Some aspects of gas transfer in the Warburg respirometer
Bryant, James Orr, 1940-
Akers, W. W.
Master of Science
A mathematical model for the Warburg constant volume respirometer was developed to describe the effect of oxygen mass transfer on kinetics of bacterial growth or oxygen uptake. Oxygen mass transfer coefficients and oxygen limited reaction rate constants were determined for the system using air, 21%, 50%, and 100% oxygen gas phases. The equations developed are Non-Limited Oxygen Uptake Oxygen Limited Oxygen Uptake Substrate Limited Oxygen Uptake occurred in the range 60-110 mg/1 oxygen uptake for air systems. The mass transfer coefficient K1a was 0.264 liters/hr for fifty milliliter samples, 72 min-1 shake rate at 20°C. The oxygen limited reaction rate constant can be calculated from the equation k' = 0.0105/P - 0.00363  Constants for equation could not be evaluated from the data obtained. Equation [15a] predicts oxygen uptake values within +/- 5% of the experimental values for 1.0 atmospheres oxygen partial pressure +/- 8% for 0.50 atmospheres oxygen partial pressure, +/- 25% for 0.21 atmospheres oxygen partial pressure, and +/- 30% for air systems. Equation [15a] is applicable from the point of deviation from exponential growth to the point of substrate limitation. Substrate limitation occurs at 36.2% of the theoretical oxygen demand for glutamic acid systems and at 29.8% of the theoretical oxygen demand for glucose systems. Application of all equations requires knowledge of the equation constants for the particular seed and substrate used. Of the constants the exponential growth rate constant and the point of deviation from exponential growth are undefined and vary widely with seed material. Equating equations  and [15a] give the initial point for equation [15a]. Equations to describe carbon dioxide partial pressure within the Warburg: system were developed. Calculated car-bon dioxide partial pressures indicate that carbon dioxide is not limiting in the Warburg system. The equations were not subject to verification in the study reported.