= Dilution rate
{title2=$D=Q/V$}
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 $\ln2/D\approx1.39\,\mathrm{h}$, 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.
Back to article page
