https://doi.org/10.1140/epje/s10189-022-00220-3
Regular Article - Soft Matter
Dependence of the contact line roughness exponent on the contact angle on substrates with dilute mesa defects: numerical study
1
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St. 4, 1113, Sofia, Bulgaria
2
ETH Zurich, Computational Physics for Engineering Materials, 8093, Zurich, Switzerland
Received:
9
April
2022
Accepted:
23
July
2022
Published online:
8
August
2022
We compute the roughness exponent of the averaged contact line width of a liquid on heterogeneous substrates with randomly distributed dilute defects in statics. We study the case of circular “mesa”-type defects placed on homogeneous base. The shape of the liquid meniscus and the contact line are obtained numerically, using the full capillary model when a vertical solid plate, partially dipped in a tank of liquid, is slowly withdrawing from the liquid. The obtained results imply that the contact line roughness exponent depends on the contact angle 
, which the liquid meniscus forms with the solid homogeneous base. The roughness exponent grows when 
decreases, and it changes from 0.5 at 
to 0.67 at 
. A wide range of contact angles (
–
) is present, where the roughness exponent is practically constant, equal to previously obtained experimental results on the magnitude of the roughness exponent and its dependence on .
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Copyright comment Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
