Page 487 - Water and wastewater engineering

12-4 WATER AND WASTEWATER ENGINEERING

Particles

Membrane
surface
Pores
(a)
Coating on wall
by small particles

(b)
Finer particles
trapped by cake

(c)
FIGURE 12-3
Mechanisms of membrane filtra-
tion: ( a ) Straining, ( b ) adsorption,
( c ) cake filtration.

Particles that are removed by straining build up a cake on the membrane surface ( Figure 12-3c ).
The cake acts as a filtration medium. It improves the efficiency of the filter because it collects
particles smaller than the nominal pore size of the membrane.

Models of Membrane Filtration

The basic models for describing membrane performance are based on the concept of rejection.
The fraction of material removed from the permeate stream is described in the form of a simple
efficiency equation:
⎛ C permeate ⎞
R 1 ⎜ C ⎟ (12-1)
⎝ feed ⎠
where R rejection, dimensionless
C permeate permeate concentration, mg/L or particles/L
C feed feed water concentration, mg/L or particles/L

This equation may also be expressed in a logarithmic form (“log-removal”):
⎛ C ⎞
LR log ⎜ feed ⎟ (12-2)
⎝ C permeate ⎠
or as percent removal
⎛ 100 ⎞
% removal 100 ⎜ LR ⎟ (12-3)
⎝ 10 ⎠