Estimation of K_la

Simple mass balance considerations for the concentration of dissolved oxygen give:

When the air is turned off, there is no supply term, and the equation becomes:

Data taken immediately after aeration ceases should be ignored because air bubbles entrained in the medium may provide some oxygen. Quickly, the concentration of oxygen assumes a linear decline with a slope equal to - RX. If there has been an independent measurement of cell mass, the specific uptake coefficient can be calculated. Usually the goal is estimating K_la, so the value of R times X is sufficient. We do not have to know R or X alone.

When aeration resumes, the supply term again becomes important. However, all terms in the equation except K_la are now known or easily found. The saturation value of dissolved oxygen can be estimated from published data or can be measured experimentally with broth free of organisms. The value of dC/dt is equal to the slope of the curve of C versus t. Substitute the numbers into the equation and solve.

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