Time 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.

Numerical Study of the Time-Periodic Electroosmotic Flow of Viscoelastic Fluid through a Short Constriction Microchannel.

Electroosmotic flow (EOF) is of utmost significance due to its numerous practical uses in controlling flow at micro/nanoscales. In the present study, the time-periodic EOF of a viscoelastic fluid is statistically analyzed using a short 10:1 constriction microfluidic channel joining two reservoirs on either side. The flow is modeled using the Oldroyd-B (OB) model and the Poisson-Boltzmann model. The EOF of a highly concentrated polyacrylamide (PAA) aqueous solution is investigated under the combined effects of an alternating current (AC) electric field and a direct current (DC) electric field. Power-law degradation is visible in the energy spectra of the velocity fluctuations over a wide frequency range, pointing to the presence of elastic instabilities in the EOF. The energy-spectra curves of the velocity fluctuations under a DC electric field exhibit peaks primarily beneath 20 Hz, with the greatest peak being observed close to 6 Hz. When under both DC and AC electric fields, the energy spectra of the velocity fluctuations exhibit a peak at the same frequency as the AC electric field, and the highest peak is obtained when the frequency of the AC electric field is near 6 Hz. Additionally, the frequency of the AC electric field affects how quickly the viscoelastic EOF flows. Higher flow rates are obtained at relatively low frequencies compared to under the DC electric field, and the greatest flow rate is found close to 6 Hz. But as the frequency rises further, the flow rate falls. The flow rate falls to a level below the DC electric field when the frequency is sufficiently high.

Effect of ion partitioning on an oscillatory electro-osmotic flow on solute transport process of fractional Jeffrey fluid through polyelectrolyte-coated nanopore with reversible wall reaction

The ion-partitioning effects on solute transport phenomena of time-periodic electro-osmotic flow in fractional Jeffrey fluid are investigated through a polyelectrolyte layer (PEL)-coated conical nanopore within a reactive wall whose ends are connected with two large reservoirs. By considering the ion-partitioning effects, analytical solutions for the induced potential and the axial velocity are presented, respectively, from the modified Poisson–Boltzmann equation and the Cauchy momentum equation with the proper constitutive equation of the fractional Jeffrey fluid model in the exterior and interior of the PEL. The analytic solution of the convection–diffusion for solute transport is established in the entire domain. The influence of the oscillating Reynolds number Rew, permittivity ratio εr between two mediums, relaxation time λ1ω, retardation time λ2ω, phase partitioning coefficient σp, PEL fixed charge density qfix, Debye–Hückel parameter κa, and softness parameter λs are investigated in this study. Asymptotic solution for the axial velocity was also presented for low-oscillating Reynolds numbers and validated. The maximum axial velocity occurs when the permittivity between the PEL and electrolyte is the same for all models. The volumetric flow rate decreases with the increase in the PEL thickness, positive PEL charge density, and softness parameter in our study. The volume flow rate of the Newtonian fluid increased 24.07% for Maxwell fluid (λ1ω=5, α = 1) and 11.56% for Jeffrey fluid (λ1ω=5, λ1ω=1, α = 1, and β=0.5), when κa=25, Rew = 10, qfix = 5, d = 0.2, εr=0.6, and λs=1.0. The mass transport rate increases with relaxation time, tidal displacement, and permittivity ratio between these layers.

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.

Asymmetric boundary conditions and their relevance in minimal passive mass species transport in time-periodic electro-osmotic flows

A set of dimensionless groups along with constraints on their values are formulated to serve as an indication of the parametric combinations, leading to minimal enhancement of streamwise passive species transport in time-periodic electro-osmotic microchannel flows with asymmetric hydrodynamic slip and zeta potential boundaries. While the slip lengths and zeta potentials are mostly treated as uncoupled in the electrokinetic transport literature, we incorporate into the analysis wall surface charge/potential coupled apparent slip lengths and find that more than one minimal enhancement instances may be achieved during a zeta potential sweep, provided that the uncharged surface slip length ratio is large enough.

Control of Mass Flow-Rate of Viscoelastic Fluids Through Time-Periodic Electro-Osmotic Flows in a Microchannel

Abstract In the present research, we address the implications of the pulsating electric field on controlling mass flow-rate characteristics for the time-periodic electro-osmotic flow of a viscoelastic fluid through a microchannel. Going beyond the Debye-Hückel linearization for the potential distribution inside the Electric Double Layer, the Phan-Thien-Tanner constitutive model is employed to describe the viscoelastic behaviour of the fluid. The analytical/semi-analytical expressions for the velocity distribution corresponding to a steady basic part, and a transient perturbed part are obtained by considering periodic pulsations in the applied electrical field. Our results based on sinusoidal pulsations reveal that enhanced shear thinning characteristics of the viscoelastic fluids show higher amplitude of pulsations with the oscillations in the velocity gradients primarily contrived within the Electric Double Layer region. The amplitude of mass flow rates increases with increasing the viscoelastic parameter , whereas, the phase lag displays a reverse trend. The analysis for an inverse problem is extended where the required magnitude of electric field pulsations for a target mass flow rate in the form of sinusoidal pulsations. It is found that with increasing shear-thinning characteristics of the viscoelastic fluid, there is a progressive reduction in the required electric field strength to maintain an aimed mass flow rate. Besides, required electric fields for controlled mass flow with triangular and trapezoidal pulsations are also determined.

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.

Heat transfer in electrokinetic micro-pumps under the influence of various oscillatory excitations

Thermal characteristics of time-periodic electroosmotic flow are analyzed in a micro-annulus under the influence of various alternating electric fields. Representative hydrodynamic and thermal quantities, i.e. volumetric flow rate and Nusselt number, demonstrate oscillatory behaviors approaching a quasi-steady state if few periods of time elapse. An important parameter named dimensionless frequency, which normally affects the diffusion mechanism, is responsible for the penetration depth of momentum and energy into the fluid in the radial direction. The higher the dimensionless frequency, the smaller the transport phenomena diffuse radially into the bulk fluid; while the advection mechanism is intensified and consequently Nusselt number is increased. The cooling-mode mean Nusselt number is slightly smaller than the heating- mode one. A variety of waveforms is examined in the present research; their performances are then compared together using proper measures. A strength index is introduced to evaluate the relative ability of each individual excitation in a half period of time. A key parameter named thermal/frictional index is also utilized to assess the total effectiveness of the system in different circumstances especially when the basic excitation functions are applied. Unlike the vigorous square waveform, the sawtooth one is the most efficient.

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.

Analytical Solution of Time-Periodic Electroosmotic Flow through Cylindrical Microchannel with Non-Uniform Surface Potential.

Time-periodic electroosmotic flow (EOF) with heterogeneous surface charges on channel walls can potentially be used to mix species or reagent molecules in microfluidic devices. Although significant research efforts have been placed to understand different aspects of EOF, its role in the mixing process is still poorly understood, especially for non-homogeneous surface charge cases. In this work, dynamic aspects of EOF in a cylindrical capillary are analyzed for heterogeneous surface charges. Closed form analytical solutions for time-periodic EOF are obtained by solving the Navier–Stokes equation. An analytical expression of induced pressure is also obtained from the velocity field solution. The results show that several vortices can be formed inside the microchannel with sinusoidal surface charge distribution. These vortices change their pattern and direction as the electric field change its strength and direction with time. In addition, the structure and strength of the vorticity depend on the frequency of the external electric field and the size of the channel. As the electric field frequency or channel diameter increases, vortices are shifted towards the channel surface and the perturbed flow region becomes smaller, which is not desired for effective mixing. Moreover, the number of vorticities depends on the periodicity of the surface charge.

Time-Periodic Electro-Osmotic Flow With Nonuniform Surface Charges

Mixing in a microfluidic device is a major challenge due to creeping flow, which is a significant roadblock for development of lab-on-a-chip device. In this study, an analytical model is presented to study the fluid flow behavior in a microfluidic mixer using time-periodic electro-osmotic flow. To facilitate mixing through microvortices, nonuniform surface charge condition is considered. A generalized analytical solution is obtained for the time-periodic electro-osmotic flow using a stream function technique. The electro-osmotic body force term is accounted as a slip boundary condition on the channel wall, which is a function of time and space. To demonstrate the applicability of the analytical model, two different surface conditions are considered: sinusoidal and step change in zeta potential along the channel surface. Depending on the zeta potential distribution, we obtained diverse flow patterns and vortices. The flow circulation and its structures depend on channel size, charge distribution, and the applied electric field frequency. Our results indicate that the sinusoidal zeta potential distribution provides elliptical shaped vortices, whereas the step change zeta potential provides rectangular shaped vortices. This analytical model is expected to aid in the effective micromixer design.

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.

Time-periodic Electroosmotic Flow of Non-newtonian Fluids in Microchannels

The alternating current electroosmotic flow of a non-Newtonian power-law fluid is studied in a circular microchannel. A numerical method is employed to solve the non-linear Poisson-Boltzmann and the momentum equations. The main parameters which affect the flow field are the flow behavior index, the dimensionless zeta potential and the dimensionless frequency. At very low dimensionless frequencies (slow oscillatory motion, small channel size, or large effective viscosity), the plug-like velocity profiles similar to steady-state electroosmotic flow are observed at nearly all times. At very high dimensionless frequencies, the flow is shown to be restricted to a thin region near the channel wall, while the bulk fluid remains essentially stationary. Velocity distributions of pseudoplastics and dilatants may be widened at low values of the dimensionless frequency depending on the dimensionless zeta potential; at high dimensionless frequencies, however, both fluids represent enhanced velocity magnitudes with the dimensionless zeta potential. In the case of high shear rate and/or suddenly-started flows, pseudoplastics tend to produce higher velocities than dilatants. These two kinds of fluids may produce same velocity profiles relying on the value of the dimensionless zeta potential as well as the ratio of their flow behavior indexes.

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.

Thermal characteristics of time-periodic electroosmotic flow in a circular microchannel

A theoretical analysis is performed to explore the thermal characteristics of electroosmotic flow in a circular microchannel under an alternating electric field. An analytical approach is presented to solve energy equation, and then, the exact solution of temperature profiles is obtained by using the Green’s function method. This study reveals that the temperature field repeats itself for each half-period. Frequency has a strong influence on the thermal behavior of the flow field. For small values of the dimensionless frequency (small channel size, large kinematic viscosity, or small frequency), the advection mechanism is dominant in the whole domain and the resultant heating (Joule heating and wall heat flux) can be transferred by the complete flow field in the axial direction; while, the middle portion of the flow field at high dimensionless frequencies does not have sufficient time to transfer heat by advection, and the bulk fluid temperature, especially in heating, may consequently become greater than the wall temperature. In a particular instance of cooling mode, a constant surface temperature case is temporarily occurred in which the axial temperature gradient will be zero. For relatively high frequencies, the unsteady bulk fluid temperature in some radial positions at some moments may be equal to the wall temperature; hence instantaneous cylindrical surfaces with zero radial heat flux may occur over a period of time. Depending on the value and sign of the thermal scale ratio, the quasi-steady-state Nusselt number (time-averaged at one period) approaches a specific value as the electrokinetic radius becomes infinity.