An effective-charge model for the trapping of impurities of fluids in channels with nanostructured walls

Abstract

We present model equations for the trapping and accumulation of particles in a short cylindrical channel with nanostructured inner walls when a fluid passes through, carrying a moderate load of impurities. The basic ingredient of the model is the introduction of a phenomenological "effective-charge density" of the walls, related to the electrical charges exposed in the nanotexture, and which is gradually reduced as the flow runs through the channel and the trapped impurities cover the internal walls. By solving the proposed equations, three regimes are predicted for the channel: a linear or clean-filter regime, a logarithmic or half-saturation regime, and the saturation limit. It is proposed that experimentally testing these regimes may help to understand the enhanced trapping capability observed in many diverse nanotextured channel structures.