Graduate Thesis Or Dissertation
 

A moving boundary model of calcium alginate gel formation and the estimation of diffusion and mass transfer coefficients

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  • Calcium alginate gels are widely used in the biotechnology, food, and pharmaceutical industries for cell immobilization, food additives, and controlling the release of therapeutic agents. Different gelation conditions can lead to different gel structures which affects the diffusion of solutes in gels, thus mathematical models were developed to describe diffusion and calcium alginate gel formation. This thesis on calcium alginate gel formation is divided into two parts, each with a mathematical model and corresponding experimental study. The objectives of this thesis were to: 1) Determine the significance of mass transfer resistance and estimate diffusion and mass transfer coefficients for calcium ions, glucose, and acetaminophen diffusing into calcium alginate gel. 2) Develop a moving boundary model of calcium alginate gel formation which predicts the rate of gelation. To study the significance of mass transfer resistance and to estimate coefficients, a mathematical model and limiting procedure were developed. This model and experimental study indicated that mass transfer resistance is significant for calcium ions and glucose, but not acetaminophen, diffusing into calcium alginate gel. The limiting algorithm developed to simultaneously estimate the diffusion and mass transfer coefficients is very sensitive to experimental error, but shows promise in situations with small numbers of accurate data points taken from non-interacting homogeneous gel systems. The model of calcium alginate gel formation was based upon a moving boundary problem, solved numerically using the implicit method of finite differences, and programmed in FORTRAN. This study of the rate of calcium alginate gel formation indicated that increasing the concentration of calcium ions and/or decreasing the concentration of alginate increases the rate of gelation. The predicted gelation rates from this mathematical model were in good agreement with the measured gelation rates based upon stoichiometric binding coefficients, experimental initial concentrations of calcium ions and alginate, and diffusion coefficients of Ca⁺⁺ and alginate.
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