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Droplet dynamics on chemically heterogeneous substrates

Published online by Cambridge University Press:  16 November 2018

Nikos Savva Open the ORCID record for Nikos Savva [Opens in a new window] ,
Danny Groves  and
Serafim Kalliadasis
Nikos Savva*
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
Danny Groves
Affiliation:
School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK
Serafim Kalliadasis
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

Slow droplet motion on chemically heterogeneous substrates is considered analytically and numerically. We adopt the long-wave approximation which yields a single partial differential equation for the droplet height in time and space. A matched asymptotic analysis in the limit of nearly circular contact lines and vanishingly small slip lengths yields a reduced model consisting of a set of ordinary differential equations for the evolution of the Fourier harmonics of the contact line. The analytical predictions are found, within the domain of their validity, to be in good agreement with the solutions to the governing partial differential equation. The limitations of the reduced model when the contact line undergoes stronger deformations are partially lifted by proposing a hybrid scheme which couples the results of the asymptotic analysis with the boundary integral method. This approach improves the agreement with the governing partial differential equation, but at a computational cost which is significantly lower compared to that required for the full problem.

JFM classification

Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 321 - 361
Copyright
© 2018 Cambridge University Press 

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