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A Mathematical Model of Membrane Gas Separation with Energy Transfer by Molecules of Gas Flowing in a Channel to Molecules Penetrating this Channel from the Adjacent Channel

100%
Szwast M., Szwast Z.
Chemical and Process Engineering
|
2015
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vol. 36
|
issue 2
151-169
EN
The paper presents the mathematical modelling of selected isothermal separation processes of gaseous mixtures, taking place in plants using membranes, in particular nonporous polymer membranes. The modelling concerns membrane modules consisting of two channels - the feeding and the permeate channels. Different shapes of the channels cross-section were taken into account. Consideration was given to co-current and counter-current flows, for feeding and permeate streams, respectively, flowing together with the inert gas receiving permeate. In the proposed mathematical model it was considered that pressure of gas changes along the length of flow channels was the result of both - the drop of pressure connected with flow resistance, and energy transfer by molecules of gas flowing in a given channel to molecules which penetrate this channel from the adjacent channel. The literature on membrane technology takes into account only the drop of pressure connected with flow resistance. Consideration given to energy transfer by molecules of gas flowing in a given channel to molecules which penetrate this channel from the adjacent channel constitute the essential novelty in the current study. The paper also presents results of calculations obtained by means of a computer program which used equations of the derived model. Physicochemical data concerning separation of the CO2/CH4 mixture with He as the sweep gas and data concerning properties of the membrane made of PDMS were assumed for calculations.
2
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Mathematical model for biological cell deformation in a cylindrical pore

81%
Szwast M., Suchecka T., Piątkiewicz W.
Chemical and Process Engineering
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2012
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vol. 33
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issue 3
385-396
EN
Some studies show that cells are able to penetrate through pores that are smaller than cell size. It concerns especially Red Blood Cells but it also may concern different types of biological cells. Such penetration of small pores is a very significant problem in the filtration process, for example in micro- or ultrafiltration. Deformability of cells allows them to go through the porous membrane and contaminate permeate. This paper shows how cells can penetrate small cylindrical holes and tries to assess mechanical stress in a cell during this process. A new mathematical approach to this phenomenon was presented, based on assumptions that were made during the microscopic observation of Red Blood Cell aspiration into a small capillary. The computational model concerns Red Blood Cell geometry. The mathematical model allows to obtain geometrical relation as well as mechanical stress relations.
3
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Modelling of Postproduction Suspensions’ Concentration Processes by “Batch” Membrane Microfiltration

81%
Szwast M., Szwast Z., Grądkowski M., Piątkiewicz W.
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|
vol. 34
|
issue 3
313-325
EN
The mathematical model of postproduction suspension concentration by microfiltration has been developed. This model describes a process conducted in a batch system with membrane washing by reverse flow of permeate. The model considerations concern filtration pseudocycles consisting of the filtration period and the membrane washing period. The balances of continuous phase volume, dispersed phase mass and energy, for each period of pseudocycle respectively, have been presented.
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