Bioreactor Design and Operation - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 949

18.9.2. Surface Adhesion Model
Microbes, especially bacteria and mammalian cells, tend to attach to surfaces. Fig. 18.14
shows a schematic of cell wall attachment in a chemostat. In small reactors, the surface to
volume ratio is high and the wall adhesion can play an important role especially at low
cell concentrations. The attachment of suspended microbes to surfaces can be modeled as
adsorption. That is

k

adX

!

Xþs

X X$s

(18.64)

k

de

Assume the surface adhesion of cells is fast and equilibriummay be considered for contin-
uous cultures:

K sX ¼ k adX

k deX ¼ q X$s

(18.65)

Xq V

where q V is the fraction of the vacant sites on the available surface that has no cells attached to

them, is the fraction of the sites on the surface that have been occupied by cells, K s X is the

adhesion constant, and X is cell concentration in culture medium. By definition:

q X $s

q V þq X $s ¼ 1 (18.66)

Eqns (18.65) and (18.66) can be solved to give

K sX X
1þK sX X

q X$s ¼ (18.67)

Therefore, the total viable concentration of cells in the reactor is given by

K sX X
1þK sX X

X T ¼ XþC s q X$s ¼ XþC s (18.68)

where C s is the concentration of total available adhesion sites on surfaces in the reactor. In
some cases, the adhesion of cells on the solid surface can be regarded as irreversible, i.e.
K s X / N

. Eqn (18.68) is then reduced to

X T ¼ XþC s (18.69)

Q, S = S 0

Feed

X = 0

V

Q

Effluent

S , X

FIGURE 18.14 A schematic of a continuous culture with both suspended cells (X) and surface attached cells.
The suspended cells are subject to removal by flow, whereas the surface attached cells are less affected by the flow.