Models of Drainage and Rupture of Thin Electrolyte Films on Flat and Structured Solid Substrates

Studies of drainage and rupture of thin layers of aqueous solutions are important for a number of applications such as flotation, development of lab-on-a-chip devices, and microscale two-phase cooling systems. We develop a model of a draining liquid elec- trolyte film between a gas bubble and solid wall. The model is based on coupling of capillarity, viscous flow, and electrostatic effects described by the nonlinear Poisson-Boltzmann equation. Our approach leads to a more accurate description of drainage than the earlier studies based on the concept of the electrostatic component of disjoining pressure since they accounted for the electrostatic contributions to the normal stress but not the shear stress balance at the fluid interface. We apply our model to the derivation of stability criteria for an electrolyte film on a charged solid substrate. Then, the problem of film stability on a substrate structured by an array of gas-filled grooves is analyzed using the Floquet theory.