab-on-a-chip devices and thus could benefit the design of these devices.

Electro-osmotic mobility of non-Newtonian fluids

Electrokinetically driven microfluidic devices are usually used to analyze and process biofluids which can be classified as non-Newtonian fluids. Conventional electrokinetic theories resulting from Newtonian hydrodynamics then fail to describe the behaviors of these fluids. In this study, a theoretical analysis of electro-osmotic mobility of non-Newtonian fluids is reported. The general Cauchy momentum equation is simplified by incorporation of the Gouy-Chapman solution to the Poisson-Boltzmann equation and the Carreau fluid constitutive model. Then a nonlinear ordinary differential equation governing the electro-osmotic velocity of Carreau fluids is obtained and solved numerically. The effects of the Weissenberg number (Wi), the surface zeta potential (ψ¯s), the power-law exponent(n), and the transitional parameter (β) on electro-osmotic mobility are examined. It is shown that the results presented in this study for the electro-osmotic mobility of Carreau fluids are quite general so that the electro-osmotic mobility for the Newtonian fluids and the power-law fluids can be obtained as two limiting cases.

Electroosmotic flows of non-Newtonian power-law fluids in a cylindrical microchannel

EOF of non‐Newtonian power‐law fluids in a cylindrical microchannel is analyzed theoretically. Specially, exact solutions of electroosmotic velocity corresponding to two special fluid behavior indices (n = 0.5 and 1.0) are found, while approximate solutions are derived for arbitrary values of fluid behavior index. It is found that because of the approximation for the first‐order modified Bessel function of the first kind, the approximate solutions introduce largest errors for predicting electroosmotic velocity when the thickness of electric double layer is comparable to channel radius, but can accurately predict the electroosmotic velocity when the thickness of electric double layer is much smaller or larger than the channel radius. Importantly, the analysis reveals that the Helmholtz‐Smoluchowski velocity of power‐law fluids in cylindrical microchannels becomes dependent on geometric dimensions (radius of channel), standing in stark contrast to the Helmholtz‐Smoluchowski velocity over planar surfaces or in parallel‐plate microchannels. Such interesting and counterintuitive effects can be attributed to the nonlinear coupling among the electrostatics, channel geometry, and non‐Newtonian hydrodynamics. Furthermore, a method for enhancement of EOFs of power‐law fluids is proposed under a combined DC and AC electric field.

AC field induced-charge electroosmosis over leaky dielectric blocks embedded in a microchannel†

An effective electrical boundary condition is formulated to describe AC field‐driven induced‐charge electrokinetic (ICEK) phenomena at the interface between a liquid and a leaky dielectric solid. Since most materials in reality possess finite dielectric and conductive properties, i.e. leaky dielectric, the present boundary condition can be used to describe the induced zeta potential on a leaky dielectric surface with consideration of both bond charges (due to polarization) and free charges (due to conduction). Two well‐known limiting cases, i.e. the perfectly dielectric and the perfectly conducting wall boundary conditions can be recovered from the present formulation. Utilizing the derived boundary condition, we obtain analytical solutions in closed form for the AC field‐driven induced‐charge electroosmosis (ICEO) over two symmetric leaky dielectric blocks embedded in the walls of an infinitely long microchannel. Two important factors for the induced zeta potential are identified to respectively account for the polarization charges and the free charges, and their effects on AC field‐driven ICEO oscillating flow patterns are analyzed. It is found that the flow patterns exhibit two counter‐rotating vortices, which can be deformed, relocated, eliminated and even reverse their rotating directions. It is very promising that such temporary evolution of flow patterns can possibly induce chaotic advection which can enhance microfluidic mixing.

Analysis of Power-Law Fluid Flow in a Microchannel with Electrokinetic Effects

The pressure driven flow of power-law fluids in microchannels subject to electrokinetic effects is analyzed in this work. The Cauchy momentum equation together with the power-law fluid constitutive equation is used to describe the power-law fluid flow in a slit microchannel with consideration of a body force resulting from the interaction of the charge density in the electrical double layer of the channel and the flow-induced electrokinetic potential. By using an appropriate approximate scheme, an expression for the induced streaming potential is obtained. The velocity profile, volumetric flow rate, apparent viscosity and friction coefficient are analytically evaluated, and the influencing factors including ionic concentration, wall zeta potential, flow behavior index and pressure difference are investigated. It is found that the pseudoplastic fluids are more susceptible to electokinetic effects than the dilatant fluids and then the flow characteristics of the pseudoplastic fluids are found to deviate dra...

Induced charge effects on electrokinetic entry flow

Electrokinetic flow, due to a nearly plug-like velocity profile, is the preferred mode for transport of fluids (by electroosmosis) and species (by electrophoresis if charged) in microfluidic devices. Thus far there have been numerous studies on electrokinetic flow within a variety of microchannel structures. However, the fluid and species behaviors at the interface of the inlet reservoir (i.e., the well that supplies the fluid and species) and microchannel are still largely unexplored. This work presents a fundamental investigation of the induced charge effects on electrokinetic entry flow due to the polarization of dielectric corners at the inlet reservoir-microchannel junction. We use small tracing particles suspended in a low ionic concentration fluid to visualize the electrokinetic flow pattern in the absence of Joule heating effects. Particles are found to get trapped and concentrated inside a pair of counter-rotating fluid circulations near the corners of the channel entrance. We also develop a dept...

Enhancement of electrophoretic mobility of microparticles near a solid wall—Experimental verification

Although the existing theories have predicted enhancement of electrophoretic mobility of microparticles near a solid wall, the relevant experimental studies are rare. This is mainly due to difficulties in experimentally controlling and measuring particle‐wall separations under dynamic electrophoretic conditions. This paper reports an experimental verification of the enhancement of electrophoretic mobility of a microparticle moving near the wall of a microchannel. This is achieved by balancing dielectrophoretic and lift forces against gravitational force acting on the microparticle so as to control the gap of particle‐wall separation. A simple experimental setup is configured and a fabrication method is developed to measure such separation gap. The experiments are conducted for various particle sizes under different electric field strengths. Our experimental results are compared against the available theoretical predictions in the literature.