Dynamic density functional study of driven colloidal particles: the effect of the system dimension

The dynamical properties of classical fluids at pico-liter scale attract experimentally and theoretically much attention in the soft-matter and biophysics communities, due to the appearance of the microfluidics, also called 'lab-on-a-chip', as one of the most relevance 21th century technologies. In this work we focus our attention on one of the key factors for the design and construction of this type of devices: {\it the system dimension}. We consider a generic system formed by a dilute solution of colloidal particles dragged by a moving potential barrier, modeled by a time dependent external potential acting on the colloidal particles but with no effect on the solvent. We base our results on a new technique named Dynamic density functional (DDF) theory which is a generalization of Density functional (DF) theory to out of equilibrium, for systems with relaxative molecule dynamics, under the hypothesis that the dynamic correlations can be approximated by those in a system with the same density distribution at equilibrium.