Coarsening of capillary drops coupled by conduit networks

A system of n spherical-cap drops, coupled by a network of conduits, coarsens due to surface tension forces. The total interfacial energy drives the fluid through the conduits such that, with time, the volume becomes increasingly localized into fewer large drops. The coarsening rate is predicted heuristically for drops coupled by orthogonal networks, a porous medium, and fractal networks of various dimensions. The predicted coarsening law as it depends upon the type and dimension of network, total number of drops, and initial drop volume is compared against numerical simulations of large n . Additionally, distributions of large drop volumes are obtained using a Lifshitz-Slyozov-Wagner (LSW) model. The predicted distributions are independent of network topology; in contrast, simulation results depend weakly on the network dimension. The heuristic coarsening rate laws are recovered using the LSW model for all but a square network topology.