Abstract
This paper investigated the steady-state mass transport process through anisotropic, composite membrane layers with variable mass transport coefficients, such as the diffusion coefficient, convective velocity, or chemical/biochemical reaction rate constant. The transfer processes can be a solution-diffusion model or diffusive plus convective process. In the theoretical part, the concentration distribution as well as the inlet and outlet mass transfer rates’ expressions are defined for physical transport processes with variable diffusion or solubility coefficients and then that for transport processes accompanied by first- and zero-order reactions, in the presence of diffusive and convective flow, with constant and variable parameters. The variation of the transport parameters as a function of the local coordinate was defined by linear equations. It was shown that the increasing diffusion coefficient or convective flow induces much lower concentrations across the membrane layer than transport processes, with their decreasing values a function of the space coordinate. Accordingly, this can strongly affect the effect of the concentration dependent chemical/biochemical reaction. The inlet mass transfer rate can also be mostly higher when the transport parameter decreases across the anisotropic membrane layer.
Highlights
The thermal motion of the transferred components through a dense membrane layer has basically the same transfer laws as that through a laminar liquid or gas phase
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 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
This study focuses on the reactant(s) transport’s description with variable transport parameters 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
Summary
The thermal motion of the transferred components through a dense membrane layer has basically the same transfer laws as that through a laminar liquid or gas phase. 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 Due to these conditions, the outlet boundary conditions differ from each other in these two operating modes. The operation mode without a sweeping phase does not induce diffusive flow inside the membrane and the membrane outer surface, only convective flow can transport reactant(s) through the membrane layer (the outlet membrane concentration will be equal to each side of the outer surface on the permeate side, when there is no chemical reaction on the membrane layer; on the other hand, the outlet membrane concentration will be equal to that of the bulk permeate concentration in the presence of a chemical reaction as well)
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