Dilution rate ($D=Q/V$)

The dilution rate is the fraction of a constant-volume chemostat replaced per unit time: volumetric flow $Q$ divided by culture volume $V$. For $Q=1\mathrm{L}{\mathrm{h}}^{-1}$ and $V=2\mathrm{L}$, $D=0.5{\mathrm{h}}^{-1}$. A well-mixed constituent with no source and absent from the feed has concentration $a(t)=a(0)e^{-Dt}$, since $\dot{a}=-Da$. Thus $1/D=2\mathrm{h}$ is the time for its concentration to fall by a factor $e$, not the time by which all original material has left.

At a positive chemostat steady state, the specific growth rate equals the dilution rate; the biomass concentration stays constant because production balances outflow. For $D=0.5{\mathrm{h}}^{-1}$, growth alone would have doubling time $\ln 2/D\approx 1.39\mathrm{h}$, even though the vessel's biomass concentration does not double. Raising the dilution rate beyond $\mu (s_{\mathrm{in}})$ causes chemostat washout; comparing it only with ${\mu }_{\max }$ misses the nutrient limitation imposed by the feed.