Scaling regimes of thermocapillarity-driven dynamics of confined long bubbles: effects of disjoining pressure

Abstract

During thermocapillary transport of a confined long bubble, we unveil the existence of a contrary-to-the-conventional disjoining-pressure-dominant scaling regime characterizing the dynamics of the thin liquid film engulfed between the bubble interface and the channel surface. Such a regime is realized for the limitingly small magnitude of the Marangoni stress (surface tension gradient) when the separating liquid region reaches an ultrathin dimension. Over this regime, we witness a severe breakdown of the seemingly intuitive scaling arguments based on the balance of viscous and capillary forces. Starting from competent balance criteria, we uncover the characteristic length scales involved, leading towards obtaining the new consistent scaling laws of the disjoining-pressure-dominant regime, in a simple closed form analytical fashion. Our scaling estimations are substantiated by full-scale numerical simulations of the pertinent thin-film equations. These new scaling laws appear to be convenient for implementing as a fundamental design basis for multiphase microfluidic systems.