Model For Electro-osmotic Flow Research Articles

Investigation of induced electroosmotic flow in small-scale capillary electrophoresis devices: Strategies for control and reversal.

Electroosmotic flow (EOF) is the bulk flow of solution in a capillary or microchannel induced by an applied electric potential. For capillary and microchip electrophoresis, the EOF enables analysis of both cations and anions in one separation and can be varied to modify separation speed and resolution. The EOF arises from an electrical double layer at the capillary wall and is normally controlled through the pH and ionic strength of the background buffer or with the use of additives. Understanding and controlling the electrical double layer is therefore critical for maintaining acceptable repeatability during method development. Surprisingly, in fused silica capillaries at low pH, studies observe an EOF even though the capillary surface should be neutralized. Previous work has suggested the presence of an "induced electroosmotic flow" from radial electric fields generated across the capillary wall due to the separation voltage and grounded components external to the capillary. Using thin-wall (15µm) fused silica separation capillaries to facilitate the study of radial fields, we show that the EOF mobility depends on both the separation voltage and the location of external grounds. This is consistent with the induced EOF model, in which radial electric fields embed positive charges at the capillary walls to create an electrical double layer. The magnitude of the effect is characterized and shown to have long-range influences that are difficult to completely null by moving grounded components away from the separation capillary. Instead, active EOF control using externally applied potentials or a passive approach using a negative separation voltage are discussed as two possible methods for controlling the induced EOF. Both methods can reverse the EOF and improve the resolution and peak efficiency in amino acid separations.

A Pore-Scale Physical Model for Electric Dewatering of Municipal Sludge Based on Fractal Geometry

Water in municipal sludge has an electric double layer (EDL), and can be rapidly removed via electroosmosis. However, the understanding of the physical mechanisms of electroosmosis is limited owing to the complex pore structure of sludge porous media, which may restrict the development of electric dewatering (EDW) technology. In this study, the sludge microstructure was measured using the computerized tomography technique and quantitatively characterized using fractal geometry. A new pore-scale physical model for the electroosmotic flow through sludge porous media was developed based on the EDL theory, and the analytical expressions for the electroosmotic flow rate and permeability coefficient were determined. The proposed fractal pore-scale model for electroosmotic flow was validated by comparing it with the measured electroosmotic flow rate using a self-designed EDW device for municipal sludge composed of a hydraulic system and applied electric field. The results show that the electroosmotic flow rate of sludge porous media depends not only on the applied electric field, but also on the sludge microstructure including porosity, maximum pore size, and pore and tortuosity fractal dimensions. However, the correlation between the electroosmotic flow rate and the voltage gradient was usually nonlinear, and became linear only if the tortuosity fractal dimension equaled to one (straight flow path). The electroosmotic permeability coefficient increases with an increase in porosity; however, it is lowered by the increased pore and tortuosity fractal dimensions under a certain porosity. The electroosmosis phenomenon can effectively remove part of the interstitial water and surface water in sludge porous media, and the proposed electroosmotic physical model provides a useful theoretical basis for the development of EDW technology for municipal sludge.

Electro-osmosis Aided Thin-Film Evaporation from a Micropillar Wick Structure.

The heat-dissipating capacity of a surface having micropillar wick structures, which resembles the evaporator section of a vapor chamber, is mainly limited by the liquid flow rate through the porous structure (permeability) and the capillary pressure gradient. The efficacy of a regular vapor chamber is determined from two parameters, namely, the dry-out heat flux and temperature of the evaporator surface. These two parameters possess a counter relation to each other. The work described herein introduces and evaluates the performance of a novel idea of electro-osmosis-aided thin-film evaporation from a micropillar array structure. This study is conducted using a discretized approach that is validated against the thin-film evaporation model and additionally the electro-osmotic flow model with pre-existing pressure gradient conditions. The unique feature of this approach is that it results in an increment in the magnitude of dry-out heat flux without significantly changing the surface temperature, wherein the increase in permeability is due to the addition of electro-osmotic flow. This comprehensive model considers various geometries, zeta potentials, and extremal electric fields and establishes the beneficial effects of the application of an external electric field. The results are used to predict the sensitivity and the dependence of the dry-out heat flux and the evaporator surface temperature on these parameters. For a host of electro-osmotic parameters considered herein, a maximum increment of up to 320% in the dry-out heat flux is observed for an external electric field of 105 V/m. The study, therefore, conclusively demonstrates the beneficial impact of electro-osmosis in enhancing the dry-out heat flux without any significant Joule heating.

Finite Difference Simulation of Fractal-Fractional Model of Electro-Osmotic Flow of Casson Fluid in a Micro Channel

In this work, an evolving definition of the fractal-fractional operator with exponential kernel was employed to examine Casson fluid flow with the electro-osmotic phenomenon. Electrically conducted Casson fluid flow with the effect of the electro-osmotic phenomenon has been assumed in a vertical microchannel. With the help of relative constitutive equations, the local mathematical model is formulated in terms of partially coupled partial differential equations along with appropriate physical initial and boundary conditions. The dimensional governing equations have been non-dimensional by using relative similarity variables to encounter the units and reduce the variables. The local mathematical model has been transformed to a fractal-fractional model by using a fractal-fractional derivative operator with exponential kernel and then analyze numerically with the discretization of finite difference (Crank-Nicolson) scheme. For an insight view of the proposed phenomena, various plots are drawn in respect of inserted parameter. From the graphical analysis, it has been observed that the electro-kinetic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> parameter retards the fluid’s motion. It is also worth noting that graphs for the fractal-fractional, fractional, and classical order parameters have been drawn. Due to the fractal order parameter, it was revealed that the fractal-fractional order model has a larger memory effect than the fractional-order and classical models.

Study of electro-osmotic nanofluid transport for scraped surface heat exchanger with heat transfer phenomenon

In this study a novel mathematical model for electroosmotic flow for Cu-water based nanofluid with heat transfer phenomenon is reported for scraped-surface heat exchanger. The flow is initiated due to motion of lower wall of the channel and axial pressure gradient. The flow is modelled with aid of low Reynolds number and lubrication approximation theory. Exact analytical expressions are gathered for axial velocity, and stream functions for various stations of scraped-surface heat exchanger. Physical phenomenon of electro osmotic parameter are investigated on velocity profile, velocity distribution and pressure rise at edge of the blades. It is reported that electro-osmotic parameter mainly works as dragging force, it can be used to control the flow. This controlling mechanism may be helpful in mixing different materials in scraped-surface heat exchanger. Pressure rise at edge of the blades mainly rises below the blades with electro-osmotic, whereas, this profiles is suppressed for region above the blades and between the blades.

A Closed-Form Solution for Electro-Osmotic Flow in Nano-Channels

In this article‎, ‎a fluid dynamic code is implemented to investigate a non-linear model for electro-osmotic flow through a one-dimensional Nano-channel‎. ‎Certain mathematical techniques are simultaneously utilized to convert the coupled system of equations into a non-linear differential correlation‎. ‎This correlation is based on the mole fraction of anion‎. ‎By using a modified homotopy perturbation method‎, ‎the achieved non-linear differential equation is converted into a few linear differential equations‎. ‎The mole fraction of anion across the channel is found by solving the linear differential equations‎. ‎Finally‎, ‎the distribution of the mole fraction of cation‎, ‎electrical potential, and velocity are accurately derived based on the mole fraction of anion‎. ‎The present study confirms that by application of a modified homotopy perturbation method‎, ‎the results are in acceptable agreement with the previously validated data‎. ‎However, using the proposed method here‎, ‎a closed-form of the solution is achieved‎.

A generalised model for electro-osmotic flow in porous media

Purpose This study aims at developing a comprehensive model for the analysis of electro-osmotic flow (EOF) through a fluid-saturated porous medium. To fully understand and exploit a number of applications, such a model for EOF through porous media is essential. Design/methodology/approach The proposed model is based on a generalised set of governing equations used for modelling flow through fluid saturated porous media. These equations are modified to incorporate appropriate modifications to represent electro-osmosis (EO). The model is solved through the finite element method (FEM). The validity of the proposed numerical model is demonstrated by comparing the numerical results of internal potential and velocity distribution with corresponding analytical expressions. The model introduced is also used to carry out a sensitivity analysis of the main parameters that control EOF. Findings The analysis carried out confirms that EO in free channels without porous obstruction is effective only at small scales, as largely discussed in the available literature. Using porous media makes EO independent of the channel scale. Indeed, as the channel size increases, the presence of the charged porous medium is essential to induce fluid flow. Moreover, results demonstrate that flow is significantly affected by the characteristics of the porous medium, such as particle size, and by the zeta potential acting on the charged surfaces. Originality/value To the best of the authors’ knowledge, a comprehensive FEM model, based on the generalised equations to simulate EOF in porous media, is proposed here for the first time.

Numerical Simulation and Mathematical Modeling of Electro-Osmotic Couette–Poiseuille Flow of MHD Power-Law Nanofluid with Entropy Generation

The basic motivation of this investigation is to develop an innovative mathematical model for electro-osmotic flow of Couette–Poiseuille nanofluids. The power-law model is treated as the base fluid suspended with nano-sized particles of aluminum oxide (Al2O3). The uniform speed of the upper wall in the axial path generates flow, whereas the lower wall is kept fixed. An analytic solution for nonlinear flow dynamics is obtained. The ramifications of entropy generation, magnetic field, and a constant pressure gradient are appraised. Moreover, the physical features of most noteworthy substantial factors such as the electro-osmotic parameter, magnetic parameter, power law fluid parameter, skin friction, Nusselt number, Brinkman number, volume fraction, and concentration are adequately delineated through various graphs and tables. The convergence analysis of the obtained solutions has been discussed explicitly. Recurrence formulae in each case are also presented.

Atangana–Baleanu fractional model for electro-osmotic flow of viscoelastic fluids

Abstract The main goal of the current research paper is to examine the magnetohydrodynamics (MHD) free convection flow of generalized Walters’-B fluid with the effect of electro-osmosis. Electro-osmosis is the motion of liquid across a porous material which is generated by the applied potential on a net mobile electric charge in a solution. The classical Walters’-B fluid model is transformed to generalize Walters’-B fluid model using the new idea of Atangana–Baleanu time fractional derivative. Exact solutions for the velocity and temperature profiles of the stated problem are obtained using the Laplace transform technique. Some interesting and important results have been obtained from the current study. The effects of various embedded parameters like Walters’-B parameter Γ, Prandtl number Pr, Grashof number Gr, Keff and electro-osmosis parameter Es have been plotted graphically using Mathcad software. It is worth nothing that for increasing values of Es, velocity decreases. Furthermore, a decrease in velocity is observed for increasing value of Walters’-B fluid parameter Γ.

Numerical Simulations of Electrical Double Layer and Electroosmotic Flow in a Nanopore By Openfoam

The microfluidic chip transfers the pretreatment, chemical reaction, separation, detection, and other functions of the sample to a chip of several square centimeters, which embodies the characteristics of miniaturization, integration, automation, and simplicity. The drive and control of microfluidic have become the key problems in the research of microfluidic chip. In this work, numerical simulation of the electrical double layer (EDL) formed next to a charged planar surface and an electroosmotic flow (EOF) in a nanopore is demonstrated using OpenFOAM. The electrostatics and the ionic mass transport are governed by the Poisson–Nernst –Planck (PNP) equations without considering fluid motion in the model for EDL. The numerical predictions of the electric field and ionic concentrations are in good agreement with the analytical solution. The model for EOF includes the modified Stokes equations for the flow field, the Poisson equation for the electrostatics, and the Nernst–Planck equations with the convective term for the ionic mass transport. The predicted EOF velocity quantitatively agrees with the analytical solution.

Theoretical modeling of electroosmotic flow in soft microchannels: A variational approach applied to the rectangular geometry

Modeling of fluid flow in polyelectrolyte layer (PEL)-grafted microchannels is challenging due to their two-layer nature. Hence, the pertinent studies are limited only to circular and slit geometries for which matching the solutions for inside and outside the PEL is simple. In this paper, a simple variational-based approach is presented for the modeling of fully developed electroosmotic flow in PEL-grafted microchannels by which the whole fluidic area is considered as a single porous medium of variable properties. The model is capable of being applied to microchannels of a complex cross-sectional area. As an application of the method, it is applied to a rectangular microchannel of uniform PEL properties. It is shown that modeling a rectangular channel as a slit may lead to considerable overestimation of the mean velocity especially when both the PEL and electric double layer (EDL) are thick. It is also demonstrated that the mean velocity is an increasing function of the fixed charge density and PEL thickness and a decreasing function of the EDL thickness and PEL friction coefficient. The influence of the PEL thickness on the mean velocity, however, vanishes when both the PEL thickness and friction coefficient are sufficiently high.

Computational Modeling of Electroosmotic Flow within a Slit Channel: Implementation Hints and Analysis of Boundary Conditions

Different approaches to the implementation of a computational model for electroosmotic flow, solved with the FlexPDE software, are discussed. A transient analysis together with specific boundary conditions set as a time ramp was found quite convenient. The way the equation system is written within the FlexPDE script, leads to different effects for identical lateral boundary conditions. In all cases tested, the fluid velocity profile at the channel center remains unaffected and is comparable to the analytical solution. However, within adjacent regions to the channel lateral borders, a diffusion-artifact appears in some cases leading to distortion of the concentration profile thereat.

Analytical study on liquid-solid particles interaction in the presence of heat and mass transfer through a wavy channel

A comprehensive study is presented on the liquid and solid particles interaction propagating through a finite symmetric wavy channel. A non-Newtonian power law model is used to determine the flow behavior with heat and mass transfer. Furthermore, a mathematical model for electro-osmotic flow with Magnetohydrodynamics effects has been presented. The mathematical model comprises on two-dimensional conservation equations for momentum, energy, concentration, continuity with Ohm's law, chemical reaction, electrokinetic body force and viscous dissipation are formulated with the help of Cartesian coordinate system. The electric field terms are formulated into electrical potential terms using Debye length approximation, Nernst–Planck equation, and Poisson-Boltzmann equation. Moreover, an approximation of long wavelength and small Reynolds number have been used to obtain the final equations for velocity, concentration, and temperature distribution. Series solutions are presented for velocity, concentration, and temperature distribution with the help of Homotopy perturbation method up to second order. The graphical results are presented against all the involved parameters. Applications for the present study involves hemodynamics flow in biomedical engineering as well as thermal electro-osmotic micro-pumps. Furthermore, the present study is also relevant to improve thermal process in microfluidics, electrophoretic process in physiology and chromatography.

Multiscale modeling of electroosmotic flow: Effects of discrete ion, enhanced viscosity, and surface friction

We propose an isothermal, one-dimensional, electroosmotic flow model for slit-shaped nanochannels. Nanoscale confinement effects are embedded into the transport model by incorporating the spatially varying solvent and ion concentration profiles that correspond to the electrochemical potential of mean force. The local viscosity is dependent on the solvent local density and is modeled using the local average density method. Excess contributions to the local viscosity are included using the Onsager-Fuoss expression that is dependent on the local ionic strength. A Dirichlet-type boundary condition is provided in the form of the slip velocity that is dependent on the macroscopic interfacial friction. This solvent-surface specific interfacial friction is estimated using a dynamical generalized Langevin equation based framework. The electroosmotic flow of Na+ and Cl− as single counterions and NaCl salt solvated in Extended Simple Point Charge (SPC/E) water confined between graphene and silicon slit-shaped nanochannels are considered as examples. The proposed model yields a good quantitative agreement with the solvent velocity profiles obtained from the non-equilibrium molecular dynamics simulations.

Contactless microfluidic pumping using microchannel-integrated carbon black composite membranes.

The ability to pump and manipulate fluid at the micron-scale is a basic requirement for microfluidic platforms. Many current manipulation methods, however, require expensive and bulky external supporting equipment, which are not typically compatible for portable applications. We have developed a contactless metal electro-osmotic micropump capable of pumping conductive buffers. The pump operates using two pairs of gallium metal electrodes, which are activated using an external voltage source and separated from a main flow channel by a thin micron-scale polydimethylsiloxane (PDMS) membrane. The thin contactless membrane allows for field penetration and electro-osmotic flow within the microchannel, but eliminates electrode damage and sample contamination commonly associated with traditional DC electro-osmotic pumps that utilize electrodes in direct contact with the working fluid. Our previous work has demonstrated the effectiveness of this method in pumping deionized water. However, due to the high resistivity of PDMS, this method proved difficult to apply towards manipulating conductive buffers. To overcome this limitation, we fabricated conductive carbon black (CB) powder directly into the contactless PDMS membranes. The increased electrical conductivity of the contactless PDMS membrane significantly increased micropump performance. Using a microfluidic T-channel device and an electro-osmotic flow model, we determined the influence that CB has on pump pressure for CB weight percents varying between 0 and 20. The results demonstrate that the CB increases pump pressure by two orders of magnitude and enables effective operations with conductive buffers.

Molecular dynamics simulation of electroosmotic flow in rough nanochannels

A three-dimensional molecular dynamics model of electroosmotic flow in rough nanochannels is developed and numerically analyzed to investigate the role of surface roughness on microscale electroosmotic flow. The water and ion concentration distributions in the fluid, velocity profiles in rough nanochannels are examined and compared with the corresponding smooth nanochannel. In addition, the role of roughness height on electroosmotic velocity and zeta potential is presented. The results indicate that the electroosmotic behavior in nanochannels is sensitive to the surface roughness. The plug-like velocity in nanochannel is reduced by the presence of surface roughness, which owes to the variation in electrical double layer and additional viscous dissipation for flow past rough surface. There is a layering distribution of water molecules and Cl− ions in the near wall region, and some ions and molecules are confined at the concave region due to fluid/solid interaction. In addition, increases in roughness height lead to a smaller electroosmotic velocity in bulk solution and also a smaller zeta potential.

Poisson-Fokker-Planck model for biomolecules translocation through nanopore driven by electroosmotic flow

A non-continuous electroosmotic flow model (PFP model) is built based on Poisson equation, Fokker-Planck equation and Navier-Stokse equation, and used to predict the DNA molecule translocation through nanopore. PFP model discards the continuum assumption of ion translocation and considers ions as discrete particles. In addition, this model includes the contributions of Coulomb electrostatic potential between ions, Brownian motion of ions and viscous friction to ion transportation. No ionic diffusion coefficient and other phenomenological parameters are needed in the PFP model. It is worth noting that the PFP model can describe non-equilibrium electroosmotic transportation of ions in a channel of a size comparable with the mean free path of ion. A modified clustering method is proposed for the numerical solution of PFP model, and ion current translocation through nanopore with a radius of 1 nm is simulated using the modified clustering method. The external electric field, wall charge density of nanopore, surface charge density of DNA, as well as ion average number density, influence the electroosmotic velocity profile of electrolyte solution, the velocity of DNA translocation through nanopore and ion current blockade. Results show that the ion average number density of electrolyte and surface charge density of nanopore have a significant effect on the translocation velocity of DNA and the ion current blockade. The translocation velocity of DNA is proportional to the surface charge density of nanopore, and is inversely proportional to ion average number density of electrolyte solution. Thus, the translocation velocity of DNAs can be controlled to improve the accuracy of sequencing by adjusting the external electric field, ion average number density of electrolyte and surface charge density of nanopore. Ion current decreases when the ion average number density is larger than the critical value and increases when the ion average number density is lower than the critical value. Our numerical simulation shows that the translocation velocity of DNA given by the PFP model agrees with the experimental, results better than that given by PNP model or PB model.

Polymeradsorption onto a micro-sphere from optical tweezers electrophoresis

We explore the design and operation of an optical-tweezers electrophoresis apparatus to resolve polymer adsorption dynamics onto a single micro-sphere in a micro-fluidic environment. Our model system represents a broader class of micro-fluidic electrophoresis experiments for biosensing and fundamental colloid and surface science diagnostics. We track the adsorption of 100 kDa poly(ethylene oxide) homopolymer onto a colloidal silica sphere that is optically trapped in a crossed parallel-plate micro-channel. The adsorption dynamics are probed on the ∼1 μm particle length scale with ∼1 s temporal resolution. Because the particle electrophoretic mobility and channel electro-osmotic flow are exquisitely sensitive to the polymer layer hydrodynamic thickness, particle dynamics can be complicated by polymer adsorption onto the micro-channel walls. Nevertheless, using experiments and a theoretical model of electro-osmotic flow in channels with non-uniform wall ζ-potentials, we show that such influences can be mitigated by adopting a symmetrical flow configuration. The equilibrium hydrodynamic layer thickness of 100 kDa poly(ethylene oxide) on colloidal silica is ∼10 nm at polymer concentrations ≳10 ppm (weight percent), with the dynamics reflecting polymer solution concentration, flow rate, and polydispersity.

Electroosmotic flow of power-law fluids at high zeta potentials

In this paper, a mathematical model for electroosmotic flow of power-law fluids in a rectangular microchannel at high zeta potential is analyzed. The electric double layer (EDL) potential distribution is considered without Debye Huckel linear approximation. Numerical solution is obtained to analyze the fluid flow behavior. Parametric studies are conducted to assess the variation of shear stress, viscosity and volumetric flow rates of various values of flow behavior index ( n). Computed results are used to explicate the possibility of using a relatively pseudoplastic fluid inside microchannel to obtain higher volumetric flow rates.

Localized, low-voltage electro-osmotic pumping across nanoporous membranes

This work demonstrates the principle of localized, low-voltage, continuous current electro-osmotic pumping across thin membranes. Localization of the pumping effect is obtained by employing ring electrodes, microfabricated on each side of nanoporous alumina membranes. Low voltage actuation is achieved by having the separation of the two electrodes in the microscale range—the thickness of the membrane. The measured electro-osmotic velocity increases linearly from 40μm∕s at 5V to 200μm∕s at 20V. Experimental results compare well with predictions of an electro-osmotic flow model considering the nonuniform distribution of the electric field between the electrodes.