Chemostat Performance — If biomass yield is constant over the operating range, how does biomass productivity vary with dilution rate D (before washout)?

Introduction:
Biomass productivity in a chemostat is the product of dilution rate and biomass concentration (PX = D * X). Understanding how PX depends on D under constant yield assumptions is central to selecting an operating point that maximizes throughput without risking washout.

Given Data / Assumptions:

• Single limiting substrate; yield Yx/s is approximately constant.
• Monod kinetics with μ = μm * S / (Ks + S).
• Steady state below washout: μ = D < μm.

Concept / Approach:

As D increases from low values, μ increases and substrate concentration rises, but biomass concentration X tends to decrease. The product D * X typically exhibits a maximum at a D near, but safely below, the washout point D ≈ μm. This is analogous to classical continuous-flow reactor optimization for growth-associated production.

Step-by-Step Solution:

Verification / Alternative check:

Plotting PX versus D using typical μm, Ks, Sf, and Yx/s shows a dome-shaped curve peaking below washout, confirming the expected trend.

Why Other Options Are Wrong:

A and D: Ignore the initial rise in PX with D. C: Contradicts dependence of X on D. E: Yield and kinetics are essential determinants, not just volume.

Common Pitfalls:

Operating too close to washout risks instability; choose D with safety margin to account for disturbances and parameter uncertainty.

Final Answer:

It increases with D up to a maximum just below washout (then collapses at washout).