Membrane mass transport modeling with the periodic boundary condition

The effect of feed spacer geometry on membrane performance and concentration polarisation based on 3D CFD simulations

“…This can be attributed to differences in boundary conditions and spacer geometries. The assumption of a constant solute rejection by the membrane, as was done in the aforementioned study [14,21] and in others [6,12,15,18,26,30,31], may need to be revisited since membrane rejection is not an intrinsic property of membranes but an output of an RO process. It would be desirable if this could be predicted as part of a CFD simulation.…”

“…Inlet velocity, concentration and outlet pressure are within RO operating ranges, and the chosen molar concentration is equivalent to approximately 35 kg/m 3 of aqueous sodium chloride solution. Based on the definition of Reynolds number used in [6,12], the channel Reynolds number corresponding to the conditions adopted in the present study is 224, which is within the laminar flow regime. …”

“…Mass transfer phenomena in reverse osmosis (RO) processes have been studied experimentally and theoretically for many decades in order to understand how water and solute permeation occur within membrane modules [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], so as to identify the factors that determine the performance of membrane modules. One of the most critical mass transfer phenomena present in an RO membrane module is concentration polarisation (CP), which is caused by the accumulation of solute(s) rejected by a selective RO membrane, resulting in an elevated solute concentration on the membrane surface [13][14][15][16].…”

“…As such, spacers of different types and geometries have been compared in terms of local shear stress and mass transfer coefficient [1-2, 5, 7, 9, 38-40]. A commonly used approach to account for solute permeation is to specify a constant membrane rejection combined with water flux and wall concentration [6,12,15,18,21,26,30,31]. This can be expressed as: J s = J w c m (1−R s ) where J s is the solute flux, J w the water flux (or flow velocity on the membrane wall), c m the solute concentration on the membrane wall and R s the membrane rejection.…”

Numerical Study of Laminar Flow and Mass Transfer for In-Line Spacer-Filled Passages

“…Mass transfer in plane ducts for parabolic flow (no recirculation) were considered by Beale [9], who also described a theoretical methodology for periodic heat/mass transfer boundary conditions [10,11]. Darcovich et al [12] subsequently considered mass transfer in a plane duct bounded by a porous membrane with stream-wise periodic boundary conditions. In this study, the methodology is extended to include the presence of convective mass transfer at the boundaries for more complex situations.…”