Analytical solutions of flow over liquid-infused and surfactant-laden surfaces #

Henry Rodriguez Broadbent, Darren Crowdy

12:10 Wednesday in 4Q07.

Part of the Granular and multiphase flows session.

Abstract #

We describe the construction of explicit solutions to a two-phase fluid problem relevant to modelling flow over a liquid-infused surface. In the longitudinal configuration, these surfaces typically comprise a periodic array of fluid-filled grooves in a no-slip surface over which flows a different working fluid. The fluid-filled grooves help to lubricate the flow of the working fluid leading to useful reduction in viscous drag. This drag reduction is quantified by explicit formulas for the slip length extracted from these analytical solutions. In the case of finite length, the asymptotic limit of the evolution of the groove fluid extent is found, quantifying so-called ‘shear-driven failure’. These methods are lastly used to find corresponding results to a similar problem, that for flow over a surfactant-laden meniscus. [Joint work with Darren Crowdy]