Mota, M.

Teixeira, J. A.

Yelshin, Alexander

Universidade do Minho: RepositoriUM

Immobilised particles in gel matrix-type porous media : homogeneous porous media model

BIOTEC’98 BBE011 211 Immobilised Particles in Gel Matrix-Type Porous Media. Homogeneous porous media model  Manuel Mota*, José A. Teixeira and Alexander Yelshin Centro de Engenharia Biológica - IBQF, Universidade do Minho, 4700 Braga, Portugal  Keywords: gel, immobilised cells, diffusion, tortuosity, porosity, and simulation.   Diffusion in pure gels and gels with immobilised cells were analysed. A model of diffusion in immobilised cell gel assuming of homogeneous cells distribution in gel was improved by introducing a tortuosity value. By theoretical analysis and numerical modelling it was shown that tortuosity of a gel with immobilised cells is the result of two factors: 1) a tortuosity generated by cells, cT , and 2) a tortuosity of the gel matrix, gT . Both variables are function of cell volume fraction, φ c . Hence, the total path length in the gel with immobilised cell is L T T Lc gΣ =  and total tortuosity will be T L L T Tc gΣ Σ= = ⋅/ .   Based on this approach it is possible to analyse the data for a gel + cells system, where in general tortuosity seems too large. It is shown in this work that the diffusivity η = D De / 0  for this system is a complex function of: 1) diffusivity in gel, gη  and 2) diffusivity in immobilised cells, Oc. Hence η c e gD D= / ,  or D De c g= η , and D D DDe cgc g/ 00= =η η η , where gD is the diffusion coefficient in pure gel matrix, and D0 is the diffusion coefficient in bulk liquid. Diffusion in a pure gel without immobilised cells is represented by the equation η εg g g gD D T= =/ /0 , where Lg is the gel porosity, and Tg is the pure gel tortuosity (average ratio of molecule path to porous media thickness).    The total diffusivity, with tortuosity cT  and gT  depending on volume fraction of immobilised cells cc εφ =− )1( , is η η η ε εε ε= = ⋅ ⋅g cggcc c g cT T T( ) ( ).  For the general case, the tortuosity created in the matrix by cells presence is Tc c c c( ) / / ( )ε ε φβ β= = −1 1 1  and the tortuosity of gel matrix filled with cells is Tg c c( ) / / ( )ε ε φγ γ= = −1 1 1 . Thus: αγβ φηφφφη )1()1()1()1(/ 0 cgcccge DD −=−−⋅−⋅= , and α β γ= + +1 , where β  and γ  are order values in the range from 0 to 1, and Og is the ratio Dg/D0 for pure gels. In the particular case when T T Tg c c c( ) ( )ε ε= = , and cT ε/1~ the equation becomes 220cgcggeTTDD εηεεη =⋅== .   The developed model gave the possibility to describe the dependence of D De / 0  on φ c . Comparison with numerous published experimental data showed a good approach. Not all experimental data could be fitted with this homogeneous model. These deviations case might be explained by non-homogeneous cell distributions inside the gel matrix.   

http://repositorium.sdum.uminho.pt/bitstream/1822/3899/1/BIOTEC98.BBE011%5b1%5d.pdf

Immobilised particles in gel matrix-type porous media : homogeneous porous media model

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Universidade do Minho: RepositoriUM

Universidade do Minho: RepositoriUM