Gradient or no gradient: Spatial hydrostatic pressure distributions in bilayer thin-film composite membranes

Abstract

Water recovery through pressure-driven bilayer thin-film composite (TFC) membranes remains an open problem, with critical uncertainty centered on its driving forces, namely the hydrostatic pressure gradient, yet systematic investigation remains limited. Here, we present a poromechanics framework that explicitly accounts for the distinct mechanical, structural, and transport properties, elucidating the interplay between flow-induced compaction and water transport in a TFC membrane governing the transport upper limit performance. Our approach naturally splits the strain energy into two regions: (i) a linear-response selective layer and (ii) a non-linear supporting one, mechanically capturing the strain-hardening behavior as the compacted support layer transitions into its bulk polymer state. While the hydrostatic pressure distribution in the selective layer merely scales upward with the increasing applied transmembrane pressure, the distribution in the support layer, however, contorts from a zero slope to a linear one and finally to a non-linear slope, demonstrating how the water transport changes to a support layer-controlled system. Overall, we show how a cancellation between permeance and the hydrostatic pressure difference across TFC membranes drives the transition between (i) support layer-controlled and (ii) selective layer-controlled regimes.