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.

Transient Electroosmotic Flow in Slit Microchannel Containing Salt-Free Medium

2009 ◽  
Author(s):  
Shih-Hsiang Chang
Keyword(s):  
Surface Charge Density ◽  
Electroosmotic Flow ◽  
Theoretical Study ◽  
Capillary Tube ◽  
Navier Stokes ◽  
Free Medium ◽  
Navier Stokes Equation ◽  
Poisson Boltzmann ◽  
Flow Through ◽  
Poisson Boltzmann Equation

A theoretical study on the transient electroosmotic flow through a slit microchannel containing a salt-free medium is presented for both constant surface charge density and constant surface potential. The exact analytical solutions for the electric potential distribution and the transient electroosmotic flow velocity are derived by solving the nonlinear Poisson-Boltzmann equation and the Navier-Stokes equation. Based on these results, a systematic parametric study on the characteristics of the transient electroosmotic flow is detailed. The general behavior of electroosmotic flow in a planar slit is similar to that in a capillary tube; however, the rate of evolution of the flow in a tube with time is faster by a factor of about 2.4 than that in a slit with its width equal to the tube diameter.

Analytical Solution of Mixed Electroosmotic and Pressure-Driven Flow in Rectangular Microchannels

2011 ◽  
Vol 483 ◽  
pp. 679-683 ◽  
Author(s):  
Da Yong Yang
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Microfluidic Chips ◽  
Layer Potential ◽  
Rectangular Microchannels ◽  
Navier Stokes Equations ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Pressure Driven Flow ◽  
Pressure Driven

Analytical solutions for potential distributions, velocity distributions of the mixed electroosmotic and pressure-driven flow in rectangular microchannels are discussed. To simulate the flow, a mathematical model, which includes the Poisson-Boltzmann equation and the modified Navier-Stokes equations, is presented and solved using the finite element method based on the Matlab software. The results show that the velocity distribution of mixed flow is compound of the “plug-like” and paraboloid at the steady state, and the pure electroosmotic flow is “plug-like”, which is similar with the electric double layer potential profile. The results provide the guidelines for the application of mix driven flow in microfluidic chips.

Vortex Flow Driven by Electroosmosis in Microchannels

2008 ◽  
Author(s):  
Wu Zhong ◽  
Yunfei Chen
Keyword(s):  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Channel Surface ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Set Up ◽  
Rotational Direction

The governing equations of electroosmotic flow, including the Navier-Stokes (N-S) equations, Laplace equation and Poisson-Boltzmann equation, are set up in a straight microchannel. The meshless method is employed as a discrete scheme for the solution domain. The semi-implicit multistep (SIMS) method is used to solve the Navier-Stokes equations. The simulation results demonstrated that different patterns of the zeta potential over the channel surface could induce different flow profiles for the vortex. The rotational direction of the vortex is determined by the electroosmotic driving force.

Frequency-dependent laminar electroosmotic flow in a closed-end rectangular microchannel

2004 ◽  
Vol 275 (2) ◽  
pp. 679-698 ◽  
Author(s):  
Marcos ◽  
C. Yang ◽  
K.T. Ooi ◽  
T.N. Wong ◽  
J.H. Masliyah
Keyword(s):  
Electroosmotic Flow ◽  
Rectangular Microchannel ◽  
Frequency Dependent

Casimir cascades in two-dimensional turbulence

2013 ◽  
Vol 729 ◽  
pp. 364-376 ◽  
Author(s):  
John C. Bowman
Keyword(s):  
Stokes Equation ◽  
Navier Stokes ◽  
Fourth Power ◽  
Two Dimensional ◽  
Vorticity Field ◽  
Navier Stokes Equation ◽  
Small Scales ◽  
Open Question ◽  
Incompressible Navier Stokes Equation

AbstractIn addition to conserving energy and enstrophy, the nonlinear terms of the two-dimensional incompressible Navier–Stokes equation are well known to conserve the global integral of any continuously differentiable function of the scalar vorticity field. However, the phenomenological role of these additional inviscid invariants, including the issue as to whether they cascade to large or small scales, is an open question. In this work, well-resolved implicitly dealiased pseudospectral simulations suggest that the fourth power of the vorticity cascades to small scales.

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.

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.

Pulsating Electroosmotic Flow and Wall Block Mixing in Microchannels

2008 ◽  
Author(s):  
G. H. Tang ◽  
X. J. Gu ◽  
R. W. Barber ◽  
D. R. Emerson ◽  
Y. H. Zhang ◽  
...  
Keyword(s):  
Electroosmotic Flow ◽  
Fluid Motion ◽  
Pulsating Flow ◽  
Practical Significance ◽  
Mixing Efficiency ◽  
Heterogeneous Surfaces ◽  
Microfluidic Systems ◽  
Navier Stokes Equation ◽  
Design And Optimization ◽  
Poisson Boltzmann Equation

Understanding electroosmotic flow in microchannels is of both fundamental and practical significance for the design and optimization of various microfluidic devices to control fluid motion. Electroosmotic flows in microfluidic systems are restricted to the low Reynolds number regime, and mixing in these systems becomes problematic due to negligible inertial effects. To enhance the species mixing effect, the current study presents a numerical investigation of steady-state electroosmotic flow mixing in smooth microchannels, channels patterned with surface blocks, channels patterned with heterogeneous surfaces, as well as pulsating electroosmotic flow. The lattice Boltzmann equations, which recover the nonlinear Poisson-Boltzmann equation, the Navier-Stokes equation including the external force term, and the diffusion equation, were solved to obtain the electric potential distribution in the electrolyte, the velocity field, and the species concentration distribution, respectively. The simulation results confirm that wall blocks, heterogeneous surfaces, and electroosmotic pulsating flow can all change the flow pattern and enhance mixing in microfluidic systems. In addition, it is shown that pulsating flow provides the most promising method for enhancing the mixing efficiency.

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