Abstract
This paper is focused on deriving an explicit analytical solution for the prediction of the electrostatic potential, commonly used on electrokinetic research and its related applications. Different from all other analytic techniques, this approach provides a simple way to ensure the convergence of series of solution so that one can always get accurate enough approximations. This new approach can be a useful tool in electrical field applications such as the separation of a mixture of macromolecules and the removal of contaminants in soil cleaning processes.
Highlights
In every electrokinetic related application, the electrostatic potential is a key function to be identified in order to understand its effect on flow regimes
The methods to calculate this electrostatic potential function depend largely on approximations based on the range of values of the applied electrical field; it would be extremely useful to identify a procedure that yields a more general solution valid for a wide range of magnitude of the electrostatic potential
It becomes very much desired that an explicit mathematical expression for the electrostatic potential should be available. This is not necessarily easy to accomplish since the conservation of charge yields a nonlinear differential equation
Summary
In every electrokinetic related application, the electrostatic potential is a key function to be identified in order to understand its effect on flow regimes. It becomes very much desired that an explicit mathematical expression for the electrostatic potential should be available This is not necessarily easy to accomplish since the conservation of charge yields a nonlinear differential equation. This is based on the fact that the equation that is the common starting point for the description of the electrostatic potential is the Poisson-Boltzmann equation 6 :. The fAO function improves the Debye-Huckel approximation It is a recursive function of the electrical potential and has a polynomial form whose coefficients are adjusted to predict the correct values of the hyperbolic sine function. By means of this kind of freedom, a complicated nonlinear problem can be transferred into an infinite number of simpler, linear subproblems, as shown by Liao and Tan 19
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