Abstract

We investigate the effect of mass transfer on the evolution of a thin (two-dimensional) partially wetting drop. While the effects of viscous dissipation, capillarity, slip and uniform mass transfer are taken into account, other effects, such as gravity, surface tension gradients, vapour transport and heat transport, are neglected in favour of mathematical tractability. Our matched-asymptotic analysis reveals that the leading-order outer formulation and contact-line law that is selected in the small-slip limit depends delicately on both the sign and size of the mass transfer flux, leading in particular to novel generalisations of Tanner’s law. We analyse the resulting evolution of the drop and report good agreement with numerical simulations.

Co-Authors: Matthew Saxton (University of Oxford), Jonathan Whiteley (University of Oxford), Dominic Vella (University of Oxford); John King (University of Nottingham).