FINITE-ELEMENT SIMULATION OF A HEATED THIN FLUID LAYER

Abstract

This investigation deals with finite-element modeling and numerical approximation of thermocapillary effects in long-wavelength evolution of inclined heated thin liquid layers. We consider several aspects, including model development, scaling and perturbation analysis, variational formulations, finite-element approximation, and application studies. A linear stability analysis of the thermocapillary problem for the layer at small inclination angle is also developed, and its implications are explored numerically over the related parameter space.

This research has been supported in part by NASA grant NCCSS-154. We would like to thank Harry Swinney for his helpful comments.

Notes

¹The static Bond number B in this study is 4π² times of that in VanHook's study [7, 8] because we scale the domain span to 1 instead of 2π.