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On contact-line dynamics with mass transfer

Published online by Cambridge University Press:  10 August 2015

J. M. OLIVER ,
J. P. WHITELEY ,
M. A. SAXTON ,
D. VELLA ,
V. S. ZUBKOV  and
J. R. KING
J. M. OLIVER
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK Email: oliver@maths.ox.ac.uk, saxton@maths.ox.ac.uk, vella@maths.ox.ac.uk, zubkov@maths.ox.ac.uk
J. P. WHITELEY
Affiliation:
Department of Computer Science, University of Oxford, Parks Road, Oxford, OX1 3QD, UK Email: jonathan.Whiteley@cs.ox.ac.uk
M. A. SAXTON
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK Email: oliver@maths.ox.ac.uk, saxton@maths.ox.ac.uk, vella@maths.ox.ac.uk, zubkov@maths.ox.ac.uk
D. VELLA
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK Email: oliver@maths.ox.ac.uk, saxton@maths.ox.ac.uk, vella@maths.ox.ac.uk, zubkov@maths.ox.ac.uk
V. S. ZUBKOV
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK Email: oliver@maths.ox.ac.uk, saxton@maths.ox.ac.uk, vella@maths.ox.ac.uk, zubkov@maths.ox.ac.uk
J. R. KING
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK Email: John.King@nottingham.ac.uk
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Abstract

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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.

Keywords

Thin filmssurface-tension driven flowsevaporationcondensationmatched asymptotic expansions
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Special Anniversay Issue 5: Celebrating 75 years , October 2015 , pp. 671 - 719
Copyright
Copyright © Cambridge University Press 2015 

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