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

Time-dependent thermocapillary convection in single and encapsulated fluid layers is considered. Through a parametric study of thermocapillary convection in a single layer of a Prandtl number 6.78 fluid, a thermal-convective mechanism for oscillatory thermocapillary convection is explored. The instability is shownto depend upon temporal coupling between large scale thermal structures within the flow field and the temperature sensitive free surface. This interaction is initiated by cooling of the free surface from below by a cool finger of fluid convected from the cold wall beneath the large central eddy. A primary result is the development of a stability diagram for the Cartesian thermocapillary system presenting the critical Marangoni number separating steady from the time-dependent flow states as a function of aspect ratio for the range of values between 2.3 and 3.8. A minimum critical aspect ratio near 2.3 and a minimum critical Marangoni number near 20000 are predicted. Below these critical parameters, steady convection is found within the parameter ranges investigated.; Extension of this work to encapsulated systems of moderate Prandtl number fluids targets both (a) water encapsulation of Fluorinert FC-75 and (b) ethylene glycol encapsulated by FC-75 from below and hexadecane from above. Particular attention is focused on modes of time-dependence and on the implications of using Antonow's Rule to predict the thermal coefficients of interface tension from surface tension data. The primary findings are that similar mechanisms for time-dependent thermocapillary convection exist for single layer and encapsulated layer fluid systems, gravity has a stabilizing influence on buoyant/thermocapillary convection with respect to time-dependence up to the transition from steady to time-dependent buoyancy driven convection, shear effects at a thermocapillary interface may reduce convection in the encapsulated fluid layer, and the absence of reliable data on the thermal coefficients of interface tension is a primary impediment to simulations of targeted fluid systems.; The computer program developed for this work integrates the two-dimensional, time-dependent Navier-Stokes equations and the energy equation by a time-accurate method on a stretched, staggered mesh. Flat free surfaces and fluid/fluid interfaces are assumed.