Hourglass pore effect and membrane osmotic diode behavior: model and simulations
arXiv:1708.08621 · doi:10.3390/membranes8010010
Abstract
A membrane can be represented by an energy landscape that solutes or colloids must cross. A model accounting for the momentum and the mass balances on the membrane energy landscape establishes a new way of writing for the Darcy law. The counter pressure in the Darcy law is no longer written as the result of an osmotic pressure difference but rather as a function of colloid-membrane interactions. Physically, the colloid-membrane interactions are slowing down the colloid velocity thus inducing a relative fluid-colloid motion that in turn leads to the counter pressure. The ability of the model to describe the physics of the filtration is discussed in detail. This model is solved on a simplified energy landscape to derive analytical relationships that describe the selectivity and the counter pressure from ab-initio operating conditions. The model shows that the stiffness of the energy landscape has an impact on the process efficiency: a gradual increase in interactions (like with hourglass pore shape) can reduce the separation energetic cost. It allows the introduction of a new paradigm to increase membrane efficiency: the accumulation that is inherent to the separation must be distributed across the membrane.
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