Transient Electroosmotic Flow Research Articles

Impact of charged soft layers on electroosmosis of Maxwell fluids in soft nanochannels

In the present paper, we theoretically study the transient electroosmotic flow of general Maxwell fluids through the polyelectrolyte grafted nanochannel with a layered distribution of charges. By applying the method of Laplace transform, we semi-analytically obtain the transient electroosmotic flow from the Cauchy momentum equation and the Maxwell constitutive equation. For the nanochannels grafted with polyelectrolyte layers having different layered distributions of charges, we consider the influence of the dimensionless relaxation time, the dimensionless polyelectrolyte layer thickness, and the dimensionless drag coefficient on the transient electroosmotic flow. We present the results for some particular cases. First, we unravel that for the case of polyzwitterionic brush that the sum of positive and negative structural charges is zero, the total electroosmotic flow is non-zero. In particular, depending on charge distribution within the end part of polyelectrolyte layers, the direction of the electroosmotic flow can be reversed critically. Second, in order to quantitatively evaluate a reversal of electroosmotic flow for two polyelectrolyte layers of opposite signs, we introduce a critical number ks as the ratio between the layered charge densities of two polyelectrolyte layers. Increasing ks allows the electroosmotic flow to be reversed easily. We verify that adjusting charge distributions of the layer can intentionally control the direction of the flows as well as the strength of electroosmotic flow.

Start-Up Multilayer Electro-Osmotic Flow of Maxwell Fluids through an Annular Microchannel under Hydrodynamic Slip Conditions

The present investigation analyzes the transient multilayer electro-osmotic flow through an annular microchannel with hydrophobic walls. The fluids are considered immiscible and viscoelastic, following the Maxwell rheological model. In the problem examined, the linearized Poisson–Boltzmann and Cauchy momentum equations are used to determine the electric potential distribution and the flow field, respectively. Here, different interfacial phenomena are studied through the imposed boundary conditions, such as the hydrodynamic slip and specified zeta potentials at solid–liquid interfaces, the velocity continuity, the electroviscous stresses balance, the potential difference, and the continuity of electrical displacements at the interfaces between fluids. The semi-analytic solution uses the Laplace transform theory. In the results, the velocity profiles and velocity tracking show the oscillatory behavior of flow, which strongly depends on the dimensionless relaxation time. Furthermore, the hydrodynamic slip on the channel walls contributes to the release of energy stored in the fluids due to elastic effects at the start-up of the flow. Similarly, other dimensionless parameters are also investigated. This research aims to predict the parallel flow behavior in microfluidic devices under electro-osmotic effects.

The Transient Electroosmotic Flow of Maxwell Fluids and Heat Transfer in a Parallel Microchannel Using Caputo Fractional Derivative

In this work, we consider transient electroosmotic flow of fractional Maxwell fluids model derived for both velocity and temperature in a micro-channel. We use the Poisson-Boltzmann equation to describe the potential electric field applied along the length of the micro-channel. Exact solutions of both velocity and temperature were obtained using Laplace transform combined with finite Fourier sine transform. Due to the complexity of the equations for velocity and temperature, the inverse Laplace transform was obtained using the numerical inversion formula based on Gaver Stehfest’s algorithms. The numerical solutions were simulated with the help of Mathcard software and the graphical results showing the effects of time, relaxation time, electrokinetic width and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameter on the temperature distribution in the microchannel were presented and discussed. The results show that the applied electric field, the electroosmotic force, electrokinetic width, and relaxation time play vital role on the velocity profile in the micro-channel and the fractional parameter can be used to regulate both the velocity and temperature in the micro-channel. The effects of the various influential parameters on both fluid velocity and temperature distribution were found to be useful for the design of microfluidic devices. These devices could be useful for biomedical diagnosis and analysis, for clinical detection of viruses and bacteria in biological processes. Keywords: Caputo fractional derivative, Electro kinetic width, Electroosmotic flow, Heat transfer, Zeta potential,

Transient heat transfer and electro-osmotic flow of Carreau–Yasuda non-Newtonian fluid through a rectangular microchannel

PurposeThe purpose of this study is to investigate heat transfer and electrokinetic non-Newtonian flow in a rectangular microchannel in the developed and transient states.Design/methodology/approachThe Carreau–Yasuda model was considered to capture the non-Newtonian behavior of the fluid. The dimensionless forms of governing equations, including the continuity equation for the Carreau–Yasuda fluid, are numerically solved by considering the volumetric force term of electric current (DC).FindingsThe impact of pertinent parameters such as electrokinetic diameter (R), Brinkman number and Peclet number is examined graphically. It is observed that for increasing R, the bulk velocity decreases. The velocity of the bulk fluid reaches from the minimum to the maximum state across the microchannel over time. At the electrokinetic diameter of 400, the maximum velocity was obtained. Temperature graphs are plotted with changes in the various Brinkman number (0.1 < r < 0.7) at different times, and local Nusselt are compared against changes in the Peclet number (0.1 < ℘e < 0.5). The results of this study show that by increasing the Brinkman number from 0.25 to 0.7, the temperature along the microchannel doubles. It was observed that increasing the Peclet number from 0.3 to 0.5 leads to 200% increment of the Nusselt number along the microchannel in some areas along the microchannel. The maximum temperature occurs at Brinkman number of 0.7 and the maximum value of the local Nusselt number is related to Peclet number 0.5. Over time in the transient mode, the Nusselt number also decreases along the microchannel. By the increasing of time, the temperature increases at given value of Brinkman, which is insignificant at Brinkman number of 0.1. The simulation results have been verified by Newtonian and non-Newtonian flows with adequate accuracy.Originality/valueThis study contributes to discovering the effects of transient flow of electroosmotic flow for non-Newtonian Carreau–Yasuda fluid and transient heat transfer through rectangular microchannel. To the authors’ knowledge, the said investigation is yet not available in existing literature.

Dynamical aspects of transient electro-osmotic flow of Burgers' fluid with zeta potential in cylindrical tube

Abstract In this article, we consider the flow of a Burgers’ fluid of transient electro-osmotic type in a small tube with a circular cross-section. Analytical results are found for the transient velocity and, electric potential profile by solving the Navier–Stokes and the linearized Poisson–Boltzmann equations. Moreover, these equations are solved with the help of the integral transform method. We consider cases in which the velocity of the fluid changes with time and those in which the velocity of the fluid does not change with time. Furthermore, special results for classical fluids such as Newtonian, second grade, Maxwell, and Oldroyd-B fluids are obtained as the particular cases of the outcomes of this work and that these results actually strengthen the results of the solution. This study of the nonlinear problem of Burgers’ fluid in a specified physical model will help us to understand the behavior of blood clotting and the block of any kind of problem in which this type of fluid is used. The solution of the complex velocity profile of Burgers’ fluid will help us in the future to solve the problems in which this transient electro-osmotic type of small tube is involved. At the end, numerical results are shown graphically that can help us to understand the complex behavior of the Burgers’ fluid, and also the analysis of the Burgers’ fluid shows dissimilarity with other fluids that are considered in this work.

Transient Analysis of the Electro-Osmotic Flow of Multilayer Immiscible Maxwell Fluids in an Annular Microchannel

This work investigates the transient multilayer electro-osmotic flow of viscoelastic fluids through an annular microchannel. The dimensionless mathematical model of multilayer flow is integrated by the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, the rheological Maxwell model, initial conditions, and the electrostatic and hydrodynamic boundary conditions at liquid-liquid and solid-liquid interfaces. Although the main force that drives the movement of fluids is due to electrokinetic effects, a pressure gradient can also be added to the flow. The semi-analytical solution for the electric potential distribution and velocity profiles considers analytical techniques as the Laplace transform method, with numerical procedures using the inverse matrix method for linear algebraic equations and the concentrated matrix exponential method for the inversion of the Laplace transform. The results presented for velocity profiles and velocity tracking at the transient regime reveal an interesting oscillatory behavior that depends on elastic fluid properties via relaxation times. The time required for the flow to reach steady-state is highly dependent on the viscosity ratios and the dimensionless relaxation times. In addition, the influence of other dimensionless parameters on the flow as the electrokinetic parameters, zeta potentials at the walls, permittivity ratios, ratio of pressure forces to electro-osmotic forces, number of fluid layers, and annular thickness are investigated. The findings of this study have significant implications for the precise control of parallel fluid transport in microfluidic devices for flow-focusing applications.

Transient Two-Layer Electroosmotic Flow and Heat Transfer of Power-Law Nanofluids in a Microchannel.

To achieve the optimum use and efficient thermal management of two-layer electroosmosis pumping systems in microdevices, this paper studies the transient hydrodynamical features in two-layer electroosmotic flow of power-law nanofluids in a slit microchannel and the corresponding heat transfer characteristics in the presence of viscous dissipation. The governing equations are established based on the Cauchy momentum equation, continuity equation, energy equation, and power-law nanofluid model, which are analytically solved in the limiting case of two-layer Newtonian fluid flow by means of Laplace transform and numerically solved for two-layer power-law nanofluid fluid flow. The transient mechanism of adopting conducting power-law nanofluid as a pumping force and that of pumping nonconducting power-law nanofluid are both discussed by presenting the two-layer velocity, flow rates, temperature, and Nusselt number at different power-law rheology, nanoparticle volume fraction, electrokinetic width and Brinkman number. The results demonstrate that shear thinning conducting nanofluid represents a promising tool to drive nonconducting samples, especially samples with shear thickening features. The increase in nanoparticle volume fraction promotes heat transfer performance, and the shear thickening feature of conducting nanofluid tends to suppress the effects of viscous dissipation and electrokinetic width on heat transfer.

Modeling electro-osmotic flow and thermal transport of Caputo fractional Burgers fluid through a micro-channel

In this paper, we construct transient electro-osmotic flow of Burgers’ fluid with Caputo fractional derivative in a micro-channel, where the Poisson–Boltzmann equation described the potential electric field applied along the length of the microchannel. The analytical solution for the component of the velocity profile was obtained, first by applying the Laplace transform combined with the classical method of partial differential equations and, second by applying Laplace transform combined with the finite Fourier sine transform. The exact solution for the component of the temperature was obtained by applying Laplace transform and finite Fourier sine transform. Further, due to the complexity of the derived models of the governing equations for both velocity and temperature, the inverse Laplace transform was obtained with the aid of numerical inversion formula based on Stehfest's algorithms with the help of MATHCAD software. The graphical representations showing the effects of the time, retardation time, electro-kinetic width, and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameters on the temperature distribution in the micro-channel were presented and analyzed. The results show that the applied electric field, electro-osmotic force, electro-kinetic width, and relaxation time play a vital role on the velocity distribution in the micro-channel. The fractional parameters can be used to regulate both the velocity and temperature in the micro-channel. The study could be used in the design of various biomedical lab-on-chip devices, which could be useful for biomedical diagnosis and analysis.

Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

Analysis of Transient Pulse Electroosmotic Flow of Maxwell Fluid through a Circular Micro-Channel Using Laplace Transform Method

A semi-analytical solution is presented using method of Laplace transform for the transient pulse electroosmotic flow (EOF) of Maxwell fluid in a circular micro-channel. The driving mode of pulse EOF here is considered as an ideal rectangle pulse. The solution involves solving the linearized Poisson-Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. The results show that the profiles of pulse EOF velocity vary rapidly and gradually stabilize as the increase of time within a half period. The velocity profiles at the center of the micro-channel increase significantly with relaxation time , especially for the smaller pulse width a. However, as the pulse width a increases, this change will be less obvious. At the same time, the different change frequency of velocity profiles will slow down, which means a long cycle time. Additionally, the time needed to attain the steady status becomes longer with the increase of relaxation time and pulse width a.

Asymmetric temporal variation of oscillating AC electroosmosis with a steady pressure-driven flow

In most electrokinetic flows in micro-/nanofluidics, electroosmotic flow (EOF) is always a fundamental phenomenon. When an external AC electric field is applied, there will be a transient EOF velocity, which is crucial for understanding the mechanism of the unsteady AC EOF. However, the transient flow velocity cannot be experimentally measured with sufficiently and simultaneously temporal and spatial resolution. Here we report that under a strong AC electric field, an asymmetric temporal variation of oscillating EOF (OEOF) can be generated near the electric double layer (EDL) on the bottom wall of a microchannel. The flow is measured by laser-induced fluorescence photobleaching anemometer (LIFPA). Both the flow velocity of the OEOF and the linearly related internal electric field in the microchannel are theoretically governed by an inviscid Burgers’ equations with an external forcing term and controlled by two coefficients which represent the magnitudes of linear ( $${Z}_{l}$$ ) and nonlinear ( $${Z}_{nl}$$ ) terms. These two coefficients are separately determined by five dimensionless parameters, including Stokes number ( $${St}$$ ), aspect ratio ( $$\gamma$$ ), Schmidt number ( $${Sc}$$ ), Peclet number of mean flow velocity ( $${P}_{e, U}$$ ) and Peclet number of electrophoresis ( $${P}_{e, {EP}}$$ ). In this work, the influence of $${P}_{e, U}$$ and $${P}_{e, {EP}}$$ which are tightly related to the local mean flow velocity and the amplitude of AC electric field is investigated. When the electric field is low, $${P}_{e, U}\gg {P}_{e,{EP}}$$ and accordingly $${Z}_{l}\gg {Z}_{nl}$$ , a temporal symmetry of the time series of velocity is observed. However, when the electric field is high, $${P}_{e, U}\ll {P}_{e, {EP}}$$ and $${Z}_{l}\ll {Z}_{nl}$$ , then the periodicity and temporal symmetry of OEOF can be significantly broken and a temporal asymmetry of the time series of velocity is resulted in, especially under the square wave external electric field. We also find increased mean flow velocity and saturation of velocity fluctuations with the increasing electric field. This work provides a new methodology to study unsteady electrokinetic flows.

Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel.

In this investigation, the transient electroosmotic flow of multi-layer immiscible viscoelastic fluids in a slit microchannel is studied. Through an appropriate combination of the momentum equation with the rheological model for Maxwell fluids, an hyperbolic partial differential equation is obtained and semi-analytically solved by using the Laplace transform method to describe the velocity field. In the solution process, different electrostatic conditions and electro-viscous stresses have to be considered in the liquid-liquid interfaces due to the transported fluids content buffer solutions based on symmetrical electrolytes. By adopting a dimensionless mathematical model for the governing and constitutive equations, certain dimensionless parameters that control the start-up of electroosmotic flow appear, as the viscosity ratios, dielectric permittivity ratios, the density ratios, the relaxation times, the electrokinetic parameters and the potential differences. In the results, it is shown that the velocity exhibits an oscillatory behavior in the transient regime as a consequence of the competition between the viscous and elastic forces; also, the flow field is affected by the electrostatic conditions at the liquid-liquid interfaces, producing steep velocity gradients, and finally, the time to reach the steady-state is strongly dependent on the relaxation times, viscosity ratios and the number of fluid layers.

Transient Electro-osmotic Slip Flow of an Oldroyd-B Fluid with Time-fractional Caputo-Fabrizio Derivative

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally, Stehfest’s algorithm is used for inverse Laplace transform. The solutions for fractional Maxwell, ordinary Maxwell and ordinary Newtonian fluids are obtained as limiting cases of the obtained solution. Finally, the influence of fractional and some important physical parameters on the fluid flow are spotlighted graphically.

Transient electro-osmotic flow of generalized second-grade fluids under slip boundary conditions

This work investigates the transient slip flow of viscoelastic fluids in a slit micro-channel under the combined influences of electro-osmotic and pressure gradient forcings. We adopt the generalized second-grade fluid model with fractional derivative as the constitutive equation and the Navier linear slip model as the boundary conditions. The analytical solution for velocity distribution of the electro-osmotic flow is determined by employing the Debye–Hückel approximation and the integral transform methods. The corresponding expressions of classical Newtonian and second-grade fluids are obtained as the limiting cases of our general results. These solutions are presented as a sum of steady-state and transient parts. The combined effects of slip boundary conditions, fluid rheology, electro-osmotic, and pressure gradient forcings on the fluid velocity distribution are also discussed graphically in terms of the pertinent dimensionless parameters. By comparison with the two cases corresponding to the Newtonian fluid and the classical second-grade fluid, it is found that the fractional derivative parameter β has a significant effect on the fluid velocity distribution and the time when the fluid flow reaches the steady state. Additionally, the slip velocity at the wall increases in a noticeable manner the flow rate in an electro-osmotic flow.

Transient electroosmosis of a Maxwell fluid in a rotating microchannel.

The transient electroosmotic flow of Maxwell fluid in a rotating microchannel is investigated both analytically and numerically. We bring out the complex dynamics of the flow during the transience due to the combination of rotation and rheological effects. We show the regimes of operation under which our analysis holds the most significance. We also shed some light on the volumetric flow rate characteristics as dictated by the underlying flow physics. Mainly we show and analyze the various regimes of operation under which viscoelastic effects actuated by electroosmotic forcing dominate over Coriolis forces and vice versa, which has not been studied before. We also observe that the analytical solution compares well with the numerical solution. We believe that the results from the present study could potentially have far reaching applications in bio-fluidic microsystems where fluids such as blood, mucus and saliva may be involved.

Unsteady Rotating Electroosmotic Flow Through a Slit Microchannel

AbstractUsing the method of Laplace transform, an analytical solution of unsteady rotating electroosmotic flow (EOF) through a parallel plate microchannel is presented. The analysis is based upon the linearized Poisson-Boltzmann equation describing electrical potential distribution and the Navies Stokes equation representing flow field in the rotating coordinate system. The discrepancy of present problem from classical EOF is that the velocity fields are two-dimensional. The rotating EOF velocity profile and flow rate greatly depend on time t, rotating parameter ω and the electrokinetic width K (ratio of half height of microchannel to thickness of electric double layer). The influence of the above dimensionless parameters on transient EOF velocity, volume flow rate and EO spiral is investigated.

Analytical solution of the transient electro-osmotic flow of a generalized fractional Maxwell fluid in a straight pipe with a circular cross-section

In this study, we examine the transient electro-osmotic flow of a generalized Maxwell fluid with a fractional derivative in a narrow capillary tube. Using the integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson–Boltzmann equation and the Navier–Stokes equation. We show that the distribution and establishment of the velocity comprises two parts: the steady and unsteady parts. We demonstrate the effects of the relaxation time, fractional derivative parameter, and the Debye–Hückel parameter on the generation of flow in a graphical manner and we analyze them numerically. The velocity overshoot and oscillation are observed and discussed.

Transient electroosmotic flow of Maxwell fluids in a slit microchannel with asymmetric zeta potentials

In this work, the transient electroosmotic flow through a slit microchannel formed by two parallel walls with asymmetric zeta potentials is studied. An appropriate combination of the momentum equation together with the rheological Maxwell model leads to a hyperbolic partial differential equation that permits to determine the velocity profile, which is found analytically by the method of separation of variables. Adopting the nondimensionalized version of the governing equations allows us to obtain the following dimensionless parameters that control the fluid flow conditions: the dimensionless relaxation time of the fluid, λ̄1, and the ratio of the zeta potentials for both walls of the microchannel, Rζ. The significance of the former is based on that the fluid flow of Maxwell fluids reaches the steady state just controlled by the value of this parameter. For the Newtonian case, the steady state is directly established depending on values of Rζ. The velocity profiles of the fluid flow exhibit a symmetric or asymmetric shape and a peculiar oscillatory behavior in the transient stage, depending on the competition between the viscous and elastic forces.

Exact Solutions of Electro-Osmotic Flow of Generalized Second-Grade Fluid with Fractional Derivative in a Straight Pipe of Circular Cross Section

Abstract The transient electro-osmotic flow of generalized second-grade fluid with fractional derivative in a narrow capillary tube is examined. With the help of the integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson-Boltzmann equation and the Navier-Stokes equation. It was shown that the distribution and establishment of the velocity consists of two parts, the steady part and the unsteady one. The effects of retardation time, fractional derivative parameter, and the Debye-Hückel parameter on the generation of flow are shown graphically.

Closed-form solutions of transient electro-osmotic flow driven by AC electric field in a microannulus

The time-periodic electro-osmotic flow of Newtonian fluids through a microannulus is studied in the Debye-Hückel approximation. Analytical series solutions for velocity and flow rate are presented with the help of an integral transform. The expression for the distribution of the velocity profile consists of a time-dependent oscillating part and a time-dependent generating or transient one, and the normalized velocity function is independent of the Reynolds number, which is very different from previous results. Then the effects of the electrokinetic width K, the wall zeta potential ratio β, and the frequency of applied external electric field ω on the distribution of the velocity profiles and flow rates are discussed numerically and theoretically. Some new physical and chemical phenomena are found theoretically. We point out that the electro-osmotic 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 the external electric field.