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Determination of effective diffusion coefficients in calcium alginate gel plates with varying yeast cell content

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Abstract

Effective diffusion coefficients (De) have been determined for lactose, glucose, galactose, and ethanol in calcium alginate gel with varying yeast cell concentration. The measurements have been performed in a diffusion cell, and the results evaluated with the quasisteady-state method. An ultrasonic meter was used for gel thickness determination with an accuracy of 1.5% and a new method for the reproducible preparation of gel plates was developed. It was found thatD e in pure alginate gel decreased to about 90% of the diffusivity in water and did not vary with alginate concentration.D e decreased considerably with increasing yeast cell concentration. For the solutes studied, the effective diffusion coefficient can be estimated according to the equationD e =D eo (1 - ϕ)/[1+(ϕ/2)], whereD eo is the effective diffusivity in pure gel and ϕ is the volume fraction of yeast cells.

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Abbreviations

A :

area (m2)

ic:

concentration in solution (mol/m3 or g/L)

c*:

concentration in gel (mol/m3 gel)

c A :

concentration of solute in upstream compartment A (g/L)

cB :

concentration of solute in downstream compartment B (g/L)

c Ao :

concentration of solute in compartment A at to (g/L)

c Bo :

concentration of solute in compartment B at to (g/L)

Cc :

concentration of yeast cells in the gel (wt%)

D :

diffusion coefficient (m2/s)

D e :

effective diffusion coefficient (m2/s)

D eo :

effective diffusion coefficient in pure alginate gel (m2/s)

D aq :

diffusion coefficient in water (m2/s)

k :

partition coefficient for the solute between gel and solution (m3 solution/m3 gel)

l :

gel plate thickness (m)

N :

molar flow (mol/s)

s :

standard deviation (% of mean value)

t :

time (min or s)

to :

time at which quasi-steady-state was obtained (min or s)

V A :

volume of compartment A (m3)

V B :

volume of compartment B (m3)

wt%:

weight percentage

ωgel :

weight of gel (g)

ωsol :

weight of alginate solution (g)

x :

length in direction of diffusion (m)

ϕ:

volume fraction of solids

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Authors and Affiliations

  1. Department of Chemical Engineering I, University of Lund, PO Box 124, S-221 00 LUND, Sweden

    Anders Axelsson & Bengt Persson

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  1. Anders Axelsson
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  2. Bengt Persson
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Axelsson, A., Persson, B. Determination of effective diffusion coefficients in calcium alginate gel plates with varying yeast cell content. Appl Biochem Biotechnol 18, 231–250 (1988). https://doi.org/10.1007/BF02930828

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  • DOI: https://doi.org/10.1007/BF02930828

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