Analytical solution of a linear nonlocal Poisson-Boltzmann equation with multiple charges in a spherical solute region surrounded by a water spherical shell

2022 ◽  
Vol 105 (1) ◽  
Author(s):  
Hans W. Volkmer ◽  
Dexuan Xie
Keyword(s):  
Boltzmann Equation ◽  
Analytical Solution ◽  
Spherical Shell ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

Electro-osmotic and Pressure-Driven Flow in an Eccentric Microannulus

2019 ◽  
Vol 74 (6) ◽  
pp. 513-521
Author(s):  
F. Talay Akyildiz ◽  
Abeer F.A. AlSohaim ◽  
Nurhan Kaplan
Keyword(s):  
Boltzmann Equation ◽  
Velocity Field ◽  
Analytical Solution ◽  
Pressure Gradient ◽  
Bipolar Coordinates ◽  
Closed Form Analytical Solution ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Pressure Driven Flow ◽  
Pressure Driven

AbstractConsideration is given to steady, fully developed mixed electro-osmotic/pressure-driven flow of Newtonian fluid in an eccentric microannulus. The governing Poisson–Boltzmann and momentum equations are solved numerically in bipolar coordinates. It is shown that for a fixed aspect ratio, fully eccentric channels sustain the maximum average viscosity (i.e. flow rate) under the same dimensionless pressure gradient and electro kinetic radius. For the Debye–Hückel approximation (linearised Poisson–Boltzmann equation), we show that closed-form analytical solution can be derived for velocity field. Finally, the effect of the electrokinetic radius, pressure gradient, and eccentricity on the flow field was investigated in detail.

Simulation of Electroosmotic Flows in Micro- and Nanochannels Using a Lattice Boltzmann Model

2004 ◽  
Author(s):  
Fuzhi Tian ◽  
Baoming Li ◽  
Daniel Y. Kwok
Keyword(s):  
Boltzmann Equation ◽  
Analytical Solution ◽  
Charge Distribution ◽  
Excellent Agreement ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Computational Tool ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Boltzmann Model

A Lattice Boltzman Model (LBM) with the Poisson-Boltzmann equation for charge distribution is presented for the simulation of electroosmotic transport in straight rectangular micro and nanochannels. Our results from the LBM are in excellent agreement with the corresponding analytical solution. We have shown that the Lattice Boltzmann Model in the presence of an external force may be used an effective computational tool to simulate the electroosmotic transport phenomena in micro- and nanochannels.

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