Abstract
Transport of liquid mixtures through porous membranes is central to processes such as desalination, chemical separations, and energy harvesting, with ultrathin membranes made from novel 2D nanomaterials showing exceptional promise. Here, we derive, for the first time, general equations for the solution and solute fluxes through a circular pore in an ultrathin planar membrane induced by a solute concentration gradient. We show that the equations accurately capture the fluid fluxes measured in finite-element numerical simulations for weak solute-membrane interactions. We also derive scaling laws for these fluxes as a function of the pore size and the strength and range of solute-membrane interactions. These scaling relationships differ markedly from those for concentration-gradient-driven flow through a long cylindrical pore or for flow induced by a pressure gradient or an electric field through a pore in an ultrathin membrane. These results have broad implications for transport of liquid mixtures through membranes with thickness on the order of the characteristic pore size.
Highlights
Fluid transport through pores and porous membranes plays a key role in many processes of fundamental and practical interest, including cellular homeostasis in biological systems,[1] chemical separations,[2] desalination,[3] and energy conversion.[4,5] a general theoretical understanding of the parameters that control these transport phenomena has broad implications for a variety of domains
For a circular aperture, we have shown that the dependence of the diffusioosmotic mobility κDO on the interaction range scales as κDO ∼ λγ with a non-universal exponent γ
We have derived general equations and scaling relationships as a function of pore radius and solute–membrane interaction strength and range for the solution and solute fluxes induced by a solute concentration gradient through a circular aperture in an ultrathin planar membrane
Summary
Fluid transport through pores and porous membranes plays a key role in many processes of fundamental and practical interest, including cellular homeostasis in biological systems,[1] chemical separations,[2] desalination,[3] and energy conversion.[4,5] a general theoretical understanding of the parameters that control these transport phenomena has broad implications for a variety of domains. Many theoretical models of fluid transport in porous membranes have considered flows only within the pores[6,7,8,9] and have neglected the effect of transport between the membrane pores and the fluid outside the membrane These socalled entrance or access effects can dominate fluid transport processes when the membrane thickness approaches the characteristic pore size[10,11] or when the fluid–solid friction becomes small.[12,13] The most extreme examples of this situation are membranes of atomic thickness made from 2D materials such as graphene and its derivatives[14–19] or molybdenum sulfide.[20,21]. These socalled entrance or access effects can dominate fluid transport processes when the membrane thickness approaches the characteristic pore size[10,11] or when the fluid–solid friction becomes small.[12,13] The most extreme examples of this situation are membranes of atomic thickness made from 2D materials such as graphene and its derivatives[14–19] or molybdenum sulfide.[20,21] Such 2D membranes are of great interest, as they have been shown to exhibit exceptional properties compared with conventional membranes for applications such as desalination[14] and electrical energy harvesting from salinity gradients.[20]
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