Electroconvection of Thin Liquid Crystals: Model Reduction and Numerical Simulations
arXiv:1903.05836 · doi:10.1016/j.jcp.2019.109140
Abstract
We propose a finite element method for the numerical simulation of electroconvection of thin liquid crystals. The liquid is located in between two concentric circular electrodes which are either assumed to be of infinite height or slim. Each configuration results in a different nonlocal electro-magnetic model defined on a two dimensional bounded domain. The numerical method consists in approximating the surface charge density, the liquid velocity and pressure, and the electric potential in the two dimensional liquid region. Finite elements for the space discretization coupled with standard time stepping methods are put forward. Unlike for the infinite electrodes configuration, our numerical simulations indicate that slim electrodes are favorable for electroconvection to occur and are able to sustain the phenomena over long period of time. Furthermore, we provide a numerical study on the influence of the three main parameters of the system: the Rayleigh number, the Prandtl number and the electrodes aspect ratio.
arXiv comment28 pages
References in corpus (10)
- An extension problem related to the fractional Laplacian
- Numerical Methods for Fractional Diffusion
- Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis
- Annular electroconvection with shear
- Aspect ratio dependence of charge transport in turbulent electroconvection
- Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film
- Electrically driven convection in a thin annular film undergoing circular Couette flow
- Localized states in sheared electroconvection
- Sequential Bifurcations in Sheared Annular Electroconvection
- Codimension-two points in annular electroconvection as a function of aspect ratio