Numerical simulation of time-dependent thermocapillary convection in layered fluid systems

Abstract

We consider steady and time-dependent thermocapillary convection in encapsulated layers of moderate Prandtl number fluids. Assuming flat free surfaces and fluid/fluid interfaces, the two-dimensional, time-dependent Navier-Stokes equations and the energy equation are integrated by a time-accurate method on a stretched, staggered mesh. Particular attention is focused on the nature of time dependence in water encapsulation of Fluorinert FC-75 and in ethylene glycol encapsulated by FC-75 and hexadecane. We show that similar mechanisms for time-dependent thermocapillary convection exist for single-layer and multiple-layer fluid systems, and that shear effects at a thermocapillary interface can reduce convection in an encapsulated fluid layer. Based on our estimates for the thermal coefficients of interface tension, an apparent benefit of fluid encapsulation is to lessen the tendency toward time dependence. Nomenclature AR = aspect ratio Cp = specific heat at constant pressure k = thermal conductivity Lx, Ly = x and y dimensions of the cavity Ma = Marangoni number, crTATLx/iJLK Nu(x) = Nusselt number, Eq. (14) Pr = Prandtl number, V!K p =