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 in 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. The ability of the model to describe the physics of the filtration is discussed in detail. This model is solved in 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 (such as 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. Asymmetric interactions thus lead to direction-dependent transfer properties and the membrane exhibits diode behavior. These new transfer opportunities are discussed.
Highlights
The transport of colloids across interfaces is still a scientific challenge meeting applications in many processes
Where, J, is the solvent flux through the membrane, L p, is the membrane permeability, η, is the solvent viscosity, ∆p, is the transmembrane pressure and, ∆Π, is the transmembrane osmotic pressure. This writing derives from the semi-empirical formulation of Kedem and Katchalsky [3] that considers non-equilibrium thermodynamics with the assumption of linearity between the fluxes and the driving forces
A model, based on a two-fluid approach, has been solved in an energy landscape to account for the colloid/membrane interactions
Summary
The transport of colloids across interfaces is still a scientific challenge meeting applications in many processes. Flow through semi-permeable membranes is a common process in living bodies (kidneys, membrane cells, etc.) and in industrial applications (filtration, desalting, etc.) [1] Beyond these applications, the recent development of microfluidic experiments and the nanoscale engineering of interfaces have revived the question of the role played by colloid-surface interactions on transport across interfaces [2]. This relationship is often considered as a flow boundary condition in a filtration problem In this approach the membrane is discontinuously treated as an infinitively thin membrane separating two compartments: the membrane is described with a partition coefficient that induces an unrealistic concentration jump at the interface. A two-fluid model that introduces an energy landscape to account for colloid-membrane interactions has been proposed [18] Such a model describes the dynamics of osmotic flows with a set of continuous equations [19]. The aim of this paper is to analyze the effect of the energy barrier profile on the efficiency of the separation with membrane processes
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