Membrane Deformation and Its Effects on Flow and Mass Transfer in the Electromembrane Processes

Abstract

In the membrane processes, a trans-membrane pressure (TMP) may arise due to design features or operating conditions. In most applications, stacks for electrodialysis (ED) or reverse electrodialysis (RED) operate at low TMP (<0.1 bar); however, large stacks with non-parallel flow patterns and/or asymmetric configurations can exhibit higher TMP values, causing membrane deformations and changes in fluid dynamics and transport phenomena. In this work, integrated mechanical and fluid dynamics simulations were performed to investigate the TMP effects on deformation, flow and mass transfer for a profiled membrane-fluid channel system with geometrical and mechanical features and fluid velocities representative of ED/RED conditions. First, a conservatively high value of TMP was assumed, and mechanical simulations were conducted to identify the geometry with the largest pitch to height ratio still able to bear this load without exhibiting a contact between opposite membranes. The selected geometry was then investigated under expansion and compression conditions in a TMP range encompassing most practical applications. Finally, friction and mass transfer coefficients in the deformed channel were predicted by computational fluid dynamics. Significant effects of membrane deformation were observed: friction and mass transfer coefficients increased in the compressed channel, while they decreased (though to a lesser extent) in the expanded channel.

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

“…The values reported in Table 1 for the membranes' Young modulus (E) and Poisson ratio (ν) are intermediate among literature data for ion exchange membranes, which range broadly from 10 to 1000 MPa for E and from 0.25 to 0.4 for ν [21][22][23][24][25][26]. The linearly elastic hypothesis is acceptable under the moderate load conditions considered here: for TMP = ±0.4 bar, the maximum computed von Mises stress is ∼2 MPa, below the limiting stress for a linearly elastic behavior as indicated by uniaxial tensile tests (see the Supplementary Material in Reference [20]). Also, the geometric parameters are representative of advanced membrane-channel configurations currently being considered for ED and RED applications [27,28].…”

“…All these properties are assumed to hold for swollen membranes because this is the actual condition under which membranes find themselves in a real operating ED/RED stack. Equilibrium, compatibility, and constitutive equations were numerically solved by using an FE method in order to find the deformed configuration of the body [20]. The small deformation approximation was not used.…”

“…In our previous work [20], FE simulations were validated by a comparison with the authors' own bulge test results, obtained for 10 × 10 cm 2 samples of real ion exchange membranes, and with analytical solutions presented by Iyengar and Naqvi [32] for the deformation of a square elastic body loaded with a uniform pressure and having all the edges clamped. A good agreement was demonstrated, with discrepancies of only a few percent in the maximum displacement.…”

“…The generic fluid channel was simulated by CFD in different deformation conditions. The "unit cell" approach, described in detail in previous papers [20,33], was adopted in order to predict fluid dynamics and mass transfer. Thus, the steady-state continuity, momentum, and mass transport equations for a Newtonian fluid were written as…”

“…In a recent paper [20], we presented integrated mechanical and fluid dynamics simulations of an electro-membrane system representative of electrodialysis or reverse electrodialysis, aimed at assessing the influence of transmembrane pressures on membrane/channel deformation and thus on pressure drop and mass transfer. The study was focused on profiled membranes of the "overlapped crossed filaments" (OCF) type, which bear on both sides straight ridges of a semicircular cross section and are piled on top of one another at a right angle.…”