@Article{CiCP-11-831,
author = {Sihong Shao and Tiezheng Qian},
title = {A Variational Model for Two-Phase Immiscible Electroosmotic Flow at Solid Surfaces},
journal = {Communications in Computational Physics},
year = {2012},
volume = {11},
number = {3},
pages = {831--862},
abstract = {<p style="text-align: justify;">We develop a continuum hydrodynamic model for two-phase immiscible
flows that involve electroosmotic effect in an electrolyte and moving contact line at
solid surfaces. The model is derived through a variational approach based on the Onsager principle of minimum energy dissipation. This approach was first presented in
the derivation of a continuum hydrodynamic model for moving contact line in neutral two-phase immiscible flows (Qian, Wang, and Sheng, J. Fluid Mech. 564, 333–360
(2006)). Physically, the electroosmotic effect can be formulated by the Onsager principle as well in the linear response regime. Therefore, the same variational approach
is applied here to the derivation of the continuum hydrodynamic model for charged
two-phase immiscible flows where one fluid component is an electrolyte exhibiting
electroosmotic effect on a charged surface. A phase field is employed to model the
diffuse interface between two immiscible fluid components, one being the electrolyte
and the other a nonconductive fluid, both allowed to slip at solid surfaces. Our model
consists of the incompressible Navier-Stokes equation for momentum transport, the
Nernst-Planck equation for ion transport, the Cahn-Hilliard phase-field equation for
interface motion, and the Poisson equation for electric potential, along with all the
necessary boundary conditions. In particular, all the dynamic boundary conditions at
solid surfaces, including the generalized Navier boundary condition for slip, are derived together with the equations of motion in the bulk region. Numerical examples
in two-dimensional space, which involve overlapped electric double layer fields, have
been presented to demonstrate the validity and applicability of the model, and a few
salient features of the two-phase immiscible electroosmotic flows at solid surface. The
wall slip in the vicinity of moving contact line and the Smoluchowski slip in the electric
double layer are both investigated.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.071210.040511a},
url = {http://global-sci.org/intro/article_detail/cicp/7393.html}
}