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 focus is on a matched-asymptotic analysis in the small-slip limit, which reveals that the leading-order outer formulation and contact-line law depend delicately on both the sign and the size of the mass transfer flux. This leads, in particular, to novel generalisations of Tanner's law. We analyse the resulting evolution of the drop on the timescale of mass transfer and validate the leading-order predictions by comparison with preliminary numerical simulations. Finally, we outline the generalisation of the leading-order formulations to prescribed non-uniform rates of mass transfer and to three dimensions.
Bibliographical noteKAUST Repository Item: Exported on 2021-11-24
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). We are grateful to Dr Erqiang Li, Professor Sigurdur D. Thoroddsen, Professor John S. Wettlaufer and Professor Thomas P. Witelski for useful discussions on this work. The authors would like to dedicate this work to Professor John R. Ockendon on the occasion of his 75th Birthday. As his research student, JMO was supported, inspired and energised by John to pursue a research career in free-boundary problems. Thank you.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Applied Mathematics