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The characteristics of the reaction of calcium carbonate $(CaCO_3)$ immobilized with alginate as buffer system for the high concentration cultivation of bifidobacteria in fermenter are described by the mathematical model, and tested for the reusing possibility of the used $CaCO_3$

The characteristics of the reaction of calcium carbonate $(CaCO_3)$ immobilized with alginate as buffer system for the high concentration cultivation of bifidobacteria in fermenter are described by the mathematical model, and tested for the reusing possibility of the used $CaCO_3$ beads. When$CaCO_3$ beads with the various diameters were reacted in 0.1 M of the mixed organic acids (0.6 M of acetic acid and 0.4 M lactic acid) and in fermenter inoculated Bifidobacterium longum ATCC 15707, the change of bead diameters can be calculated with the amount of the decreased $CaCO_3$ from the surface of bead using the mathematical model. These values was similar to the directly measured bead diameter by a micrometer. Therefore, it was considered that the mathematical model could be used for explaining the reaction charateristics of the $CaCO_3$ bead reacted with the organic acids. When Bifidobacterium longum was incubated at $37^{\circ}C$ for 20 hours in fermenter with $CaCO_3$ beads, the buffering effect of $CaCO_3$, the reduce rate of the bead diameter, and the growth rate of Bifidobacterium longum were higher at the smaller beads than beads with the larger diameters. Also, when Bifidobacterium longum was incubated in fermenter with the mixed beads which were added new beads to the recovered beads in order to equalize with the total surface area of initial beads, the buffering effect of $CaCO_3$ bead and the growth rate of Bifidobacterium longum were very corresponded with the results of the fermentation using the only initial beads. Therfore, it is expected that the used beads can be reused by adding the initial beads.

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