Electroosmotic Flow In Microchannels Research Articles

Electroosmotic microchannel flow of blood conveying copper and cupric nanoparticles: Ciliary motion experiencing entropy generation using backpropagated networks

AbstractA novel mathematical model for a hybrid (Cu–CuO/blood) Jeffrey nanofluid passing a vertical symmetric microchannel along with an electroosmosis pump is presented. The focuses on the advancement of mathematical modeling techniques, its comprehensive analysis of microfluidic system dynamics, and its potential to inform the optimal design of devices using nanofluids with broad applications in various fields. Arrhenius's law is used to analyze endothermic–exothermic reactions and activation energy. The governing partial differential equations of the fixed frame are transformed into ordinary differential equations of the wave frame using self‐similarity transformations. Low Reynolds number and long‐wavelength approximations helped to find solutions of the equations by applying a suitable BVP solver in MATLAB. The fluid's velocity, temperature, concentration, and electroosmosis properties are studied graphically. Two‐dimensional contour plots of fluid velocity and three‐dimensional surface plots of fluid properties are discussed. Physically significant quantities of mass transfer rate, skin friction coefficient, entropy generation, and heat transfer rate are studied using contour plots. Artificial neural network simulation using Bayesian regularization backpropagation algorithms is analyzed for training state, error histogram, fit, performance, and regression plots. Conclusively, the comprehensive analysis of the fluid dynamics, entropy generation, mass and heat transfer, and in the microchannel, coupled with the successful implementation of artificial neural network simulation, contributes to an improved understanding of the system's behavior. Entropy generation was raised for enhanced Brownian motion number and reduced values of thermophoresis, activation energy, and endothermic–exothermic reaction parameters. This study's results can be used to improve the efficiency and effectiveness of microfluidic devices used in fields as diverse as electrical cooling and medicine delivery.

Investigating simultaneous effects of temperature, surface heterogeneity and geometry on fluid mixing in electroosmotic flow considering temperature dependent properties by Nernst–Planck Poisson method

Numerical study of the effect of temperature and heat transfer as well as surface heterogeneity effects on mixing and electroosmotic flow in microchannels with convergent/divergent and straight mixing chamber is carried out. The fluid properties and surface zeta potentials are assumed to be temperature dependent. Based on the Nernst–Planck Poisson model, the governing equations of this problem include the Laplace equation, Poisson equation, Navier–Stokes and the propagation equation as well as the energy equation, respectively for the distribution of external electric field, distribution of internal electric field due to the charge of ions, fluid motion, concentration field and temperature distribution, which are solved by the finite element method. Flow rate, the mixing efficiency and a new parameter called mixing capacity, which is achieved by multiplying flow rate by mixing efficiency, are obtained for convergent/divergent and straight microchannels in a constant external electric field distributed under different wall temperatures, and performance of the geometries in flow transfer and mixing development is investigated. For electroosmotic flow, heterogeneous microchannels create vortices which improve mixing. Different arrangements of heterogeneous pieces of the surface create different patterns of vortices, each of which has different effects in the various geometries on fluid flow and mixing. Also, the dependence of the molecular diffusion on temperature causes increasing the mixing of species with the temperature increment. The results show that divergent microchannels have the maximum flow rate and the minimum mixing efficiency, but this efficiency can be increased by increasing the wall temperature. Convergent microchannels also have high mixing efficiency due to low flow rates and sufficient time for mixing even at low and near ambient temperatures, although their mixing capacity is less than the divergent microchannels.

Bivariant species mixing and pressure drop within a hybrid periodic modulated microslit

In this article, a mathematical study is presented on electroosmotic flow (EOF) of power law fluids driven by an external electric field, where the heterogeneity of a microslit is created by multiple wavy triangular modulated polarized wall hurdles. The primary aim of this paper is to demonstrate and depict the mixing performance that generating more retention time and enhancing the interface area, which is evaluated both analytically and computationally. EOF in microchannels is restricted to low Reynolds numbers with a relatively high viscosity effect, which could predict advection domination in flow mixing due to heterogeneities that can supersede the need of flow turbulence. The numerical experiment is performed for the flow phenomena of this novel alternating microgrooves' patterning to generate an intensively transverse flow field, which represents strong reverse flow due to a higher pressure drop. The geometry modification and potential heterogeneity are the key factors to disturb the flow stream by fluid folding and stretching, leading to significant improvement in mixing efficiency. The numerical computations are performed for the nonlinear coupled Nernst–Planck–Navier Stokes equations using a control volume approach over a staggered grid algorithm to elaborate the performance of the electric potential distribution, the external electric field, the flow field, and the species concentration, which are the major contributors of the mixing efficiency. The evaluated results confirm that surface modulation substantially reduces the mass flow rate, effectively resulting in an increase in the retention time of the flow diffusion, which is justified through analytical testing. The nonlinear coupling effects are found to be more pronounced for shear thickening fluids rather than shear thinning and Newtonian solutions, resulting in a low torque corresponding to equilibrium conditions. To achieve a targeted mixing performance, it is observed that flow behavior indices should be optimized in terms of aversion of flow behavior index, viscous dissipation, and yield stress effect.

An analytical study on electroosmotic flow within a microchannel disregarding the Debye–Huckel approximation

The present work investigates analytically an electroosmotic flow (EOF) of a Newtonian liquid in a microchannel between two parallel plates. Homotopy perturbation method (HPM) is used to solve the constitutive governing equations. The Poisson-Boltzmann equation for electrical potential distribution is considered. Present work disregards the Debye–Huckel approximation to minimize exactness of present results. Consequently, using the electric potential profile obtained, a modified Navier–Stokes equation is solved for velocity distribution. The energy equation is also altered based on scale analysis to find temperature distribution. Finally, based on the temperature profile Nusselt number is determined. The proposed results are shown in comparison with a numerical and an established result which considers the Debye–Huckel approximation. It is seen that the present results agree well with the numerical predictions for a varied range of zeta potential. But, the established conventional method differs from the numerical result for higher range of zeta potential. Nusselt number is evaluated and shown as function of the electrokinetic length for different zeta potentials. The work finally concludes that the proposed model can be applied for predicting EOF in microchannels for wider range of zeta potential.

An Analytical Modeling on Flow and Heat Transfer for a Pressure-Driven Electroosmotic Flow in Microchannel Considering First Order Slip Model

An analytical solution to study fundamental behaviors of a pressure-driven electroosmotic flow in a parallel plate microchannel is presented in the present work. A thermally fully developed flow of a Newtonian liquid is considered. The fluid motion is assumed to be caused with a pressure gradient applied externally and an electrostatic potential field. The electrical potential field is determined by solving the Poisson–Boltzmann equation. The Debye–Huckel approximation is not considered for higher accuracy of results. A modified form of the Navier–Stokes equation with slip boundary conditions is considered to evaluate velocity field and skin friction coefficient, whereas the energy equation is simplified to obtain temperature profile as well as Nusselt number. Homotopy perturbation method (HPM) is applied to solve the Poisson–Boltzmann equation, whereas the momentum and the energy equations has been solved analytically to achieve the velocity and temperature profiles, respectively. The predicted results are compared with existing work and show a good harmony. Results obtained for electric potential, velocity and temperature fields have been shown graphically varying wall zeta potential, slip coefficient and pressure gradient. Subsequently, a parametric study is presented for skin friction coefficient and the Nusselt number. Finally, an effort is made to determine local volumetric entropy generation and global entropy generation. The proposed results exhibit both the influence of the Brinkman number and pressure gradient on the entropy generation.

The effects of external force and electrical field on the agglomeration of Fe3O4 nanoparticles in electroosmotic flows in microchannels using molecular dynamics simulation

Recent progress in nanoparticle construction can be seen as a breakthrough in increasing heat transfer methods. The small size of particles and low volume fraction of particles leads to solving agglomeration and pressure drop problems and reduce the cost of storing and transporting nanofluids. Molecular dynamics simulation is one of the essential branches of computational physics that can predict various structures' atomic behavior. In this study, the effects of external electrostatic force and external electrical field on the density, velocity, temperature of atomic structures, and agglomeration of Fe3O4 nanoparticles in a copper microchannel are investigated. The results of the physical properties of this structure are estimated using molecular dynamics simulation and LAMMPS software. The results show that with increasing the applied external electrostatic force the maximum velocity is converged to 0.0071 Å /ps. Also, adding an external electrical field to the simulated nanofluid, the maximum values of density, velocity, and temperature are estimated to 1.32 g/cm3, 0.0078 Å /ps, and 345 K, respectively. The external electrical field has a significant and essential role in the agglomeration process in atomic structures. Finally, it is observed that by increasing the external electrical field, the time required for the agglomeration process increases to 2.26 ns.

Towards bio-inspired artificial muscle: a mechanism based on electro-osmotic flow simulated using dissipative particle dynamics

One of the unresolved issues in physiology is how exactly myosin moves in a filament as the smallest responsible organ for contracting of a natural muscle. In this research, inspired by nature, a model is presented consisting of DPD (dissipative particle dynamics) particles driven by electro-osmotic flow (EOF) in micro channel that a thin movable impermeable polymer membrane has been attached across channel width, thus momentum of fluid can directly transfer to myosin stem. At the first, by validation of electro-osmotic flow in micro channel in different conditions with accuracy of less than 10 percentage error compared to analytical results, the DPD results have been developed to displacement of an impermeable polymer membrane in EOF. It has been shown that by the presence of electric field of 250 V/m and Zeta potential − 25 mV and the dimensionless ratio of the channel width to the thickness of the electric double layer or kH = 8, about 15% displacement in 8 s time will be obtained compared to channel width. The influential parameters on the displacement of the polymer membrane from DPD particles in EOF such as changes in electric field, ion concentration, zeta potential effect, polymer material and the amount of membrane elasticity have been investigated which in each cases, the radius of gyration and auto correlation velocity of different polymer membrane cases have been compared together. This simulation method in addition of probably helping understand natural myosin displacement mechanism, can be extended to design the contraction of an artificial muscle tissue close to nature.

Analysis of an electroosmotic flow in wavy wall microchannels using the lubrication approximation

We present the analysis of an electroosmotic flow (EOF) of a Newtonian fluid in a wavy-wall microchannel. In order to describe the flow and electrical fields, the lubrication and Debye-Hückel approximations are used. The simplified governing equations of continuity, momentum and Poisson-Boltzmann, together with the boundary conditions are presented in dimensionless form. For solving the mathematical problem, numerical and asymptotic techniques were applied. The asymptotic solution is obtained in the limit of very thin electric double layers (EDLs). We show that the lubrication theory is a powerful technique for solving the hydrodynamic field in electroosmotic flows in microchannels where the amplitude of the waviness changes on the order of the mean semi-channel height. Approximate analytical expressions for the velocity components and pressure distribution are derived, and a closed formula for the volumetric flow rate is obtained. The results show that the principal parameters that govern this EOF are the geometrical parameter, ε, which characterizes the waviness of the microchannel and the ratio of the mean semi-channel height to the thickness of the EDL, κ.

Mixing Enhancement of Electroosmotic Flow in Microchannels under DC and AC Electric Field

Mixing Enhancement of Electroosmotic Flow in Microchannels under DC and AC Electric Field

Graetz problem for combined pressure-driven and electroosmotic flow in microchannels with distributed wall heat flux

There has been a growing interest in the development of microchannel heat sinks deploying electrically modulated fluid flow in recent years. The efficient design of such devices requires heat transfer models that can account for complex distributions of heat generation in microelectronics. In this paper, expressions are obtained for temperature distribution and Nusselt number of thermally developing mixed electroosmotic and pressure-driven flow through circular/slit microchannels of axially non-uniform wall heat flux. The heating section is considered to be of a finite length in order to simulate a physically more realistic situation. Both the Joule heating and axial conduction effects are considered in the model. By comparing the results for linear, sinusoidal, and exponential distributions of the wall heat flux with the predictions of full numerical simulations, it is shown that the analytical solutions presented are accurate up to a Péclet number of 10. This threshold is demonstrated to be larger than the maximum Péclet number encountered in practical applications involving electroosmotic pumping mechanisms. After justification of the model, a parametric analysis is executed, revealing that the average Nusselt number is a decreasing function of the EDL thickness and pressure-driven velocity, irrespective of the wall heat flux distribution. Moreover, whereas a higher Joule heating rate is accompanied by a smaller value of the average Nusselt number for pure electroosmotic and pressure-assisted flows, the opposite is true in the presence of a significant back pressure.

Effects of surface roughness and electrokinetic heterogeneity on electroosmotic flow in microchannel

In this paper, a hybrid lattice-Boltzmann and finite-difference (LB-FD) model is applied to simulate the effects of three-dimensional surface roughness and electrokinetic heterogeneity on electroosmotic flow (EOF) in a microchannel. The lattice-Boltzmann (LB) method has been employed to obtain the flow field and a finite-difference (FD) method is used to solve the Poisson-Boltzmann (PB) equation for the electrostatic potential distribution. Numerical simulation of flow through a square cross-section microchannel with designed roughness is conducted and the results are critically analysed. The effects of surface heterogeneity on the electroosmotic transport are investigated for different roughness height, width, roughness interval spacing, and roughness surface potential. Numerical simulations reveal that the presence of surface roughness changes the nature of electroosmotic transport through the microchannel. It is found that the electroosmotic velocity decreases with the increase in roughness height and the velocity profile becomes asymmetric. For the same height of the roughness elements, the EOF velocity rises with the increase in roughness width. For the heterogeneously charged rough channel, the velocity profile shows a distinct deviation from the conventional plug-like flow pattern. The simulation results also indicate locally induced flow vortices which can be utilized to enhance the flow and mixing within the microchannel. The present study has important implications towards electrokinetic flow control in the microchannel, and can provide an efficient way to design a microfluidic system of practical interest.

Experimental verification of overlimiting current by surface conduction and electro-osmotic flow in microchannels.

Direct evidence is provided for the transition from surface conduction (SC) to electro-osmotic flow (EOF) above a critical channel depth (d) of a nanofluidic device. The dependence of the overlimiting conductance (OLC) on d is consistent with theoretical predictions, scaling as d(-1) for SC and d(4/5) for EOF with a minimum around d=8 μm. The propagation of transient deionization shocks is also visualized, revealing complex patterns of EOF vortices and unstable convection with increasing d. This unified picture of surface-driven OLC can guide further advances in electrokinetic theory, as well as engineering applications of ion concentration polarization in microfluidics and porous media.

Mixing enhancement of low-Reynolds electro-osmotic flows in microchannels with temperature-patterned walls

Mixing becomes challenging in microchannels because of the low Reynolds number. This study aims to present a mixing enhancement method for electro-osmotic flows in microchannels using vortices caused by temperature-patterned walls. Since the fluid is non-isothermal, the conventional form of Nernst–Planck equation is modified by adding a new migration term which is dependent on both temperature and internal electric potential gradient. This term results in the so-called thermo-electrochemical migration phenomenon. The coupled Navier–Stokes, Poisson, modified Nernst–Planck, energy and advection–diffusion equations are iteratively solved by multiple lattice Boltzmann methods to obtain the velocity, internal electric potential, ion distribution, temperature and species concentration fields, respectively. To enhance the mixing, three schemes of temperature-patterned walls have been considered with symmetrical or asymmetrical arrangements of blocks with surface charge and temperature. Modeling results show that the asymmetric arrangement scheme is the most efficient scheme and enhances the mixing of species by 39% when the Reynolds number is on the order of 10−3. Current results may help improve the design of micro-mixers at low Reynolds number.

Enhancement of flow mixing in micro and nano channels

The aim is to increase the mixing potential of ion species in micro and nano channels with heterogeneous surface potential. We discuss the generation of vortical flow, due to the presence of wall heterogeneity at different locations in the channel. The flow characteristics are obtained by numerical solution of the Poisson equation, the Nernst--Planck equation, and the Navier--Stokes equation, simultaneously. A numerical method based on the pressure correction iterative algorithm is adopted to compute the flow field and mole fraction of the ions. The strong recirculation vortices which appear above the heterogeneities generate a strong pressure gradient which increases mixing performance. References F. Tian, B. Li and D. Y. Kwok, Tradeoff between mixing and transport for EOF in hetero. microchannels with nonuniform surface potentials. Langmuir 21:1126–1131, 2005. doi:10.1021/la048203e R. H. Liu, M. A. Stremler, K. V. Sharp, M. G. Olsen, J. G. Santiago, R. J. Adrian, H. Aref and D. J. Beebe, Passive mixing in a three dimensional serpentine microchannel. J. Microelectromech. S. 9:190–197, 2000. doi:10.1109/84.846699 Z. M. Wu, Z. J. Zhao, J. X. Yang, L. P. Liu and X. L. Yang, Freq.-modulation-type MI sensor with nanocrystalline ribbon core. Sensor. Actuat. A:Phys. 121:430–433, 2005. doi:10.1016/j.sna.2005.03.019 S. Bhattacharyya and A. K. Nayak, Combined Effect of Surface Roughness and Heterogeneity of Wall Potential on Electroosmosis in Microfluidic/Nanofuidic Channels. J. Fluids Eng. 132:041103, 2010. doi:10.1115/1.4001308 A. Ajdari, Electro-Osmosis on Inhomogeneously Charged Surfaces. Phy. Rev. Lett. 75:755–758, 1995. doi:10.1103/PhysRevLett.75.755 D. Erickson and D. Li Influence of surface heterogeneity on electrokinetically driven microfluidic mixing. Langmuir 18:1883–1892, 2002. doi:10.1021/la015646z L. M. Fu , J. Y. Lin and R. J. Yang, Analysis of electroosmtoic flow with step change in zeta potential. J. Colloid. Interf. Sci. 258:266–275, 2003. doi:10.1016/S0021-9797(02)00078-4 H. Watzig, S. Kaupp and M. Graf, Inner surface properties of capillaries for electrophoresis. Trac-Trend. Anal. Chem. 22:588–604, 2003. doi:10.1016/S0165-9936(03)01102-6 Z. Zheng and D. Hansford, and A. T. Conlisk, Effect of multivalent ions on EOF in micro- and nanochannels. Electrophoresis 24:3006–3017, 2003. doi:10.1002/elps.200305561 J. Wang, M. Wang and Z. Li, Lattice Poisson–Boltzmann Simulations of Electro-Osmotic Flows in Microchannels. J. Colloid. Interf. Sci. 296:729–736, 2006. doi:10.1016/j.jcis.2005.09.042 A. K. Nayak, An Analysis of Steady/Unsteady Electroosmotic flows Through Charged cylindrical nano channel. Theor. Comp. Fluid Dyn. 27:885–902, 2013. doi:10.1007/s00162-013-0295-0

Characteristics of Transient Electroosmotic Flow in Microchannels With Complex-Wavy Surface and Periodic Time-Varying Electric Field

A numerical investigation is performed into the flow characteristics of the electroosmotic flow induced within a microchannel with a complex-wavy surface by a time-varying periodic electric field. The simulations focus specifically on the effects of the Strouhal number of the periodic electric potential, the amplitude of the periodic electric potential, the amplitude of the complex-wavy surface, and the waveform geometry. The results show that under steady-time periodic conditions, the flow pattern induced within the microchannel varies over the course of the oscillation period. In particular, it is shown that a flow recirculation structure is generated in the trough region of the wavy surface as the applied electric field falls to zero if the amplitude of the wavy surface exceeds a certain threshold value. In addition, it is shown that the phases of the electric field and electroosmotic velocity near the wall surface are almost identical. However, a phase shift exists between the electric field and the bulk flow velocity in the central region of the channel; particularly at larger values of the Strouhal number. Finally, it is shown that the velocity profile near the wavy surface is more sensitive to changes in the waveform geometry than that in the center of the channel. Overall, the simulation results presented in the study provide a useful source of reference for the development of new microfluidic systems incorporating microchannels with complex-wavy surfaces.

Electroosmotic flow in a water column surrounded by an immiscible liquid

In this paper, we conducted numerical simulation of the electroosmotic flow in a column of an aqueous solution surrounded by an immiscible liquid. While governing equations in this case are the same as that in the electroosmotic flow through a microchannel with solid walls, the main difference is the types of interfacial boundary conditions. The effects of electric double layer (EDL) and surface charge (SC) are considered to apply the most realistic model for the velocity boundary condition at the interface of the two fluids. Effects on the flow field of ς-potential and viscosity ratio of the two fluids were investigated. Similar to the electroosmotic flow in microchannels, an approximately flat velocity profile exists in the aqueous solution. In the immiscible fluid phase, the velocity decreases to zero from the interface toward the immiscible fluid phase. The velocity in both phases increases with ς-potential at the interface of the two fluids. The higher values of ς-potential also increase the slip velocity at the interface of the two fluids. For the same applied electric field and the same ς-potential at the interface of the two fluids, the more viscous immiscible fluid, the slower the system moves. The viscosity of the immiscible fluid phase also affects the flatness of the velocity profile in the aqueous solution.

Analytical expressions for pH-regulated electroosmotic flow in microchannels

We derived analytical expressions for the pH-regulated electroosmotic flow in a microchannel for arbitrary level of surface potential and type of electrolyte solution; previous results are almost always based on the conditions of low, constant surface potential, which are inaccurate and unrealistic. In addition, an analytical expression for the dependence of the surface potential on the electrolyte concentration and solution pH is obtained, which is capable of explaining the behavior of the empirical relation used in the literature. The analytical results derived are readily applicable to further electrokinetic analyses, and to interpret experimental observations and/or design devices involving electroosmosis such as biosensors and lab-on-a-chip.

Electroosmotic Flow in Microchannels with Nanostructures

Here we report that nanopillar array structures have an intrinsic ability to suppress electroosmotic flow (EOF). Currently using glass chips for electrophoresis requires laborious surface coating to control EOF, which works as a counterflow to the electrophoresis mobility of negatively charged samples such as DNA and sodium dodecyl sulfate (SDS) denatured proteins. Due to the intrinsic ability of the nanopillar array to suppress the EOF, we carried out electrophoresis of SDS-protein complexes in nanopillar chips without adding any reagent to suppress protein adsorption and the EOF. We also show that the EOF profile inside a nanopillar region was deformed to an inverse parabolic flow. We used a combination of EOF measurements and fluorescence observations to compare EOF in microchannel, nanochannel, and nanopillar array chips. Our results of EOF measurements in micro- and nanochannel chips were in complete agreement with the conventional equation of the EOF mobility (μ(EOF-channel) = αC(i)(-0.5), where C(i) is the bulk concentration of the i-ions and α differs in micro- and nanochannels), whereas EOF in the nanopillar chips did not follow this equation. Therefore we developed a new modified form of the conventional EOF equation, μ(EOF-nanopillar) ≈ β[C(i) - (C(i)(2)/N(i))], where N(i) is the number of sites available to i-ions and β differs for each nanopillar chip because of different spacings or patterns, etc. The modified equation of the EOF mobility that we proposed here was in good agreement with our experimental results. In this equation, we showed that the charge density of the nanopillar region, that is, the total number of nanopillars inside the microchannel, affected the suppression of EOF, and the arrangement of nanopillars into a tilted or square array had no effect on it.

A numerical investigation into electroosmotic flow in microchannels with complex wavy surfaces

This study investigates the flow characteristics of electroosmotic flow in a microchannel with complex wavy surfaces. A general method of coordinate transformation is used to solve the governing equations describing the electroosmotic flow in the microchannel. Numerical simulations are performed to analyze the effects of wave amplitude on the electrical field, flow streamlines, and flow fields in the microchannel. The simulation results show that, compared to a traditional pressure-driven flow, flow recirculation is not developed in the electroosmotic flow in a microchannel with complex wavy surfaces. The simulations also show that the electrical field and velocity profiles change along the channel in the region of wavy surfaces. Non-flat velocity profiles are observed in different cross-sections of the channel in the region of wavy surfaces.

A hybrid model for electroosmotic flows in microchannels induced by internal electrodes

AbstractInternal electrodes, adjacent to insulating walls at defined zeta potential, lead to a non‐continuous potential distribution at the wall. Hence, simplified treatment appears problematic due to the singularity of the electrical field strength. To avoid this difficulty, we develop a hybrid model, which solves the electrical problem, including a resolution of the EDL, while the flow problem is solved in the fluid bulk only. We apply this hybrid model to investigate the position of internal electrodes with regard to their influence onto the flow field, driven by electroosmosis in a modular rectangular microchannel. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)