Robert D. Tanner

Hopf bifurcations for a variable yield continuous fermentation model

Abstract In this paper the authors investigate the Hopf bifurcation of solutions to a certain mathematical model for a continuous fermentation process. In particular, it is shown that the model, which incorporates Monod kinetics and a variable yield term which depends linearly on the underlying substrate, possesses a one-parameter family of periodic solutions when certain system parameters of the model assume a specific ratio.

Bubble and foam concentration of cellulase

Experiments were conducted to determine the effect of pH and sparging-gas composition on the bubble and foam separation of an aqueous protein solution. Cellulase was chosen as a model system that provided its own foam, unlike the previously studied invertase and amylase systems, which did not produce significant foaming. A 1-L graduated cylinder was used as the column into which the sparging gas (CO2 or air) was introduced. Contact between the rising sparging gas and the bulk solution was espected to lead to a protein concentration gradient (bubble fractionation) within the solution, as it did previously for yeast, invertase (1). A concentration gradient in the cellulase bulk solution was not observed with either air or CO2, however, but a high concentration was observed in the foam layer above the liquid solution (foam fractionation). With CO2 sparging, the bulk foam concentration reached a peak of eight times the solutions concentration at pH=5. When foam-top samples were collected, moreover, the concentration was as high as 220 times the bulk solutions concentration, suggesting a concentration gradient within the foam.Exposure to the air seems to reduce the viability of the cellulase harvested in the foam, presumably because of cellulase oxidative deactivation. Oxidative deactivation, if found to be controlling, may perhaps be minimized through the use of an inert sparging gas and foam blanketing atmosphere.

Kudzu (Pueraria Lobata): Potential agricultural and industrial resource

Kudzu was introduced to the southern United States in the 1930s to help restore the soil and reduce erosion. However, since it is a legume with an extensive root structure and without natural enemies in the United States, it has adapted to the land too successfully. States like Georgia, Alabama and Mississippi are now invaded by kudzu which, at the present time, has no commercial outlet. It is suggested in this paper that the plant be considered for several uses: the root starch as a source of carbohydrate and as a medium for yeast and ethanol production; the fiber for use in paper, in grass wallpaper, and in textiles and clothing; and the leaves for a high protein animal fodder. Preliminary experiments indicate that the root provides a vitamin enriched source of starch for ethanol and yeast fermentations. The vine can also be processed to expose the desired high tensile strength fiber for apparel use. A process is also proposed for removing the low concentration ethanol from a fermentation solution, which requires only a small fraction of the external energy required for the conventional distillation process.

The effect of pH on the foam fractionation of β-glucosidase and cellulase

Abstract The surface tension–pH profile of β-glucosidase was established to determine its relationship to the corresponding profile of cellulase and to the foam fractionation of that cellulase. The goal of this work was to determine the optimal foaming points for both cellulase and cellobiase. This data may prove useful in the separation of certain components of cellulase, since the non-foaming hydrophilic β-glucosidase does not foam as well as the hydrophobic components of cellulase at low concentrations. A key finding from these experiments was that there are two local minima in the surface tension–pH trajectory for Trichoderma reesei cellulase, as contrasted to the usual single minimum. The lower of these minimum points corresponds to the cellulase isoelectric point. The double minimum surface tension–pH profile was also observed for cellobiase alone. The optimal foaming pH for cellobiase alone was determined to be around 10.5, while for cellulase it was between 6 and 9.

The effect of imperfect mixing on an idealized kinetic fermentation model

Abstract Mixing patterns in stirred reactors are analyzed in this study from the point of view of the hysteresis behavior of final product rate as a function of the intermediate concentration in the sequential reaction A → B → C . A two-tank system model with an internal recycle stream is studied, in order to simulate the effect of imperfect mixing in a single batch reactor. The extent of mixing between positions at which product and intermediate species concentrations are measured in the reactor is revealed in both the direction of the hysteresis function and the relative magnitude of the inscribed area. Another approach, which apparently simplifies the analysis, is to measure the concentration of B in each of the two tanks and cross-plot the two variables. This latter technique not only avoids the errors resulting from differencing the data, but also leads to correlations between the circumscribed areas and the degree of mixing.

Modeling a Protein Foam Fractionation Process

A simple staged model for the protein foam fractionation process is proposed in this article. This simplified model does not detail the complex foam structure and gas-liquid hydrodynamics in the foam phase but, rather, is built on the conventional theoretical stage concept considering upward bubbles with entrained liquid and downward liquid (drainage) as counter-current flows. To simulate the protein concentration distribution in the liquid along the column by the model, the bubble size and liquid hold-up with respect to the position must be known, as well as the adsorption isotherm of the protein being considered. The model is evaluated for one stage by data from the semibatch foam fractionation of egg albumin and data from the continuous foam fractionation of bovine serum albumin. The effect of two significant variables (superficial gas velocity and feed protein concentration) on enrichment is well predicted by the model, especially for continuous operation and semibatch operation when initial concentration is high.

Foam fractionation of a dilute solution of bovine lactoferrin.

Lactoferrin (Lf), a protein found in human and bovine milk, tears, blood, and other secretory fluids, has been used to prevent infection from potential microbial pathogens by its ability to bind with iron (Fe3+). Currently, bovine lactoferrin can be purified from milk using ion exchange resin, which is a costly procedure making lactoferrin expensive. The purpose of this work was to investigate a low-cost foam fractionation process as the first step in separating lactoferrin from milk.

Effect of pH on the Startup of a Continuous Foam Fractionation Process Containing Ovalbumin

The effect of pH on the bubble size distribution, void fraction, and enrichment ratio of a continuous foam fractionation column containing ovalbumin was investigated. The bubble size and void fraction were measured using a photoelectric capillary probe for different solution pHs (3.5, 4.5, 6.5, and 9.7). The bubble diameters for pH 3.5 and 4.5 were the largest of the four pHs studied. At these two pHs, the foam was less stable and formed aggregates, leading to lower enrichment and mass recovery. For the nearly neutral pH 6.5 or the more basic pH 9.7, the bubble size was smaller and the foam was more stable, resulting in both high enrichment and high mass recovery. The void fraction was smallest for pH 6.5, but the effect of pH on void fraction was not significant. In the lower foam phase, the calculated specific area increased as the pH increased from 3.5 to 9.7, which may partially contribute to the higher enrichments at pH 6.5 and 9.7.

Periodic Fermentor Yield and Enhanced Product Enrichment from Autonomous Oscillations

Four decades of work have clearly established the existence of autonomous oscillations in budding yeast culture across a range of operational parameters and in a few strains. Autonomous oscillations impact substrate conversion to biomass and products. Relatively little work has been done to quantify yield in this case. We have analyzed the yield of autonomously oscillating systems, grown under different conditions, and demonstrate that it too oscillates. Using experimental data and mathematical models of yeast growth and division, we demonstrate strategies to increase the efficient recovery of products. The analysis makes advantage of the population structure and synchrony of the system and our ability to target production within the cell cycle. While oscillatory phenomena in culture have generally been regarded with trepidation in the engineering art of bioprocess control, our results provide further evidence that autonomously oscillating systems can be a powerful tool, rather than an obstruction.

Variation of bubble size distribution in a protein foam fractionation column measured using a capillary probe with photoelectric sensors.

Bubble size is used to characterize not only bubble-specific interfacial area but also bubble coalescence in a foam column. The bubble size distributions were obtained in a continuous foam fractionation process for concentrating ovalbumin using a developed photoelectric probe. When the continuous process reached steady state, the bubble size distribution pattern remained stable. Bubble size distribution data above (+1 cm) or below (-1 cm) the bulk liquid-foam interface showed symmetry along the diameter of the column (14 cm ID). The bubble size distribution was affected by the column wall. The nearly constant protein concentration distribution across the column cross-section indicated that the bubble flow distribution approached a flat profile across the column. A log-normal bubble distribution pattern best fit the weighted range of bubbles in the column at column lengths above and below the liquid-foam interface. These observations may prove to be useful in understanding the mechanisms underlying the foam fractionation of proteins.