The depinning transition of 2D and 3D driven drops on a heterogeneous substrate
U. Thiele (School of Mathematics, Loughborough University, UK)
On non-ideal real substrates used in experiments the onset of droplet motion under driving along the substrate is strongly influenced by chemical or physical defects. A finite driving force is necessary to overcome the pinning influence of the heterogeneities occurring on a micro- or mesoscale. This is thought to be responsible, for instance, for the observed hysteresis between advancing and receding contact angles and also the stick-slip motion of weakly driven contact lines [1-3].
We study the process of depinning using a long-wave evolution equation for the film thickness profile in the case of localized hydrophilic or hydrophobic wettability defects. As a result the drop may be pinned at the rear by an enhanced wetting region, or at its front by a region of reduced wettability. The results are obtained by a combination of branch following methods, linear stability theory and direct numerical simulation of the model equation in two- [4,5] and three [6] dimensions.
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[6] P. Beltrame and U. Thiele, in preparation (2008).