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

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