Mass Transport Through a Membrane Layer

Analysis of Mass Transport through Anisotropic, Catalytic/Bio-Catalytic Membrane Reactors

“…The convective velocity mostly increases (it depends on its direction) the substrate (reagent) concentration across the anisotropic membrane layer (as it will be shown later), thus its usage can be useful in the case of concentration dependent reaction rates, e.g., in the case of a first-order reaction. The differential mass balance equation in the dimensionless form [6] (p. 230) to be solved in this case is:…”

“…The most important mass transfer expressions for gas-liquid or liquid-liquid systems, without [1,2] and with chemical reaction [1,3,4] with constant or variable diffusion coefficients [1], were described in detail in previous literature [1][2][3][4]. Though the diffusion process, at least during single component transport, has a similar mechanism in the membrane layer than in a laminar fluid layer, against which there are two essential differences in the mass transport processes between the two cases [5,6], namely: (i) A convective velocity can exist in membrane transport, which can increase or decrease the overall (diffusive plus convective) flux, depending on the membrane's structure, the transmembrane pressure difference, and the interconnection between molecules, etc. ; (ii) the absence or presence of a sweeping phase on the permeate side.…”

“…It is important to note that the often strong physico-chemical connection between the simultaneously transported molecules and the polymer molecules can induce special transport mechanisms, e.g., coupling transport of components expressed by the Maxwell-Stefan approach etc. [6][7][8][9][10][11]. These latest…”

“…The value of the superficial convective velocity can vary across the membrane, depending on its structure, porosity change, and/or the change of the volumetric flow rate due to a reaction, etc. The effect of the chemical reactions with different reaction kinetics was relatively intensively studied in the literature for simple diffusive transport [12,13], but perhaps less intensively for the diffusive plus convective transport process [25][26][27][28][29][30][31][32].This study focuses on the reactant(s) transport's description with variable transport parameters (diffusion coefficient, convective velocity) without chemical/biochemical reactions and those accompanied by chemical/biochemical reactions, assuming constant and variable diffusion coefficients and/or reaction rate constant [6], as well as with constant and variable solvent/solute convective velocities. The effect of the variable convective velocity is of emphasized importance in this discussion.…”

“…This study focuses on the reactant(s) transport's description with variable transport parameters (diffusion coefficient, convective velocity) without chemical/biochemical reactions and those accompanied by chemical/biochemical reactions, assuming constant and variable diffusion coefficients and/or reaction rate constant [6], as well as with constant and variable solvent/solute convective velocities. The effect of the variable convective velocity is of emphasized importance in this discussion.…”