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 Electroviscous Effect of Power Law Fluids in a Slit Microchannel With Asymmetric Wall Zeta Potentials

2018 ◽  
Vol 35 (4) ◽  
pp. 537-547 ◽  
Author(s):  
A. Sailaja ◽  
B. Srinivas ◽  
I. Sreedhar
Keyword(s):  
Zeta Potential ◽  
Power Law ◽  
Streaming Potential ◽  
Shear Thickening ◽  
Narrow Slit ◽  
Electroviscous Effect ◽  
Streaming Potentials ◽  
Zeta Potentials ◽  
Power Law Fluids ◽  
Poisson Boltzmann Equation

ABSTRACTThis work analyzes the pressure driven flow of a power law fluid in a slit microchannel of asymmetric walls with electroviscous effects. The steady state Cauchy momentum and the Poisson-Boltzmann equation are solved for the velocity and the potential distribution inside the microchannel. The Debye-Huckel approximation as applicable for low zeta potentials is not made in the present work. The unknown streaming potential is solved by casting the governing equations as an optimization problem using COMSOL Multiphysics. This proposed method is very robust and can be used for a wide variety of cases. It is found that the asymmetry of the zeta potential at the two walls plays an important role on the streaming potential developed. There is a unique zeta potential ratio at which the streaming potential exhibits a maxima for both Debye-Huckel parameter and the power law index. Shear thinning fluids exhibit a stronger dependency of the streaming potential on asymmetry of the zeta potential than shear thickening fluids. For Newtonian fluids narrow slit microchannels develop larger streaming potentials compared to wider microchannels for a given asymmetry.

Study of Electroosmotic Flow in a Nanotube with Power Law Fluid

2011 ◽  
Vol 110-116 ◽  
pp. 3633-3638
Author(s):  
Davood D. Ganji ◽  
Mofid Gorji-Bandpy ◽  
Mehdi Mostofi
Keyword(s):  
Power Law ◽  
Navier Stokes ◽  
Equilibrium Equations ◽  
Flow Channels ◽  
Power Law Fluids ◽  
Fluid Properties ◽  
Poisson Boltzmann ◽  
The Subject ◽  
Poisson Boltzmann Equation ◽  
Electrochemical Equilibrium

In this paper, electroosmotic phenomena in power law fluids are investigated. This assumption is applicable in many cases such as blood. Flow channels assumed to be in nanoscale. Navier-Stokes, Poisson-Boltzmann and electrochemical equilibrium equations govern these phenomena. It is notable that, these governing equations should be modified according to fluid complexity. Electroosmotic phenomena occur in the presence of electric double layer (EDL). Potential in the edge of the inner layer (stern layer) is called zeta potential. In this paper, according to follow the applicability of the subject, zeta potential is assumed to be so small, that makes the Poisson-Boltzmann equation linear and be able to solve analytically. Method employed for analytical solution is based on developed Bessel differential equation. This paper aims to investigate the fluid properties, zeta potential and Debye-Huckel parameter effect on the viscosity, electroosmotic mobility and velocity field in the nanotube. These expected achievements help us to study the properties of blood and some other non-Newtonian fluids more precisely.

Unsteady Flow of Fluids With Arbitrarily Time-Dependent Rheological Behavior

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Irene Daprà ◽  
Giambattista Scarpi
Keyword(s):  
Analytical Solution ◽  
Kinematic Viscosity ◽  
Applied Pressure ◽  
Gibbs Phenomenon ◽  
Momentum Equation ◽  
Unsteady Motion ◽  
Circular Pipes ◽  
Direct Numerical Solution ◽  
The Difference ◽  
Radial Variable

This paper presents an analytical solution of the momentum equation for the unsteady motion of fluids in circular pipes, in which the kinematic viscosity is allowed to change arbitrarily in time. Velocity and flow rate are expressed as a series expansion of Bessel and Kelvin functions of the radial variable, whereas the dependence on time is expressed as Fourierlike series. The analytical solution for the velocity is compared with the direct numerical solution of the momentum equation in a particular case, verifying that the difference between analytical and numerical values of axial velocity is less than 1%, except near the discontinuity of the applied pressure gradient, where the typical behavior due to the Gibbs phenomenon is to be noted.

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.

scholarly journals Reliable Computer Simulation Methods for Electrostatic Biomolecular Models Based on the Poisson–Boltzmann Equation

2020 ◽  
Vol 20 (4) ◽  
pp. 643-676 ◽  
Author(s):  
Johannes Kraus ◽  
Svetoslav Nakov ◽  
Sergey Repin
Keyword(s):  
Boltzmann Equation ◽  
Numerical Solution ◽  
Real Life ◽  
Generalized Solution ◽  
Normal Derivative ◽  
Computational Method ◽  
Weak Formulation ◽  
Poisson Boltzmann ◽  
The Difference ◽  
Poisson Boltzmann Equation

AbstractThe paper is concerned with the reliable numerical solution of a class of nonlinear interface problems governed by the Poisson–Boltzmann equation. Arising in electrostatic biomolecular models these problems typically contain measure-type source terms and their solution often exposes drastically different behaviour in different subdomains. The interface conditions reflect the requirement that the potential and its normal derivative must be continuous. In the first part of the paper, we discuss an appropriate weak formulation of the problem that guarantees existence and uniqueness of the generalized solution. In the context of the considered class of nonlinear equations, this question is not trivial and requires additional analysis, which is based on a special splitting of the problem into simpler subproblems whose weak solutions can be defined in standard Sobolev spaces. This splitting also suggests a rational numerical solution strategy and a way of deriving fully guaranteed error bounds. These bounds (error majorants) are derived for each subproblem separately and, finally, yield a fully computable majorant of the difference between the exact solution of the original problem and any energy-type approximation of it.The efficiency of the suggested computational method is verified in a series of numerical tests related to real-life biophysical systems.

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.

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