Periodic Electroosmotic Flow Research Articles

Periodic electroosmotic flow of nanofluids with slip-dependent high zeta potential

The time periodic electroosmotic flow of nanofluids is investigated analytically in a hydrophobic microchannel. In this study, we consider the interdependence relationship between the wall electrical potential and slip. According to the non-linear slip-dependent zeta potential, we obtain an analytical solution of electrical potential for arbitrary value of wall electrical potential. Subsequently, we give the analytical integration expression of time periodic electroosmotic velocity of nanofluids. Based on the obtained electrical potential distribution, the oscillating flow velocity and rate are calculated numerically. The flow characteristics are determined by the oscillating frequency of electrical field, the volume fraction of nanoparticles and wall electrical potential. The noteworthy results are that, the oscillating electrical field can result in the oscillation of nanofluids. However, such oscillation is strongly dependent on the electrical field frequency and the flow characteristics are significantly different for various frequencies. Moreover, when the nanoparticles are introduced into the time periodic electroosmotic flow, the oscillation can be restrained. This may be helpful to understand the electrohydrodynamic instability of nanofluids.

Oscillatory electro-magneto-kinetics of confined-Stokes-second-problem micro-flows

We semi-analytically investigate the electro-magneto-hydrodynamics of time periodic electroosmotic flow of a Newtonian electrolyte through microchannels with oscillating boundaries, resembling a confined-Stokes-second-problem type system. Herein, a constant orthogonal magnetic field and a constant transverse electric field have been used along with the driving time periodic electric field to have better control over mixing in the microchannel or to augment the pumping. The Poisson–Boltzmann equation has been solved with Debye–Hückel linearization for the thin electric double layer to obtain the electric potential distribution. We determine the flow field for low Hartmann number (Ha) cases by the regular perturbation method. Furthermore, Laplace transformation has been used to solve the flow field for each order in the obtained perturbation series. We have obtained the solution of flow field up to O(Ha) and found an excellent match with the complete numerical solution for our range of Ha. The dependence of flow field on dimensionless parameters, such as Ha, electrokinetic number (M), and Womersley number (Wo), has been discussed thoroughly, where Ha and M are functions of the strength of applied magnetic field and transverse electric field, respectively, and Wo is the function of Debye length, kinematic viscosity, and frequency of the time periodic electric field. Interestingly, for large values Wo, we find wave like motion in the flow field, which induces vorticity as well as better mixing caliber. Additionally, we find that the interplay between Ha and M controls the mixing and modifies the flow rate according to the need. Various combinations of such parameters have been discussed to promote mixing as well as pumping for such strongly coupled microfluidic phenomena.

Time periodic pulse electroosmotic flow of Jeffrey fluids in a circular microchannel under the depletion effect

Time periodic pulse electroosmotic flow of Jeffrey fluids in a circular microchannel under the depletion effect

Time periodic electroosmotic flow in a pH-regulated parallel-plate nanochannel

In this paper, the separation of variables method is applied to investigate the effects of solution pH, background salt concentration and AC electric field frequency on time periodic electroosmotic flow in a pH-regulated parallel-plate nanochannel. The surface charge is generated by the protonation and deprotonation of the functional group SiOH. The background salt is KCl. The pH value of the solution is adjusted by HCl and KOH. Analytical and semi-analytical solutions for electric potential and velocity distributions are obtained. The results show that the electric potential caused by the electric double layer depends greatly on the solution pH and background salt concentration. The amplitudes of the velocity and flow rate of the time periodic electroosmotic flow decrease with the background salt concentration and increase with the deviation of the solution pH from the isoelectric point. In a nanochannel having a height less than 100 nm, the electroosmotic velocity amplitude is not affected by the AC electric field frequency because the oscillating Reynolds number is much less than unity.

Time periodic pulse electroosmotic flow of Jeffreys fluids through a parallel plate microchannel

AbstractThe purpose of this paper is to investigate the time periodic pulse electroosmotic flow (EOF) of Jeffreys fluids through a parallel plate microchannel. The driving mode of pulse EOF here is considered as a rectangle pulse. Using the method of Laplace transform, the analytical solution of velocity and volumetric flow rate of pulse EOF is derived. The effects of pertinent dimensionless parameters on the velocity and volumetric flow rate are discussed in detail. Results show that the pulse width is a valuable parameter for analyzing the influence of relaxation time and retardation time on magnitude of velocity and volumetric flow rate when the fluid flow reaches the steady state. Increasing the relaxation time reduces he magnitude of velocity and volumetric flow rate at low value pulse width , yet the trend is opposite for larger pulse width . The increase of retardation time will reduce the magnitude of velocity and volumetric flow rate no matter whether the value of pulse width is large or not. Furthermore, the frequency of velocity profile and volumetric flow rate is different because of the different pulse width . With the increase of pulse width , the different change frequency of velocity profile and volumetric flow rate slows down, which means a long cycle time. And as the relaxation time and pulse width grow, the time required for the fluid flow to reach a steady state will become longer. The conclusions have theoretical significance for biofluid based microfluidic transport systems driven by pulsed electric field.

Talk about Several Time Periodic Pulse Electroosmotic Flow of Maxwell Fluid in a Circular Microchannel

Using the method of Laplace transform, analytical expressions are derived for the time periodic pulse electroosmotic flow (EOF) velocity of the triangle and sawtooth of Maxwell fluid in circular microchannel. The solution involves analytically solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations of inverse Laplace transform, the effects of electrokinetic width K, relaxation time and pulse width a on the above several pulse EOF velocities are investigated. In addition, we focused on the comparison and analysis of the formulas and graphs between the triangle and sawtooth pulse EOF with the rectangle pulse EOF. The study found that there are obvious differences in formulas and graphs between triangle and sawtooth pulse EOF with rectangle pulse EOF, and the difference mainly depends on the different definitions of the three kinds of time periodic pulse waves. Finally, we also studied the stability of the above three kinds of pulse EOF and the influence of relaxation time on pulse EOF velocity under different pulse widths is discussed. We find that the rectangle pulse EOF is more stable than the triangle and sawtooth pulse EOF. For any pulse, as the pulse width a increases, the influence of the relaxation time on the pulse EOF velocity will be weakened.

Linearized lattice Boltzmann Method for time periodic electro-osmotic flows in micro- and nanochannels

Time periodic electro-osmosis (TPEO) is a popular means to pump liquids or manipulate species of interest in today’s micro- and nanofluidic devices. In this article, we propose a double distribution-function lattice Boltzmann (LB) model to describe its oscillatory flows coupled with electrokinetics in micro- and nanochannels. To remove advective effects, we derive the LB model from a linearized Boltzmann Bhatnagar–Gross–Krook-like equation and formulate its equations depending on the alternating current (AC) frequency, instead of time. This treatment facilitates a direct comparison of the LB results to experimental measurements in practical applications. We assessed accuracy of the proposed frequency-based Linearized LB model by simulating time periodic electro-osmotic flows (TPEOFs) with a thin and a thick electric double layer (EDL) at different Stokes parameters. The results are in excellent agreement with analytical solutions. The model was used to simulate TPEOFs with various EDL thicknesses and those driven by an AC electric field combined with an oscillatory pressure gradient. The simulations show distinct distributions of the electric potential and solution velocity subject to different length ratios and frequency ratios in the flows and interesting flow responses to compounding influences of the applied electric and mechanical driving fields. Importantly, diverse vortex patterns and vorticity variations were also revealed for TPEOFs in heterogeneously charged channels. These results demonstrate that the LB model developed in this article can well capture rich TPEO flow characteristics in micro- and nanochannels. It is effective for design and optimization of TPEO-based micro- and nanofluidic devices.

Dispersion for periodic electro-osmotic flow of Maxwell fluid through a microtube

This paper mainly studies the solute dispersion driven by the periodic oscillatory electro-osmotic flow of viscoelastic fluid described by Maxwell constitutive modeling. Series expansion and transform methods are used to solve the unsteady convection dispersion equation. Analytic expressions of the natural dispersion coefficient K(t) and the mean concentration Cm are derived. By numerical computation, the influences of several nondimensional parameters, such as electrokinetic width K, oscillating angular frequency ω of the external forced electrical field, oscillating Reynolds number Re and relaxation time De on the dispersion coefficient K(t) and mean concentration Cm are investigated. The augment in amplitude of K(t) and quick decrease of Cm reflect the enhancement of the mass transfer process. Results indicate that smaller K and ω lead to larger amplitude of K(t) and quicker reduction of Cm. Moreover, the increase in De also can magnify the amplitude of K(t) and decrease the mean concentration Cm. In addition, we find there exists a critical oscillating Reynold number Re by analyzing the variations of K(t) and Cm with Re. Finally, comparing to the case of Newtonian fluid by setting De=0, a more effective dispersion process for Maxwell fluid can be observed interestingly. The present study is likely to have important bearing on the problem of dispersion of tracers in blood flow through arteries.

Investigation of the effects of time periodic pressure and potential gradients on viscoelastic fluid flow in circular narrow confinements

In this paper we present an in-depth analysis and analytical solution for time periodic hydrodynamic flow (driven by a time-dependent pressure gradient and electric field) of viscoelastic fluid through cylindrical micro- and nanochannels. Particularly, we solve the linearized Poisson–Boltzmann equation, together with the incompressible Cauchy momentum equation under no-slip boundary conditions for viscoelastic fluid in the case of a combination of time periodic pressure-driven and electro-osmotic flow. The resulting solutions allow us to predict the electrical current and solution flow rate. As expected from the assumption of linear viscoelasticity, the results satisfy the Onsager reciprocal relation, which is important since it enables an analogy between fluidic networks in this flow configuration and electric circuits. The results especially are of interest for micro- and nanofluidic energy conversion applications. We also found that time periodic electro-osmotic flow in many cases is much stronger enhanced than time periodic pressure-driven flow when comparing the flow profiles of oscillating PDF and EOF in micro- and nanochannels. The findings advance our understanding of time periodic electrokinetic phenomena of viscoelastic fluids and provide insight into flow characteristic as well as assist the design of devices for lab-on-chip applications.

Alternating current electroosmotic flow in polyelectrolyte-grafted nanochannel

In this work, we investigate the time periodic electroosmotic flow (EOF) of an electrolyte solution through a slit polyelectrolyte-grafted (PE-grafted) nanochannel under applied alternating current (AC) electrical field. The PE-grafted nanochannel is represented by a rigid surface covered by a polyelectrolyte layer (PEL) in a brush-like configuration. Under Debye-Hückel approximation, we obtain analytical solutions of electrical potential in decoupled regime of PE-grafted nanochannel, where the thickness of PEL is independent of the electrostatic effects triggered by polyelectrolyte charges. Based upon the electrical potential obtained above, we calculate EOF velocities with uniform and non-uniform drag coefficients for PE-grafted nanochannel and compare their results. The effects of pertinent dimensionless parameters on EOF velocity amplitude are discussed in detail. Moreover, the amplitude of EOF velocity in a PE-grafted nanochannel is compared with that in a rigid one. It is shown that larger EOF velocity and volume flow rate are found for a PE-grafted nanochannel. In addition, AC EOF velocity is further investigated. The oscillation of velocity reduces and is restricted within the region near the PEL-electrolyte interface for higher oscillating Reynolds number Re.

Time periodic electroosmotic flow of micropolar fluids through microparallel channel

The time periodic electroosmotic flow of an incompressible micropolar fluid between two infinitely extended microparallel plates is studied. The analytical solutions of the velocity and microrotation are derived under the Debye-H¨uckel approximation. The effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and microrotation are investigated. The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1. The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid. However, the dependence of the microrotation on the related parameters mentioned above is complex. In order to describe these effects clearly, the dimensionless microrotation strength and the penetration depth of the microrotation are defined, which are used to explain the variation of the microrotation. In addition, the effects of various parameters on the dimensionless stress tensor at the walls are studied.

Analytical Solutions of Time Periodic Electroosmotic Flow in a Semicircular Microchannel

The time periodic electroosmotic flow of Newtonian fluids through a semicircular microchannel is studied under the Debye–Hückel approximation. Analytical series of solutions are found, and they consist of a time-dependent oscillating part and a time-dependent generating or transient part. Some new physical phenomena are found. The electroosmotic flow driven by an alternating electric field is not periodic in time, but quasi-periodic. There is a phase shift between voltage and flow, which is only dependent on the frequency of external electric field.

Solution of Time Periodic Electroosmosis Flow with Slip Boundary

Recent research confirms that slip of a fluid on the solid surface occurs at micrometer scale. Slip on solid surface may cause the change of interior material deformation which consequently leads to the change of velocity profile and stress field. This paper concerns the time periodic electroosmotic flow in a channel with slip boundary driven by an alternating electric field, which arises from the study of particle manipulation and separation such as flow pumping and mixing enhancement. Although exact solutions to various flow problems of electroosmotic flows under the no-slip condition have been obtained, exact solutions for problems under slip boundary conditions have seldom been addressed. In this paper, an exact solution is derived for the time periodic electroosmotic flow in two-dimensional straight channels under slip boundary conditions.

Effect of interfacial Maxwell stress on time periodic electro‐osmotic flow in a thin liquid film with a flat interface

Electro-osmotic flows (EOF) have seen remarkable applications in lab-on-a-chip based microdevices owing to their lack of moving components, durability, and nondispersive nature of the flow profiles under specifically designed conditions. However, such flows may typically suffer from classical Faradaic artifacts like electrolysis of the solvent, which affects the flow rate control. Such a problem has been seen to be overcome by employing time periodic EOFs. Electric field induced transport of a conductive liquid is another nontrivial problem that requires careful study of interfacial dynamics in response to such an oscillatory flow actuation. The present study highlights the role of electric field generated Maxwell stress and free surface potential along with the electric double layer thickness and forcing frequency, toward influencing the interfacial transport and fluid flow in free-surface electro-osmosis under a periodically varying external electric field, in a semi-analytical formalism. Our results reveal interesting regimes over which the pertinent interfacial phenomena as well as bulk transport characteristics may be favorably tuned by employing time varying electrical fields.

Time periodic electroosmosis of linear viscoelastic liquids over patterned charged surfaces in microfluidic channels

In the present study, we aim to highlight the interactions between fluid rheology and interfacial electrokinetic phenomenon pertaining to time periodic electroosmotic flows of viscoelastic fluids, obeying linearized Maxwell model, over charge-modulated substrates. We successfully demonstrate that by altering the forcing frequency, fluid rheology, and charge-patterning characteristics, one may obtain drastically altered flow fields and hence mixing characteristics. Accordingly, we suggest that one may explore the paradigm of enhanced microfluidic mixing by exploiting the fluid rheology, supplementing the traditionally used methods such as topographical and geometrical modifications.

Assessment of mesoscopic particle-based methods in microfluidic geometries

We assess the accuracy and efficiency of two particle-based mesoscopic simulation methods, namely, Dissipative Particle Dynamics (DPD) and Stochastic Rotation Dynamics (SRD) for predicting a complex flow in a microfluidic geometry. Since both DPD and SRD use soft or weakly interacting particles to carry momentum, both methods contain unavoidable inertial effects and unphysically high fluid compressibility. To assess these effects, we compare the predictions of DPD and SRD for both an exact Stokes-flow solution and nearly exact solutions at finite Reynolds numbers from the finite element method for flow in a straight channel with periodic slip boundary conditions. This flow represents a periodic electro-osmotic flow, which is a complex flow with an analytical solution for zero Reynolds number. We find that SRD is roughly ten-fold faster than DPD in predicting the flow field, with better accuracy at low Reynolds numbers. However, SRD has more severe problems with compressibility effects than does DPD, which limits the Reynolds numbers attainable in SRD to around 25-50, while DPD can achieve Re higher than this before compressibility effects become too large. However, since the SRD method runs much faster than DPD does, we can afford to enlarge the number of grid cells in SRD to reduce the fluid compressibility at high Reynolds number. Our simulations provide a method to estimate the range of conditions for which SRD or DPD is preferable for mesoscopic simulations.

Time Periodic Electroosmotic Flow of The Generalized Maxwell Fluids in a Semicircular Microchannel

Analytical solutions are presented using method of separation of variables for the time periodic electroosmotic flow (EOF) of linear viscoelastic fluids in semicircular microchannel. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson—Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of electric oscillating Reynolds number Re and Deborah number De on velocity amplitude are presented. For small Re, results show that the larger velocity amplitude is confined to the region near the charged wall when De is small. With the increase of the Deborah number De, the velocity far away the charged wall becomes larger for large Deborah number De. However, for larger Re, the oscillating characteristic of the velocity amplitude occurs and becomes significant with the increase of De, especially for larger Deborah number.

Alternating current (AC) electroosmotic flow of generalized Maxwell fluids through a circular microtube

An analytical solution for the time periodic electroosmotic flow (EOF) of the generalized Maxwell model through a circular microtube is presented by solving the linearized Poisson-Boltzmann equation, together with Cauchy momentum equation and General Maxwell constitutive equation. By numerical calculations, we find that for lower Ω and smaller De, classical plug-like profile of Newtonian fluids is reduced. At lower frequency, the flow field can extend to the whole microtube. At higher frequency, however, the velocity amplitude variations away from electric double layer (EDL) almost decrease to zero. In addition, larger De leads to rapid variations of EOF velocity profiles with increased amplitude. The velocity amplitude of microtube is larger than that of plate microchannel by comparison. Key words: Circular microtube, alternating current (AC) electroosmotic flow, generalized Maxwell fluid, normalized oscillation frequency, relaxation time.

A mathematical model of mixing enhancement in microfluidic channel with a constriction under periodic electro-osmotic flow

A microfluidic channel with a constriction produced poor mixing conditions under periodic electro-osmotic flow. However, the mixing performance may be enhanced significantly by altering other parameters. Numerical simulations are used to investigate the effect of the direct current electric field (EDC), phase difference (ϕ), and length of constriction (L). A mathematical model, based on the structural features of the Lagrange function rather than its application, is proposed to establish a relationship between the mixing performance and these three parameters. The feasibility analysis has been carried out, and the results are verified by the data from simulation and experiment.

Time periodic electroosmotic flow of the generalized Maxwell fluids between two micro-parallel plates with high Zeta potential

In this study, semi-analytical solutions are presented for the time periodic (electroosmotic flow) of linear viscoelastic fluids between micro-parallel plates. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the nonlinear Poisson-Boltzmann (P-B) equation, the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of the dimensionless wall Zeta potential0, the periodic EOF electric oscillating Reynolds number Re, and normalized relaxation times 1 on velocity profiles are presented. Results show that for prescribed electrokinetic width K, relaxation time 1 and oscillating Reynolds number Re, higher Zeta potential 0 will lead to larger amplitude of EOF velocity, and the variation of velocity is restricted to a very narrow region close to the Electric double-layer. In addition, with the increase of relaxation time 1, the elasticity of the fluid becomes conspicuous and the velocity variations can be expanded to the whole flow field. For prescribed Re, longer relaxation time 1 will lead to quick change of the EOF velocity profile, and the amplitude becomes larger gradually.