Pressure-Induced Deformation of Pillar-Type Profiled Membranes and Its Effects on Flow and Mass Transfer

Abstract

In electro-membrane processes, a pressure difference may arise between solutions flowing in alternate channels. This transmembrane pressure (TMP) causes a deformation of the membranes and of the fluid compartments. This, in turn, affects pressure losses and mass transfer rates with respect to undeformed conditions and may result in uneven flow rate and mass flux distributions. These phenomena were analyzed here for round pillar-type profiled membranes by integrated mechanical and fluid dynamics simulations. The analysis involved three steps: (1) A conservatively large value of TMP was imposed, and mechanical simulations were performed to identify the geometry with the minimum pillar density still able to withstand this TMP without collapsing (i.e., without exhibiting contacts between opposite membranes); (2) the geometry thus identified was subject to expansion and compression conditions in a TMP interval including the values expected in practical applications, and for each TMP, the corresponding deformed configuration was predicted; and (3) for each computed deformed configuration, flow and mass transfer were predicted by computational fluid dynamics. Membrane deformation was found to have important effects; friction and mass transfer coefficients generally increased in compressed channels and decreased in expanded channels, while a more complex behavior was obtained for mass transfer coefficients.

Fluid–Structure Interaction and Flow Redistribution in Membrane-Bounded Channels

“…In the ideal case of a uniform (along the whole channel) transmembrane pressure (TMP), a relatively simple chain of effects and consequences would be triggered: (a) Membrane/channel deformation; (b) changes in the friction coefficients in both fluid compartments with respect to those in the undeformed configuration; and, finally, (c) consequent changes in the solutions flow rates for any given inlet-to-outlet imposed pressure drop. Such TMP effects in ED and RED processes were documented in our previous studies [22,23], which revealed a significant influence of membrane deformation on the hydrodynamics and mass transfer in channels equipped with different profiled membranes.…”

“…equations expressing the channel's apparent permeability as a function of the transmembrane pressure and superficial velocity, as defined in Section 2.1. As discussed above, such equations can be derived from our previous 3-D mechanical-fluid dynamics investigation at the lower scale level of a unit cell [22,23]. The sign convention for TMP adopted in the present paper is consistent with that adopted in our previous work: TMP is positive if the concentrate channel is compressed and the diluate channel is expanded, whereas it is negative if the concentrate channel is expanded and the diluate channel is compressed.…”

“…In our previous works [22,23], in order to investigate the flow characteristics in fluid-filled channels provided with profiled membranes (either in their nominal, i.e., undeformed configuration, or deformed by a transmembrane pressure), the "unit cell" approach was employed. In particular, Figure 1 shows how a periodic unit can be isolated from a fluid channel delimited by profiled membranes of the overlapped crossed filaments (OCFs) type.…”

“…The geometry investigated in the present work is characterized by P/H = 8. Following the approach adopted in previous papers [5,6,22,23], the velocity and length scale used for the definition of the Reynolds number were the superficial velocity, U s , and the hydraulic diameter of the void and undeformed plane channel, 2H:…”

Computational Approaches in Membrane Science and Engineering

“…Also at the macroscopic scale, a combination of fluid dynamics and mechanical simulations is applied by Battaglia et al [14] to investigate the effect of the transmembrane pressure in electro-membrane processes using round pillar type-profiled membranes. This study shows that the pressure that arises between the solutions flowing in alternate channels causes a slight deformation of the membrane, which may affect its mass transport properties.…”