Abstract
The increase of the diffusion coefficient, due to its concentration dependency, can strongly increase the mass transfer rate through the membrane. Accordingly, the negative effect of the mass transfer resistance of the polarization layer can essentially be increased on the separation efficiency, especially in the case of low solute concentration in the feed phase. This effect can also exist at high solute concentration at extremely high pervaporation rate as it is illustrated by the case study. The simultaneous effect of the concentration polarization and membrane layers is discussed in this paper in case of exponentially or linearly concentration dependent diffusion coefficient. Mass transfer rate, enrichment and the polarization modulus are expressed in implicit, closed mathematical equations involving the transport parameters of the two layers, i.e.the kL, Pe, km, H values. How the increasing diffusion coefficient affects the concentration distribution in the polarization and the membrane layers and due to it, the mass transfer rate, enrichment or the polarization modulus, indicating the effect of the polarization layer, is discussed. It is shown how strongly the dimensionless plasticizing coefficient can decrease the polarization modulus and can affect the concentration distribution in the polarization and the membrane layers as well as the ratio of the diffusion dependent mass transfer rate to that without plasticizing effect, namely if . The case study illustrates the effect of the external mass transfer resistance on the mass transfer rate and on the concentration distribution in the case of high value of a plasticization coefficient.
Highlights
The pervaporation process became a very promising separation process with wide industrial application possibilities [1,2,3,4,5,6]
Pervaporation process is discussed in the case of concentration dependent diffusion coefficient, namely its exponential and linear functions, in the membrane layer taking into account the simultaneous effect of both the polarization and membrane layers
The external resistance can decrease the liquid concentration at the inner edge of the polarization layer, c* or the membrane concentration, it decreases the effect of the membrane concentration on the diffusion coefficient
Summary
The pervaporation process became a very promising separation process with wide industrial application possibilities [1,2,3,4,5,6]. Its usage in a hybrid process can essentially decrease the energy demand of e.g. the concentration of the alcohol, ethanol, butanol from the fermeation broth [5] which is crucial in order to make the biofuel production more economic. The mathematical description of this separation process, taking into account the simultaneous effect of both the polarization, with diffusive plus convective flows, and membrane layer, with diffusive flow on the separation efficiency, can essentially contribute to get more economic process. Despite of the large efforts in this task, a general model of it is still missing or partly solved. This paper discusses this problem with exponentially or linearly concentration dependent diffusivity in the membrane phase applying polymeric membrane layer. Several papers published in the last decades dealing with the mass transport mechanisms in the organic membrane layer [1,2,3,4,5,6,7,8,9,10] applying Maxwell-
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