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. / Graduation date: 1997

Advection-dispersion is generally solved numerically with methods that treat the problem from one of three perspectives. These are described as the Eulerian reference, the Lagrangian reference or a combination of the two that will be referred to as Eulerian-Lagrangian. Methods that use the Eulerian-Lagrangian approach incorporate the computational power of the Lagrangian treatment of advection with the simplicity of the fixed Eulerian grid. A modified version of a relatively new adaptive Eulerian-Lagrangian finite element method is presented for the simulation of advection-dispersion. Advection is solved by an adaptive technique that automatically chooses a local solution technique based upon a criterion involving the spatial variation of the gradient of the concentration. Moving particles (the method of characteristics; MOC) are used to define the concentration field in areas with significant variation of the concentration gradient. A modified method of characteristics (MMOC) called single-step reverse particle tracking is used to treat advection in areas with fairly uniform concentration gradients. As the simulation proceeds, the adaptive technique, as needed to maintain solution accuracy and optimal simulation efficiency, adjusts the advection solution process by inserting and deleting moving particles to shift between MMOC and MOC. Dispersion is simulated by a finite element formulation that involves only symmetric and diagonal matrices. Despite evidence from other investigators that diagonalization of the mass matrix may lead to poor solutions to advection-dispersion problems, this method seems to allow "lumping" of the mass matrix by essentially decoupling advection and dispersion. Based on tests of problems with analytical solutions, the method seems capable of reliably simulating the entire range of Peclet numbers with Courant numbers that range to 15.

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published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

No description available.

In this dissertation, the quantitative and qualitative aspects of modeling shallow water flow driven mainly by gravitational forces and dominated by shear stress, using an effective equation often referred to in the literature as the diffusive wave approximation of the shallow water equations (DSW) are presented. These flow conditions arise for example in overland flow and water flow in vegetated areas such as wetlands. The DSWequation arises in shallow water flow models when special assumptions are used to simplify the shallow water equations and contains as particular cases: the Porous Medium equation and the time evolution of the p-Laplacian. It has been successfully applied as a suitable model to simulate overland flow and water flow in vegetated areas such as wetlands; yet, no formal mathematical analysis has been carried out addressing, for example, conditions for which weak solutions may exist, and conditions for which a numerical scheme can be successful in approximating them. This thesis represents a first step in that direction. The outline of the thesis is as follows. First, a survey of relevant results coming from the studies of doubly nonlinear diffusion equations that can be applied to the DSWequation when topographic effects are ignored, is presented. Furthermore, an original proof of existence of weak solutions using constructive techniques that directly lead to the implementation of numerical algorithms to obtain approximate solutions is shown. Some regularity results about weak solutions are presented as well. Second, a numerical approach is proposed as a means to understand some properties of solutions to the DSW equation, when topographic effects are considered, and conditions for which the continuous and discontinuous Galerkin methods will succeed in approximating these weak solutions are established. / text

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

Two approaches, one using an atmospheric diffusion model and the other an atmospheric tracer, were used to predict the source strength of trace gases from observations of the downwind concentration field. Both approaches do not disturb the prevailing environmental and physical conditions nor the existing biogenic processes. An analytical solution to the advection-diffusion equation was used to back-calculate the source strength from the downwind concentration measurements of (i) single and multipoint (4 and 16 points) trace gas (sulphur hexafluoride (SF6) and methane (CH4)) release experiments conducted over microplots over an open field, and (ii) single point source SF6 release experiments conducted over a forested terrain. Best predictions of the source strength (to within +/-20%) were obtained from concentration observations made along the centreline of the diffusing plumes with the predictions improving when observations at the mean plume height were used. The diffusion model was then used to compute footprint estimates for neutral and unstable conditions, for tower and aircraft based observation platforms above the forest. They showed spatially constrained footprints in the surface layer, due to effective vertical coupling, so that observations from towers and low flying aircraft must be expected to be very site specific, and scaling up to larger areas will have to be done with careful consideration of surface mosaics. Above-canopy sampling of trace gases to determine volatile organic compound emissions were then interpreted in terms of footprint considerations. This was accomplished by defining the upwind canopy areas effectively sampled under the given wind and stability conditions. The analysis demonstrated, for example, that the variability observed in measured isoprene fluxes could be accounted for by varying numbers of randomly distributed clumps of emitter species within a varying footprint. It suggested that heterogeneity of the forest canopy, in ter / Sulphur hexafluoride was also used as an atmospheric tracer in order to estimate CH4 emissions from manure slurry and cattle housed in barns and feedlots. (Abstract shortened by UMI.)

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No description available.