Math introduction
Our courses have strong emphases on equations for microbial process and computer simulation. You can skip this page for now, but it will show how easy is much of the math.
Most of the basic equations for cell concentration and nutrient concentration are simple mass balances.
This top equation is the statement of the mass balance principle:
For a batch system with no inputs or outputs, there is only a reaction term. Since growth rate and rate of nutrient consumption are proportional to cell mass, the batch equations use the specific growth rate coefficient µ .
Y = the biomass yield coefficient and S = the substrate concentration. This introductory treatment assumes that the only reactions are growth and consumption of nutrient. More realistic systems may treat death and interactions such a predation where one organism consumes another.
There are input and output terms for continuous flow systems, but we can usually neglect organisms entering because there are none when the fresh feed is sterile or the input organisms may not thrive in our bioprocess. We introduce the term D for dilution rate (feed rate divided by reactor volume) and use it in the input and output terms. The small subscript o signifies the concentration of the substrate entering.
while on sabbatical leave, ESB, Porto, Portugal July 1996