Page 318 - Biosystems Engineering

Bioseparation Pr ocesses 295

Equation (9.13) is the same as Eq. (9.12). Expanding Eq. (9.13)
we get
V + 2VV + V = Kθ +Kθ (9.14)
2
2
0 0 0
2
Dividing by KV, and noting that for V = 0, V = Kθ , and K = 1/K , we
0 0 1
obtain Eq. (9.12).
Filtration at a Constant Rate
During constant rate filtration, pressure increases with an increase in
cake thickness. Therefore, filtration variables are pressure, filtrate
volume, or pressure and filtration time, and so on. The relationships
are as follows [arranging Eq. (9.10)]:
⎡ αμ w dV ⎞ ⎤ μ R ⎛ dV ⎞
⎛
P = ⎢ ⎜ ⎟ v ⎥ + f ⎜ ⎟ = KV (9.15)
d ⎠
2
d ⎠ ⎦
⎣ AG ⎝ θ AG ⎝ θ 2
c
c
and, in terms of P and θ as variables,
⎡ αμ ⎛ 2 ⎞ ⎤ μ R ⎛ dV ⎞
⎜
P = ⎢ w dV ⎟⎥ K θ + f ⎜ ⎟ ⎟ = K θ (9.16)
⎣ ⎢ AG ⎝ dθ ⎠ ⎦ ⎥ 3 aG ⎝ θ 3
2
d ⎠
c
c
Washing Rate
In most industrial operations, it is required to wash the cake (which
may have water, acid, or alkali in it). Because of its configuration, the
washing rate in a plate-and-frame filter press becomes one-fourth of
the filtration rate. However, in a leaf filter, the washing rate equals the
filtration rate.
Filtration Cycle
Industrial filters, especially if they are discontinuous in operation,
require some time for dumping plates and frames, cleaning the cake,
and reassembling. Consequently, a filtration cycle should consist of
filtration time, washing time (if necessary), and time required for
cleaning and dumping. If C is filtration cycle, where as θ is filtration
F
time, θ is the watching time, θ is cleaning and dumping, and the
W d
volume of filtrate collected in a given cycle is V, then
C = V (9.17)
θ +θ +θ
F w d
It can be shown that for a nonwashing plate-and-frame filter
press, the optimum time of filtration equals the time required for clean-
ing and dumping.
Pretreating Cells to Alleviate Filtration Resistance
It is well-known that broth cultures of actinomycetes and streptomy-
ces, for example, exhibit tremendous resistance to filtration. Many