Flow and transport in brush-coated capillaries: A molecular dynamics simulation

Abstract

We apply an efficient method of forced imbibition to (nano-)capillaries, coated internally with a polymer brush, to derive the change in permeability and suction force, corresponding to different grafting densities and lengths of the polymer chains. While the fluid is modeled by simple point particles interacting with Lennard-Jones forces, the (end-grafted, fully flexible) polymers, which form the brush coating, are described by a standard bead-spring model. Our computer experiments reveal a significant increase in the suction force (by a factor of 4, as compared to the case of a capillary with bare walls) when the brush width approaches the tube radius. A similar growth in the suction force is found when the grafting density of the brush is systematically increased. Even though the permeability of the tube is found to decline with both growing brush width and grafting density, the combined effect on the overall fluid influx into the capillary turns out to be weak, i.e., the total fluid uptake under spontaneous imbibition decreases only moderately. Thus we demonstrate that one may transport the fluid in vertical brush-coated capillaries to a much larger height than in an equivalent capillary with bare walls. Eventually, we also study the spreading of tracer particles transported by the uptaking fluid in brush-coated capillaries with regard to the grafting density of the brush and the length of the polymers. The observed characteristic asymmetric concentration profiles of the tracers and their evolution with elapsed time are interpreted in terms of a drift-diffusion equation with a reflecting boundary that moves with the fluid front. The resulting theoretical density profiles of the tracer particles are found to be in good agreement with those observed in the computer experiment.