Electrokinetic Width Research Articles

Effects of Hydrodynamic Slip on Rotating Magneto-Electro-Osmotic Flow through a Periodic Microfluidic System

The study is concerned with the effects of slip velocity on a non-uniform rotating electroosmotic flow in a micro-channel. Electroosmotic driven fluid flow is obtained by the application of a potential electric field which describes the nonlinear Poisson-Boltzmann equation. The external electric potential is applied along the x and y directions which provides the necessary driving force for the electroosmotic flow. Two semi analytical techniques were employed to obtain the solution of the nonlinear Poisson-Boltzmann equation. The first method incorporates the complex normalized function into the Laplace transform and the second method is the combination of the Laplace transform and D’Alembert technique. Further, the complex normalized function became difficult to invert in closed form, hence we resort to the use of numerical procedure based on the Stehfest's algorithm. The graphical solutions to the axial velocities on both x and y components have been obtained and analyzed for the effects of the slip parameter and the amplitude of oscillation of the micro-channel walls. The solutions show that the rotating electroosmotic flow profile and the flow rate greatly depend on time, rotating parameter and the electrokinetic width. The results also indicate that the applied electric field and the electroosmotic force, play vital role on the velocity distribution in the micro-channel. The fact is that the solutions obtained in this study synthesize most of the solutions available in the previous studies. Finally, this study will be relevant in biological applications particularly in pumping mechanism to help transport substances within different parts of the systems.

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.

Effects of Retardation Time on Non-Newtonian Electro-Osmotic Flow in a Micro-Channel

In this paper, we have studied the effects of retardation time of non-Newtonian Oldroyd-B type fluid driven by Helmholtz-Smoluchowski velocity in a micro-channel. The potential electric field is applied along the length of the micro-channel describing by the Poisson–Boltzmann equation. The governing model equation was solved analytically using the classical method of partial differential equations. Analytical solution was simulated with the help of MATHEMATICA software and the graphical results for various physical flow parameters were analyzed. Results shows that for larger values of retardation time of a viscoelastic fluid the higher the viscoelastic effect of the fluid and this makes it to need more time for the stress to respond to deformation. Also, the electrokinetic width of micro-channel play a vital rule on the performance of velocity distribution.

周期壁面电势调制下平行板微管道中的电磁电渗流动

Two-dimensional magnetohydrodynamic (MHD) electroosmotic flow (EOF) in zeta potential patterned micro-parallel channels was studied. The flow was driven by the combination of the Lorentz force and the electric field force produced due to an externally imposed vertical magnetic field and two horizontal electric fields. The analytical solutions of stream function and velocity distribution were obtained under the condition of hydrodynamic slippage. The variations of velocities with related non-dimensional parameters, such as Hartmann number Ha,slip length B and electrokinetic width K were addressed in detail. Results show that, the patterned charged surfaces induce a vertical velocity component leading to the formation of the vortexes. Also, the magnitudes of velocities increase with slip length B and electrokinetic width K.Moreover, it is interesting to note that the magnitudes of velocities become small with the increasing value of Ha, unlike the situation where there exists a critical value of Ha in one-dimensional flow. The present theoretical results can be utilized to design efficient microfluidic devices.

Magnetohydrodynamic Electroosmotic Flow with Patterned Charged Surface and Modulated Wettability in a Parallel Plate Microchannel**Supported by the National Natural Science Foundation of China under Grant Nos. 11772162 and 11472140, the Natural Science Foundation of Inner Mongolia Autonomous Region of China under Grant Nos. 2016MS0106 and 2018MS01015, the Inner Mongolia Grassland Talent under Grant No. 12000-12102013, the Research Program of science

This paper investigates the magnetohydrodynamic (MHD) electroosmotic flow (EOF) of Newtonian fluid through a zeta potential modulated parallel plate microchannel with patterned hydrodynamic slippage. The driven mechanism of the flow originates from the Lorentz force generated by the interaction of externally imposed lateral electric field Ey and vertical magnetic field Bz and electric field force produced by an externally applied electric field Ex. It is assumed that the wall zeta potential and the slip length are periodic functions of axial coordinate x, an analytical solution of the stream function is achieved by utilizing the method of separation of variables and perturbation expansion. The pictures of streamlines are plotted and the vortex configurations produced in flow field due to patterned wall potential and hydrodynamic slippage are discussed. Based on the stream function, the velocity field and volume flow rate are obtained, which are greatly depend on some dimensionless parameters, such as slip length ls, electrokinetic width λ, the amplitude δ of the patterned slip length, the amplitude m of the modulated zeta potential and Hartmann number Ha. The variations of velocity and volume flow rate with these dimensionless parameters are discussed in details. These theoretical results may provide some guidance effectively operating micropump in practical nanofluidic applications.

Thermally Fully Developed Electroosmotic Flow of Power-Law Nanofluid in a Rectangular Microchannel.

The hydrodynamic and thermal behavior of the electroosmotic flow of power-law nanofluid is studied. A modified Cauchy momentum equation governing the hydrodynamic behavior of power-law nanofluid flow in a rectangular microchannel is firstly developed. To explore the thermal behavior of power-law nanofluid flow, the energy equation is developed, which is coupled to the velocity field. A numerical algorithm based on the Crank–Nicolson method and compact difference schemes is proposed, whereby the velocity, temperature, and Nusselt number are computed for different parameters. A larger nanoparticle volume fraction significantly reduces the velocity and enhances the temperature regardless of the base fluid rheology. The Nusselt number increases with the flow behavior index and with electrokinetic width when considering the surface heating effect, which decreases with the Joule heating parameter. The heat transfer rate of electroosmotic flow is enhanced for shear thickening nanofluids or at a greater nanoparticle volume fraction.

Electro-osmotic pumping through a bumpy microtube: Boundary perturbation and detection of roughness

To machine precision, a micro-duct cannot be fabricated without producing surface roughness. It is of essential importance to examine the effects and predict the level of roughness on electro-osmotic (EO) pumping for ducts of fundamental shapes. In this study, we consider a bumpy microtube with its wall shape modeled by the product of two sinusoidal functions. Boundary perturbation is carried out with respect to the amplitude roughness ε (relative to the Debye length) up to the second-order by considering the Debye-Hückel approximation and viscous Stokes equation for the electrolyte transport. Besides the amplitude roughness ε, the key parameters include the azimuthal wave number n and the axial wave number α of the bumpiness, as well as the non-dimensional electrokinetic width K. It is shown that the EO pumping rate Q is modified by a second-order term −ε2πχ, namely, Q = Q0 − ε2πχ, where Q0 denotes the pumping rate through the smooth tube. The net effect χ = χ1 + χ2 comprises two components: χ1 = χ1(K) < 0 increases with increasing K, representing a pure gain, while χ2 has no definite sign and is a complex function of K, n, and α. In particular, χ is negative at small α whilst being positive at large α, and the dividing line of signs also depends on K. For small α (<1), χ increases with increasing n at all K, while for large α (>1), χ decreases with increasing n at large K (>20). For a given number of oscillations Ac = nα (>1), there exists an intermediate n at which the EO pumping rate is maximized at small K (<20). Moreover, we identify a long-wavelength limit singularity in the EO pumping rate as α → 0 for all n, i.e., in the longitudinal sense. In addition, the velocity component along the tube axis is modified by a second-order term of the roughness, though the same velocity component near the wavy wall exhibits periodic behaviors in phase with the wall roughness. Physical reasoning is given to all the derived mathematical results, and their implication in practical applications as a model for predicting tube roughness is explained. As the tube shape represents a conduit of practical use, a particular emphasis is placed upon potential applications of the derived result.

Streaming potential analysis on the hydrodynamic transport of pressure-driven flow through a rotational microchannel

In this study, the streaming potential and electrokinetic energy conversion efficiency are discussed under the low zeta potential approximation through a microparallel channel with consideration of rotational effect. By solving Poisson-Boltzmann equation and modified Navier–Stokes equation, the analytical expressions of the streaming potential and electrokinetic energy conversion efficiency in the electrolyte solution are obtained. Combining with the numerical calculation, the influences of the dimensionless electrokinetic width K and the rotational angular velocity ω on streaming potential and the electrokinetic energy conversion efficiency are discussed. The results show that the streaming potential fields decrease both in mainstream and secondary directions with the electrokinetic width K, it decreases with the non-dimensional rotational angular velocity in the mainstream direction and it shows a first increasing then decreasing trend in the secondary flow direction. In addition, the influences of related non-dimensional parameters, including electrokinetic width, wall electric potential and rotational angular velocity, on the electrokinetic energy conversion efficiency are also discussed in detail. The rotating effect can enhance conversion efficiency comparing to the case of no rotation. The increase of wall electric potential gives rise to an augment in electrokinetic energy conversion efficiency. These theoretical results make sense to the energy harvesting in the rotating microfluidic systems.

Rotating electroosmotic flow of two-layer fluids through a microparallel channel

In this study, rotating electroosmotic flow of two immiscible fluids in a microparallel channel is investigated. The electric double layer (EDL) potential distribution is considered by using linear Poisson–Boltzmann (P-B) equation. Based upon the analytical charge density distribution, an analytical solution of flow velocity can be obtained by solving the modified Navier–Stokes (N-S) equation in the rotating frame. Besides, the equilibrium condition of stress, including shear stress and Maxwell stress, is taken into account as boundary conditions at the interface to analyze the distribution of the two-layer fluids velocity. It is found that, due to the rotational effect of the microchannel, the Coriolis force can generate a (secondary) transverse flow in horizontal direction perpendicular to the mainstream direction and the velocity amplitude of two-layer fluids has a reduced flow along the mainstream direction. In addition, the results indicate that double fluid velocity distribution is strongly influenced by several non-dimensional parameters, such as the dielectric constant ratio ε, density ratio ρ, viscosity ratio μ of the two layer fluids, rotating angular velocity ω, interface zeta potential difference Δφ*, interface charge density jump Q, the normalized thickness of two layer Newtonian fluids h1*, h2* and electrokinetic width K1, K2. Smaller μ and larger ε, Δφ* lead to larger velocity amplitude for lower fluid (noted as fluid II), but an opposite trend can be found for upper fluid (namely fluid I). The increase of Q or decrease of ρ leads to the increases of velocity amplitude for both fluid I and fluid II. Furthermore, interestingly, we observe that the mainstream speed at the interface does not depend on the interface zeta potential difference Δφ*, the dielectric constant ratio ε and electrokinetic width K2 of fluid II when the depths of h1* and h2* are identical.

The Parametric Study of Electroosmotically Driven Flow of Power-Law Fluid in a Cylindrical Microcapillary at High Zeta Potential.

Due to the increasingly wide application of electroosmotic flow in micromachines, this paper investigates the electroosmotic flow of the power-law fluid under high zeta potential in a cylindrical microcapillary for different dimensionless parameters. The electric potential distribution inside a cylindrical microcapillary is presented by the complete Poisson-Boltzmann equation applicable to an arbitrary zeta potential. By solving the Cauchy momentum equation of power-law fluids, the velocity profile, the volumetric flow rate, the average velocity, the shear stress distribution and dynamic viscosity of electroosmotic flow of power-law fluids in a cylindrical microcapillary are studied for different low/high zeta potential, flow behavior index, dimensionless electrokinetic width. The velocity profile gradually changes from parabolic to plug-like shape as the flow behavior index decreases or as the dimensionless electrokinetic width increases. For shear thinning fluids, the viscosity is greater in the center of the microchannel than that near the channel wall, the reverse is true for the shear thickening fluids. Greater volumetric rate and average velocity can be achieved by enhancing the dimensionless electrokinetic width, flow behavior index and zeta potential. It is noted that zeta potential and flow behavior index are important parameters to adjust electroosmotic flow behavior in a cylindrical microcapillary.

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.

Transient electro-magneto-hydrodynamic two-phase blood flow and thermal transport through a capillary vessel

Therapies with magnetic/electromagnetic field are employed to relieve pains or, to accelerate flow of blood-particles, particularly during the surgery. In this paper, a theoretical study of the blood flow along with particles suspension through capillary was made by the electro-magneto-hydrodynamic approach. Analytical solutions to the non-dimensional blood velocity and non-dimensional particles velocity are obtained by means of the Laplace transform with respect to the time variable and the finite Hankel transform with respect to the radial coordinate. The study of thermally transfer characteristics is based on the energy equation for two-phase thermal transport of blood and particles suspension with viscous dissipation, the volumetric heat generation due to Joule heating effect and electromagnetic couple effect. The solution of the nonlinear heat transfer problem is derived by using the velocity field and the integral transform method. The influence of dimensionless system parameters like the electrokinetic width, the Hartman number, Prandtl number, the coefficient of heat generation due to Joule heating and Eckert number on the velocity and temperature fields was studied using the Mathcad software. Results are presented by graphical illustrations.

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.

Electroosmotic flow through a microtube with sinusoidal roughness

In this paper, a perturbation method is introduced to study the electroosmotic flow (EOF) in a microtube with slightly corrugated wall. The corrugation of the wall is described as periodic sinusoidal wave with small amplitude. Based on linearized Poisson–Boltzmann equation and the Cauchy momentum equation, the perturbation solutions for velocity and volume flow rate are obtained. The influences of the amplitude δ, the wave number λ, the nondimensional electrokinetic width K and the nondimensional pressure gradient G on the velocity and flow rate are analyzed graphically and discussed in detail. The results show that the flow rate Q of the EOF through a corrugated channel tends to the flow rate Q0 of the EOF through a smooth channel when amplitude δ tends to zero, but the flow rate Q is always smaller than the flow rate Q0 in the smooth channel. The flow retardation of the roughness on the flow rate of the EOF always increases with the augment of the nondimensional electrokinetic width K.

Heat transfer of nanofluids in microtubes under the effects of streaming potential

In the current study, the heat transfer characteristics of thermally developed electrokinetic flow of the nanofluid (water-Al2O3) through a microtube are investigated. The flow is actuated by the combined effects of pressure-driven and electroosmotic transport induced by streaming potential. A uniform flux at the surfaces of the microtube is exerted and the influences of viscous dissipation as well as Joule heating are taken into account. Based on the Debye–Hückel linearization approximation, the relevant velocity and temperature distributions are derived. Furthermore, Nusselt number variations are evaluated. Physical feathers of pertinent parameters such as electrokinetic width K, volume friction ϕ, slip lengthen γ, Brinkman number Br and Joule parameter S are presented graphically and discussed in detail. It is revealed that nanoparticles have significant influences on the electrokinetics and heat transfer characteristics of nanofluids under the streaming potential.

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.

Electroosmotic flow through a microparallel channel with 3D wall roughness.

In this paper, a perturbation method is introduced to study the EOF in a microparallel channel with 3D wall roughness. The corrugations of the two walls are periodic sinusoidal waves of small amplitude in two directions either in phase or half-period out of phase. Based on linearized Poisson-Boltzmann equation, Laplace equation, and the Navier-Stokes equations, the perturbation solutions of velocity, electrical potential, and volume flow rate are obtained. By using numerical computation, the influences of the wall corrugations on the mean velocity are analyzed. The variations of electrical potential, velocity profile, mean velocity, and their dependences on the wave number α and β of wall corrugations in two directions, the nondimensional electrokinetic width K, and the zeta potential ratio between the lower wall and the upper wall ς are analyzed graphically.

Rotating electro-osmotic flow of third grade fluids between two microparallel plates

In this paper, a rotating electro-osmotic flow (EOF) of an incompressible third grade fluid between micro-parallel plates is considered. The analysis is based upon the modified Navier–Stokes (N–S) equation for a transport electrolyte in a rotating frame of reference. Within the framework of linearized Poisson–Boltzmann (P–B) equation, exact solutions of the electric potential distribution are given. The approximate analytical solutions of the velocity and the flow rate are achieved by using perturbation techniques under the assumption of small non-Newtonian parameter Λ. In addition, the finite difference method is used to obtain the numerical solutions. We compare the analytical solutions with the numerical solutions within admissible parameter range, and obtain a good agreement between these solutions. The influences of the Reynolds number Re, the dimensionless non-Newtonian parameter Λ, the dimensionless electro-kinetic width K on the rotating EOF velocity profiles and volume flow rate are investigated in detail. With the increasing Reynolds number Re and non-Newtonian parameter Λ, the velocity is decreasing. The large angular velocity has an obvious effect near the center core of the micro-channel and causes a reversal in the velocity direction.

Numerical Study of Mixed Electroosmotic/Pressure Driven Flow of Power-law Fluids in T-shaped Microchannels

This paper aims to discuss mixed electroosmotic/pressure driven flow of power-law fluids in a T-shaped microchannel subject to externally applied electric filed. The Possion-Boltzmann equation and Laplace equation are numerically solved and substituted into the modified Navier-Stokes equations. Considering the Possion-Boltzmann equation in the form without Debye-Hückel approximation, high order compact finite difference schemes are used for better simulation of velocity field and pressure field as a function of flow behavior index, zeta potential and dimensionless electrokinetic width. By setting the electric force at the inlet, detailed numerical results indicate that the shear thinning fluids are more sensitive to effects of zeta potential and dimensionless electrokinetic width compared with Newtonian and shear thickening fluids. If we set the electric force at the inlet and along the horizontal walls, the dimensionless electrokinetic width effects on the flow increase as the flow behavior index decreases, and the zeta potential effects result in the buildup of reverse flow in vertical channel, independent of the value of the flow behavior index.

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.