Continuous Culture Kinetics — Definition of Dilution Rate: In a chemostat at steady state, which expression correctly defines the dilution rate D in terms of volumetric flow F and reactor culture volume VR (and the specific growth rate μ at steady state)?

Introduction:
The dilution rate D is a fundamental parameter in continuous culture systems such as chemostats. It links the incoming and outgoing flow to the culture volume and determines the steady-state specific growth rate when the system is stable. Correctly defining D is crucial for predicting washout, productivity, and substrate utilization.

Given Data / Assumptions:

• Well-mixed continuous stirred reactor with constant volume VR.
• Inlet and outlet flow rates are equal to F at steady state.
• Steady-state assumption implies μ equals D below washout.

Concept / Approach:

The dilution rate is defined as volumetric throughput per reactor volume per unit time. Mathematically, D = F / VR. At steady state for a non-limiting toxicity regime, the specific growth rate μ equals D, provided washout has not occurred. This identity allows control of microbial growth by adjusting F at fixed VR.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional analysis confirms that F / VR has dimensions of 1 / time. Experimental steady-state data typically show μ approximates D until approaching washout.

Why Other Options Are Wrong:

B inverts the ratio and has wrong units. C and D mix unrelated variables. E is dimensionally inconsistent for D.

Common Pitfalls:

Confusing D with μm, or forgetting that μ = D is a steady-state result and does not hold during transients or near washout if assumptions break.

Final Answer:

D = F / VR