Multiphase Bioreactor Design

Q being the flow rate and A the area of filtration.
The membrane permeability, Lp, can be obtained through the relation with the
transmembrane pressure, ∆PTM:

(16)

The porosity of the membrane, εm, may also be estimated from:

(17)

where lp is the pore length, η the viscosity and dp, the pore diameter.
The number of membrane pores per unit area, np, can be obtained from:

(18)

The internal area of each pore, Ap is:

(19)

and the total internal area of the pores is:

(20)

The volume of each pore, Vp, is given by:

(21)

In asymmetric or anisotropic membranes the pore length is usually 1–2μm as determined
by field emission scanning electron microscopy (FESEM) (Doyen et al., 1996). However,
the separation takes place in a layer of high density usually designated by “active surface
of the membrane”, which is considerably thinner. According to Mulder (1992) this active
layer has a thickness between 0.1 and 0.5 μm (see Figure 7.3).

Membrane rejection coefficients

Transmission experiments have also to be performed to assess membrane rejection
coefficients, (σ0bs) for the different system components.
The NMWCO allows a prediction of membrane exclusion behaviour, although the
dispersion of pore size, the hydrophobic/hydrophilic character of the membrane,
orientation and conformation of the solutes and interactions may severely interfere with
the final result which makes operational verification essential. The rejection coefficient is
defined as:

(22)

Multiphase bioreactor design 212