Dependence of the contact line roughness exponent on the contact angle on substrates with dilute mesa defects: numerical study

Stanimir Iliev; Nina Pesheva; Pavel Iliev

doi:10.1140/epje/s10189-022-00220-3

Dependence of the contact line roughness exponent on the contact angle on substrates with dilute mesa defects: numerical study

Eur Phys J E Soft Matter. 2022 Aug 8;45(8):66. doi: 10.1140/epje/s10189-022-00220-3.

Authors

Stanimir Iliev¹, Nina Pesheva², Pavel Iliev³

Affiliations

¹ Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St. 4, 1113, Sofia, Bulgaria. stani@imbm.bas.bg.
² Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St. 4, 1113, Sofia, Bulgaria.
³ ETH Zurich, Computational Physics for Engineering Materials, 8093, Zurich, Switzerland.

PMID: 35941336
DOI: 10.1140/epje/s10189-022-00220-3

Abstract

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 [Formula: see text], which the liquid meniscus forms with the solid homogeneous base. The roughness exponent grows when [Formula: see text] decreases, and it changes from 0.5 at [Formula: see text] to 0.67 at [Formula: see text]. A wide range of contact angles ([Formula: see text]-[Formula: see text]) 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 [Formula: see text].