Modeling shapes and dynamics of confined bubbles

We review mathematical models of confined bubbles, emphasizing physical mechanisms as expressed in simple geometrics. Molecular interactions between liquid, gas, and the confining solid are all important and are described through the disjoining pressure concept. Methods for finding static shapes are considered. The static solution is a springboard for discussing pressure-driven and surface-tension-driven flows in, both of which involve Viscous effects and macroscopic films entrained near apparent contact lines. We next discuss vapor bubbles produced by thermal effects. Vaporization localized near contact lines and condensation distributed in colder parts of the interface lead to steady vapor bubbles. Their size is determined through global constraints. Unsteady vapor bubbles are discussed and we end with thoughts on open problems.