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Depinning transitions in selected interface-dominated driven soft-matter systems

Abstract:

Depinning transitions where a steady structure transforms into a moving one are ubiquitous in nature, and are normally accompanied by qualitative changes in the transport behaviour of the studied system. Drops pinned by substrate heterogeneities are a common example. They begin to slide if a driving force along the substrate reaches a critical value [1-2]. A similar depinning mechanism may occur for droplets of partially wetting liquid on a rotating cylinder [5]. There, gravity takes the role of the heterogeneity and the rotation corresponds to the lateral driving. After establishing the parallels in the underlying thin film evolution equations we analyse the bifurcation behaviour in the 2d case (for the rotating cylinder and heterogeneous substrate) and the 3d case (for the heterogeneous substrate). In particular, we describe various depinning scenarios in the 3d case where Rayleigh and depinning instabilities may interact.

Related phenomena may be observed in the dc-driven transport of interacting particles through a long narrow corrugated channel [7], e.g., the transport of a suspension of colloidal particles through a nanopore. We use dynamical density functional theory to investigate the occuring depinnng transitions and their influence on the average particle current.

We conclude this part with a comparison of the different types of depinning transitions introduced before and then briefly discuss the application of the scheme to other systems where such transitions occur. In particular, we focus on the deposition of line patterns at (i) at receding three-phase contact lines of evaporating solutions [5] and (ii) in the Langmuir-Blodgett transfer of surfactant monolayers [6].

[1] U. Thiele and E. Knobloch, Phys. Rev. Lett. 97, 204501 (2006); New J. Phys. 8, 313 (2006).
[2] P. Beltrame, P. Hanggi and U. Thiele, Europhys. Lett. 86, 24006 (2009); P. Beltrame, E. Knobloch, P. Hanggi and U. Thiele, Phys. Rev. E 83 016305 (2011).
[3] U. Thiele, J. Fluid Mech 671, 121-136 (2011).
[4] A. Pototsky et al., Phys. Rev. E 83, 061401 (2011).
[5] L. Frastia, A. J. Archer and U. Thiele, Phys. Rev. Lett. 106, 077801 (2011).
[6] M. H. Kopf, S. V. Gurevich, R. Friedrich and U. Thiele, submitted (2011).
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