Each glowing speck inside the vessel is a microbial cell (bacterium or yeast, depending on the batch), reproducing by division while a nutrient broth (substrate) is consumed and product molecules accumulate. Growth follows the classic batch-culture curve: a lag phase while cells adapt, an exponential phase where the specific growth rate μ is near its maximum, a stationary phase once substrate or oxygen becomes limiting, and a death phase as waste and depleted nutrients take over. pH, temperature and dissolved oxygen each scale μ through a bell-shaped tolerance curve around the organism's optimum — push any one far enough from center and growth collapses even with plenty of food left.
μ(pH,T,O₂) = μmax · f(pH) · f(T) · f(O₂)
dX/dt = μ·X − kd·X (biomass)
dS/dt = −(1/Yxs)·μ·X (substrate)
dP/dt = (qp)·X (product, growth-associated)
- pH — most industrial fermentations run 5.5–7.5; too acidic or too alkaline slows enzymes and division.
- Temperature — every organism has an optimum band; overheating denatures enzymes fast (death phase arrives early), while cold slows metabolism without killing it.
- Dissolved O₂ — aerobic fermentations (single-cell protein, many antibiotics) need it; starve it and growth plateaus even with substrate left, which is exactly why bioreactors are stirred and sparged.
- Agitation — mixing speed; higher agitation raises effective oxygen transfer but adds shear stress, modeled here as a small drag on max growth rate at extreme settings.
Real-world relevance: this loop — measure pH/DO/temperature, adjust feed and stirring, track the growth curve — is exactly what a fermentation technologist does at pilot and production scale for yogurt cultures, biofuel ethanol, industrial enzymes and antibiotic production.