Transient AC Electro-Osmotic Flow of Generalized Maxwell Fluids through Microchannels

2014 ◽  
Vol 548-549 ◽  
pp. 216-223
Author(s):  
Ze Yin ◽  
Yong Jun Jian ◽  
Long Chang ◽  
Ren Na ◽  
Quan Sheng Liu
Keyword(s):  
Reynolds Number ◽  
Relaxation Time ◽  
Electroosmotic Flow ◽  
Momentum Equation ◽  
Parallel Channel ◽  
Maxwell Fluids ◽  
Transient Velocity ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Electro Osmotic Flow

In this paper, we represent analytical solutions of transient velocity for electroosmotic flow (EOF) of generalized Maxwell fluids through both micro-parallel channel and micro-tube using the method of Laplace transform. We solve the problem including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation and generalized Maxwell constitutive equation. By numerical calculation, the results show that the EOF velocity is greatly depends on oscillating Reynolds number and normalized relaxation time.

Roughness Effect on Pressure Drop for Electroosmotic (EO) Flow in Microtubes

2008 ◽  
Author(s):  
Hossein Shokouhmand ◽  
Maziar Aghvami ◽  
Mostafa Moghadami ◽  
Hamed Babazadeh
Keyword(s):  
Pressure Drop ◽  
Friction Factor ◽  
Electroosmotic Flow ◽  
Body Force ◽  
Momentum Equation ◽  
Wall Roughness ◽  
Roughness Effect ◽  
Isotropic Distribution ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

This paper presents a theoretical model of the roughness effect on friction factor and pressure drop of fully developed, laminar flow in microtubes by considering the effect of the electrical double layer. The EDL potential distribution is calculated using the Poisson–Boltzmann equation and then the velocity profile is obtained by solving the fluid momentum equation with a body force term. The wall roughness in microtubes is modeled by utilizing a Gaussian, isotropic distribution. It is found that the effect of roughness is to increase the friction factor and pressure drop of the electroosmotic flow in microtubes.

Electroosmotic Flow and Mass Species Transport in a Microcapillary Under Influences of Joule Heating

2003 ◽  
Author(s):  
Gongyue Tang ◽  
Chun Yang ◽  
Cheekiong Chai ◽  
Haiqing Gong
Keyword(s):  
Joule Heating ◽  
Electroosmotic Flow ◽  
Mathematic Model ◽  
Transfer Coefficients ◽  
Mass Transfer Equation ◽  
Buffer Solution ◽  
Species Transport ◽  
Heat Transfer Coefficients ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

This study presents a numerical analysis of Joule heating effect on the electroosmotic flow and species transport, which has a direct application in the capillary electrophoresis based BioChip technology. A rigorous mathematic model for describing the Joule heating in an electroosmotic flow including Poisson-Boltzmann equation, modified Navier-Stokers equations and energy equation is developed. All these equations are coupled together through the temperature-dependent parameters. By numerically solving aforementioned equations simultaneously, the electroosmotic flow field and the temperature distributions in a cylindrical microcapillary are obtained. A systematic study is carried out under influences of different geometry sizes, buffer solution concentrations, applied electric field strengths, and heat transfer coefficients. In addition, sample species transport in a microcapillary is also investigated by numerically solving the mass transfer equation with consideration of temperature-dependant diffusion coefficient and electrophoresis mobility. The characteristics of the Joule heating, electroosmotic flow, and sample species transport in microcapillaries are discussed. The simulations reveal that the presence of the Joule heating could have a great impact on the electroosmotic flow and sample species transport.

scholarly journals An Exact Solution for Power-Law Fluids in a Slit Microchannel with Different Zeta Potentials under Electroosmotic Forces

Micromachines ◽  
2018 ◽  
Vol 9 (10) ◽  
pp. 504 ◽  
Author(s):  
Du-Soon Choi ◽  
Sungchan Yun ◽  
WooSeok Choi
Keyword(s):  
Power Law ◽  
Applied Pressure ◽  
Debye Length ◽  
Momentum Equation ◽  
Microfluidic System ◽  
Zeta Potentials ◽  
Power Law Fluids ◽  
Poisson Boltzmann ◽  
The Difference ◽  
Poisson Boltzmann Equation

Electroosmotic flow (EOF) is one of the most important techniques in a microfluidic system. Many microfluidic devices are made from a combination of different materials, and thus asymmetric electrochemical boundary conditions should be applied for the reasonable analysis of the EOF. In this study, the EOF of power-law fluids in a slit microchannel with different zeta potentials at the top and bottom walls are studied analytically. The flow is assumed to be steady, fully developed, and unidirectional with no applied pressure. The continuity equation, the Cauchy momentum equation, and the linearized Poisson-Boltzmann equation are solved for the velocity field. The exact solutions of the velocity distribution are obtained in terms of the Appell’s first hypergeometric functions. The velocity distributions are investigated and discussed as a function of the fluid behavior index, Debye length, and the difference in the zeta potential between the top and bottom.

scholarly journals Electro-osmotic flow of a third-grade fluid past a channel having stretching walls

2019 ◽  
Vol 8 (1) ◽  
pp. 56-64 ◽  
Author(s):  
Mamata Parida ◽  
Sudarsan Padhy
Keyword(s):  
Differential Equation ◽  
Boltzmann Equation ◽  
Linear Partial Differential Equation ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Osmotic Flow ◽  
Grade Fluid ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Electro Osmotic Flow

Abstract The electro-osmotic flow of a third grade fluid past a channel having stretching walls has been studied in this paper. The channel height is taken much greater than the thickness of the electric double layer comprising of the Stern and diffuse layers. The equations governing the flow are obtained from continuity equation, the Cauchy’s momentum equation and the Poisson-Boltzmann equation. The Debye-Hückel approximation is adopted to linearize the Poisson-Boltzmann equation. Suitable similarity transformations are used to reduce the resulting non-linear partial differential equation to ordinary differential equation. The reduced equation is solved numerically using damped Newton’s method. The results computed are presented in form of graphs.

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

2020 ◽  
Vol 26 ◽  
pp. 39-52
Author(s):  
G.T. Adamu ◽  
A.M. Kwami ◽  
Mohammed Abdulhameed ◽  
D.G. Yakubu
Keyword(s):  
Boltzmann Equation ◽  
Model Equation ◽  
Classical Method ◽  
Micro Channel ◽  
Retardation Time ◽  
Flow Parameters ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Mathematica Software ◽  
Electro Osmotic Flow

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.

Frequency Dependent Velocity and Vorticity Fields of Electroosmotic Flow in a Closed-End Rectangular Microchannel

2004 ◽  
Author(s):  
Marcos
Keyword(s):  
Electroosmotic Flow ◽  
Navier Stokes ◽  
Vorticity Field ◽  
Navier Stokes Equation ◽  
Rectangular Microchannel ◽  
Layer Potential ◽  
Frequency Dependent ◽  
Variable Approach ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

The frequency dependent electroosmotic flow in a closed-end rectangular microchannel is analyzed in this study. Dynamic AC electroosmotic flow field is obtained analytically by solving the Navier-Stokes equation using the Green’s function formulation in combination with a complex variable approach. With the Debye-Hu¨ckel approximation, the electrical double layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Additionally, the Onsager’s principle of reciprocity is demonstrated to be valid for AC electroosmotic flow. The effects of frequency-dependent AC electric field on the oscillating electroosmotic flow and the induced backpressure gradient are studied. Furthermore, the expression for the electroosmotic vorticity field is derived, and the characteristic of the vorticity field in AC electroosmotic flow is discussed. Based on the Stokes second problem, the solution of the slip velocity approximation is also presented for comparison with the results obtained from the analytical solution developed in this study.

Electroosmotic Flow Through a Circular Tube With Slip-Stick Striped Wall

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Henry C. W. Chu ◽  
Chiu-On Ng
Keyword(s):  
Electroosmotic Flow ◽  
Circular Tube ◽  
Plane Surface ◽  
Slip Length ◽  
Point Collocation ◽  
Hydrodynamic Slip ◽  
Poisson Boltzmann ◽  
Flow Enhancement ◽  
Circular Surface ◽  
Poisson Boltzmann Equation

This is an analytical study on electrohydrodynamic flows through a circular tube, of which the wall is micropatterned with a periodic array of longitudinal or transverse slip-stick stripes. One unit of the wall pattern comprises two stripes, one slipping and the other nonslipping, and each with a distinct ζ potential. Using the methods of eigenfunction expansion and point collocation, the electric potential and velocity fields are determined by solving the linearized Poisson–Boltzmann equation and the Stokes equation subject to the mixed electrohydrodynamic boundary conditions. The effective equations for the fluid and current fluxes are deduced as functions of the slipping area fraction of the wall, the intrinsic hydrodynamic slip length, the Debye parameter, and the ζ potentials. The theoretical limits for some particular wall patterns, which are available in the literature only for plane channels, are extended in this paper to the case of a circular channel. We confirm that some remarks made earlier for electroosmotic flow over a plane surface are also applicable to the present problem involving patterns on a circular surface. We pay particular attention to the effects of the pattern pitch on the flow in both the longitudinal and transverse configurations. When the wall is uniformly charged, the adverse effect on the electroosmotic flow enhancement due to a small fraction of area being covered by no-slip slots can be amplified if the pitch decreases. Reducing the pitch will also lead to a greater deviation from the Helmholtz–Smoluchowski limit when the slipping regions are uncharged. With oppositely charged slipping regions, local recirculation or a net reversed flow is possible, even when the wall is on the average electropositive or neutral. The flow morphology is found to be subject to the combined influence of the geometry of the tube and the electrohydrodynamic properties of the wall.

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

Micromachines ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 757
Author(s):  
Juan Escandón ◽  
David Torres ◽  
Clara Hernández ◽  
René Vargas
Keyword(s):  
Electroosmotic Flow ◽  
Relaxation Times ◽  
Solution Process ◽  
Momentum Equation ◽  
Oscillatory Behavior ◽  
Liquid Interfaces ◽  
Transform Method ◽  
Maxwell Fluids ◽  
Start Up ◽  
Density Ratios

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.

Unsteady Rotating Electroosmotic Flow Through a Slit Microchannel

2016 ◽  
Vol 32 (5) ◽  
pp. 603-611 ◽  
Author(s):  
D.-Q. Si ◽  
Y.-J. Jian ◽  
L. Chang ◽  
Q.-S. Liu
Keyword(s):  
Flow Rate ◽  
Electroosmotic Flow ◽  
Volume Flow Rate ◽  
Electrical Potential ◽  
Velocity Fields ◽  
Volume Flow ◽  
Half Height ◽  
Poisson Boltzmann ◽  
Flow Through ◽  
Poisson Boltzmann Equation

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.

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