Iliev S, Pesheva N, Iliev P. 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;
45:66. [PMID:
35941336 DOI:
10.1140/epje/s10189-022-00220-3]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2022] [Accepted: 07/23/2022] [Indexed: 06/15/2023]
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].
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