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# Manipulating transport phenomena of colloidal particles at surfaces

Tarlan A. Vezirov:

Colloidal particles under the combined influence of an external driving force and restricted geometry exhibit a wealth of non-linear phenomena, which are relevant in diverse fields such as directed particle transport, sorting mechanisms and friction phenomena at the nanoscale. Here we discuss recent examples and present first developments to manipulate such driven colloidal systems by feedback control strategies. We focus on the following situations:

First, we consider a crystalline bilayer of charged colloids squeezed between two planar surfaces. Switching on an external shear flow we find, by using particle-based Brownian Dynamic simulations, a sequence of states characterised by pinning, shear-induced melting and reentrant ordering into a moving hexagonal state with synchronised oscillations of the particles [1]. By adding an additional feedback equation of motion we are able to stabilise specic properties such as the degree of hexagonal ordering or the shear stress. This opens the route for a deliberate control of friction properties.

Second, we discuss the transport of colloids through a one-dimensional periodic, static potential. In such systems, feedback control strategies can induce a current reversal as well as time-dependent oscillatory density proles [2, 3]. Here we present analytical treatment of the diffusion properties of single colloids at short and intermediate time scales [4], as well as attempts to feedback-control the density distribution of interacting colloids in the framework of Dynamical Density Functional Theory. The third system involves again a one-dimensional potential which is however, spatially asymmetric and time-dependent (rocking ratchet). Based on a Fokker-Planck equation we introduce time-delayed feedback control with the mean particle position as control target. We analyze the resulting dynamics and the net current as opposed to that observed with open-loop control [5].

[1] T. A. Vezirov and S. H. L. Klapp, Phys. Rev. E, submitted (2013).

[2] K. Lichtner and S. H. L. Klapp, EPL 92, 40007 (2010).

[3] K. Lichtner, A. Pototsky, and S. H. L. Klapp, Phys. Rev. E 86, 051405 (2012).

[4] C. Emary, R. Gernert, and S. H. L. Klapp, Phys. Rev. E 86, 061135 (2012).

[5] S. A. M. Loos, R. Gernert, and S. H. L. Klapp, in preparation.