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Droplet dynamics on chemically heterogeneous substrates

Savva, Nikos, Groves, Danny and Kalliadasis, Serafim 2019. Droplet dynamics on chemically heterogeneous substrates. Journal of Fluid Mechanics 859 , pp. 321-361. 10.1017/jfm.2018.758

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Cambridge University Press
ISSN: 0022-1120
Funders: EPSRC
Date of First Compliant Deposit: 11 January 2019
Date of Acceptance: 17 September 2018
Last Modified: 14 Oct 2021 04:09

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