Evaluation of the path integral for flow through random porous media.

We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multivariate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three dimensions is discussed.

Anomalous system-size dependence of electrolytic cells with an electrified oil-water interface.

Manipulation of the charge of the dielectric interface between two bulk liquids not only enables the adjustment of the interfacial tension but also controls the storage capacity of ions in the ionic double layers adjacent to each side of the interface. However, adjusting this interfacial charge by static external electric fields is difficult since the external electric fields are readily screened by ionic double layers that form in the vicinity of the external electrodes. This leaves the liquid-liquid interface, which is at a macroscopic distance from the electrodes, unaffected. In this study we show theoretically, in agreement with recent experiments, that control over this surface charge at the liquid-liquid interface is nonetheless possible for macroscopically large but finite closed systems in equilibrium, even when the distance between the electrode and interface is orders of magnitude larger than the Debye screening lengths of the two liquids. We identify a crossover system-size below which the interface and the electrodes are effectively coupled. Our calculations of the interfacial tension for various electrode potentials are in good agreement with recent experimental data.

Are antagonistic salts surfactants?

It is well known that surfactants decrease both water/air and water/oil interfacial tensions whereas in contrast inorganic salts increase both. We study a new, third class of surface-active ionic solutes, which have been called antagonistic salts, consisting of an organic group with a small inorganic counterion. These show decreased interfacial tension at the oil/water interface due to a redistribution of the organic group in the oil but do not show any surface activity at the air/water interface and are consequently different from surfactants that lower both tensions. We use a simple modeling using Poisson-Boltzmann theory that accounts for the surface activity of the antagonistic salt at the water/oil interface.