Question

In microfiltration what is Dependence of the TMP on the permeate flow, liquid viscosity, membrane resistance, and cake resistance.

Answer 1

Transmembrane pressure (TMP) is the difference between avarage feed pressure and the permeat pressure.

Where

• is the pressure on the Feed Side
• is the pressure of the Permeate

At higher flow rates, with increasing transmembrane pressure, the permeate flux initially increases, eventually reaching a stationary value.

Liquid viscosity:- In the microfiltration, TMP is directly proportional to the viscosity.

an equation can relate the two:-

Where:

J_t = flux at temperature T, Lmh (gfd)

R_t = total membrane resistance, psi/gfd-cp

µ_T = viscosity in centipoises at water temperature T, cp

Membrane resistance:- The total membrane resistance, R_t, is composed of the intrinsic membrane resistance and the resistance of the foulant layer on the membrane

As in above eqation membrane resistance is proportional to the TMP  

and

Where:

R_m = intrinsic membrane resistance, psi/gfd-cp

R_f = resistance of the foulant layer, psi/gfd-cp

Cake resistance:-  Dissolved molecules accumulating at the surface reduce the solvent activity and this reduces the solvent flow through the membrane. This can be represented as a reduction in the effective transmembrane pressure (TMP) driving force due to an osmotic pressure difference between the filtrate and the feed solution immediately adjacent to the membrane surface.

Adeposit of particles can grow layer by layer at the membrane surface, leading to an important additional hydraulic resistance. This is often referred to as a cake resistance.

As the cake resistance will increase, pressure difference across the membrane will decrease and the TMP will also decrease.