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Moving contact line dynamics: from diffuse to sharp interfaces

Kusumaatmaja, H; Hemingway, E.J.; Fielding, S.M.


E.J. Hemingway


We reconcile two scaling laws that have been proposed in the literature for the slip length associated with a moving contact line in diffuse interface models, by demonstrating each to apply in a different regime of the ratio of the microscopic interfacial width l and the macroscopic diffusive length lD=(Mη)1/2, where η is the fluid viscosity and M the mobility governing intermolecular diffusion. For small lD/l we find a diffuse interface regime in which the slip length scales as ξ∼(lDl)1/2. For larger lD/l>1 we find a sharp interface regime in which the slip length depends only on the diffusive length, ξ∼lD∼(Mη)1/2, and therefore only on the macroscopic variables η and M, independent of the microscopic interfacial width l. We also give evidence that modifying the microscopic interfacial terms in the model’s free energy functional appears to affect the value of the slip length only in the diffuse interface regime, consistent with the slip length depending only on macroscopic variables in the sharp interface regime. Finally, we demonstrate the dependence of the dynamic contact angle on the capillary number to be in excellent agreement with the theoretical prediction of Cox (J. Fluid Mech., vol. 168, 1986, p. 169), provided we allow the slip length to be rescaled by a dimensionless prefactor. This prefactor appears to converge to unity in the sharp interface limit, but is smaller in the diffuse interface limit. The excellent agreement of results obtained using three independent numerical methods, across several decades of the relevant dimensionless variables, demonstrates our findings to be free of numerical artefacts.


Kusumaatmaja, H., Hemingway, E., & Fielding, S. (2016). Moving contact line dynamics: from diffuse to sharp interfaces. Journal of Fluid Mechanics, 788, 209-227.

Journal Article Type Article
Acceptance Date Nov 20, 2015
Online Publication Date Dec 22, 2015
Publication Date Feb 1, 2016
Deposit Date Jan 4, 2016
Publicly Available Date May 22, 2016
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 788
Pages 209-227


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