When viable cells are immobilised on the surface of a support, the cells grow on the
available surface area A(m^2 l−^1 ), until the support-loading capacity (g dry cell weight
m−^2 ) is reached, and the bulk given by Xb(gl−^1 ).
It is assumed that the cells first grow on the surface with a specific growth rate, μS,
where:
(68)
When the support is completely loaded the cells grow into the bulk solution with a
specific growth rate, μb, different (higher) from the surface growth rate μs.
The total biomass (Xtotal) is given by:
(69)
For a CSTR the following equation can be obtained:
(70)
where D(=Q/V) is the dilution rate and YX is the biomass yield coefficient.
When Xim → 0, it can be seen that the typical continuous culture relationship μs=D
can be obtained.
For an immobilised viable cell process the relationship D>μs is is obtained at all
values of D. This implies that for a given D, the exit cell concentration for the
immobilised cell process is always higher than for the continuous culture system. Hence,
the immobilised viable cell reactor is superior to continuous culture in terms of
conversion efficiencies and the washout conditions in submerged continuous cultures are
eliminated by using immobilised cells.
For metabolite production by immobilised viable cells the Luedeking-Piret model can
be used:
(71)
where P is the metabolite concentration.
If K 2 >K 1 , the rate of product formation (primary or growth-associated metabolite) is
given by:
(72)
Maximizing the primary metabolite productivity is the same as maximizing biomass
productivity.
When K 1 >K 2 , a secondary metabolite is obtained and is dependent primarily on the
cell concentration:
(73)
Multiphase bioreactor design 120