Chemostate analysis

Consider this schematic:

where

[S] is the concentration of growth limiting substrate

F or V is the volumetric flow rate of S into the chemostat

V is the reactor volume

x is the biomass per unit volume (x = biomass/V)

is the biomass growth rate

is the residence time in the reactor (=V/F)

D is the dilution rate (D=F/V)

Cell growth kinetics: rx=x

a) What are the units for rx?

b) Assuming sterile feed, write a steady-state material balance for x.

c) Make a plot of x (y-axis) and S (second y-axis) as a function of D.

d) What happens if D is very large?

Good luck