Static arrangement of a capillary porous system (CPS): Modelling

Abstract

The static arrangement is studied of a thin CPS wafer which is filled from below with a liquid metal. The CPS is modelled as a thin cylindrical disk that is resting on a flat wall. It is in contact with a reservoir that provides liquid lithium. Isothermal conditions are considered and a liquid metal layer is assumed to have been established on top of the CPS and reached an axisymmetric static arrangement. A numerical solution is obtained via the finite element methodology that solves the Young-Laplace equation which incorporates surface tension, gravitational, pressure and electrostatic forces. The layer thickness is predicted at static equilibrium as a function of the imposed pressure drop across the wafer, i.e. between the reservoir and the surrounding medium, and the wetting and dielectric properties of the liquid metal. It is seen that at large reservoir overpressure surface tension balances pressure forces and the liquid metal assumes the form of an almost hemispherical drop of small radius. Gravity is not important in this limit. As the pressure drop decreases the drop assumes an oblate shape and a thin film is gradually formed that entirely covers the CPS and extends onto the wetted rigid substrate. In this range, gravity balances pressure drop and surface tension and the film thickness is on the millimeter range, which is relatively large and has negative implications on the stability of the liquid metal layer as the electric field strength increases. Below a certain pressure drop the film in conjectured to become very thin, on the order of μm, and the disjoining pressure is expected to balance the imposed pressure drop across it. Such static arrangements have been reported in the literature and are favored in terms of stability of the CPS against j→×B→ effects. © 2016 EURATOM