Nano-channels filling flow of arbitrary cross-sections

The filling kinetics of liquids in straight nano-channels of arbitrary cross-sections is discussed. We assume that the capillary force induces a fluid flow in channels characterized by their compactness, C = P²/A, where P is the perimeter and A is the cross-sectional area. Analytical expressions for the distance between the capillary meniscus and the capillary inlet, l, as a function of the elapsed time, t, are given for several typical cross-sections. The comparison between our theoretical predictions and a set of reported data for a complex nano-channel [A. Han, J. Colloid Interface. Sci. 293 (2006) 151] allows us to conclude that the model describes well the filling kinetics.