Confinement-Induced Control of Similarity Solutions in Premelting Dynamics and Other Thin Film Problems

Abstract

We study the combined effects of nonlocal elasticity and confinement induced ordering on the dynamics of thermomolecular pressure gradient driven premelted films bound by an elastic membrane. The confinement induced ordering is modeled using a film thickness dependent viscosity. When there is no confinement induced ordering, we recover the similarity solution for the evolution of the elastic membrane, which exhibits an infinite sequence of oscillations. However, when the confinement induced viscosity is comparable to the bulk viscosity, the numerical solutions of the full system reveal the conditions under which the oscillations and similarity solutions vanish. Implications of our results for general thermomechanical dynamics, frost heave observations and cryogenic cell preservation are discussed. Finally, through its influence on the viscosity, the confinement effect implicitly introduces a new universal length scale into the volume flux. Thus, there are a host of thin film problems, from droplet breakup to wetting/dewetting dynamics, whose properties (similarity solutions, regularization, and compact support) will change under the action of the confinement effect. Therefore, our study suggests revisiting the mathematical structure and experimental implications of a wide range of problems within the framework of the confinement effect.