Theory

MICROFILTRATION

It is the separation of fine particles and colloids from a liquid or of particulates from a gas using a porous membrane having pore sizes in the range 100-104 nm. Separation occurs by sieving mechanism at a low pressure difference(within 2 bar). A crossflow arrangement is preferred as it involves less accumulation of solid particles on the membrane. The feed usually is liquid/gas containing suspended particulates and the permeated species mostly is the suspending medium and liquid or gas.

Uses

Separation of cells, sterilization of liquid/ gas streams, separation of emulsified oil from water, clarification of liquids/beverages in food industries.

ULTRAFILTRATION

It is the process of separation or concentration by a sieving mechanism of a large molecular weight solute or a colloidal suspension by using a membrane having pore sizes in range of 1-100 nm(in between MF and RO). Some molecules get adsorbed on membrane surface, reducing the pore size significantly. The selectivity criterion of a UF membrane is commonly called molecular weight cut off. It requires a pressure difference of 1-10 bar. The feed may be liquid and the permeated species may be low Molecular weight solute and solvent.

Uses

Separation of biomolecules, proteins,emulsions, dispersed droplets, macromolecules, auto paints from solutions.

Concentration polarization

The reverse accumulation of the rejected solute in the fluid phase at the membrane-fluid interface as the solvent passes through the membrane. When solvent passes through the pores of a membrane, the solute particles are left behind at the feed-side interface of the membrane. As time progresses this solute concentration builds up on the membrane surface and this phenomenon offers a resistance to flow.

The most significant resistances are-

1. Concentration polarization
   
2. Gel formation
   
3. Adsorption
   
4. Pore blockage
   A decline in flux of solvent may occur due to the above resistances. Now let us analyse the situation with some mathematical equations-
   
   

$$Suppose \ J_w \ = \ solvent \ flux$$

$$C_p =\ solute \ concentration$$

C=local concentration of solute in the film or boundary layer

D=diffusivity of the solute

$$C_b =solute \ concentration \ in \ the \ bulk \ solution$$

$$C_m = \ solute \ concentration \ in \ the \ liquid \ in \ the \ membrane \ surface$$

$$L=\ film \ or \ boundary \ layer \ thickness \ from \ where \ the \ concentration \ varies \ from C_m \ to \ C_b$$

Solute flux through the membrane = Convective flux towards the membrane surface – Flux of back diffusion of the solute to the bulk of the liquid

$$=>J_w C_p=J_w C-(-D \frac{dC}{dz})$$

For simple case take boundary conditions as
At z=0 C=Cm
At z=L C=Cb
Liquid side mass transfer coefficient at membrane surface is kL=D/L The rejection coefficient is defined as
R'=1-(Cp/Cm) On simplification,
$$\frac{C_m}{C_b}=\frac{exp(\frac{J_w}{kL})}{R'+(1-R')exp(\frac{J_w}{kL})}$$

Cm/Cb is called the polarisation modulus.
This increases with flux, with increasing retention R' and decreasing kL.
For complete retention
R'=1 and Cm/Cb=exp(Jw/kL)

Gel polarization model

Due to concentration polarisation, the solute concentration at the membrane surface may be very large. Solutes like a polymer or protein may form a slimy layer called gel if a limiting concentration Cg is reached. At steady state, a constant thickness of the gel and a limiting flux J0 are attained. The macromolecules are transported to the membrane convectively as before and back diffused under the gradient (Cg−Cb) . Total resistance is expressed as the sum of membrane and gel resistances.

$$J_0= \frac{∆P}{µ*(R_m+R_g)}$$

Also

$$J_o=k_L ln(\frac{C_g-C_p}{C_b-C_p})$$

$$If the solute rejection is high (C_pb)$$

$$J_0=k_L(lnC_g-lnC_b)$$

REVERSE OSMOSIS

When an aqueous solution of a substance is kept separated from water by a semi-permeable membrane in a two compartment cell, water diffuses through the membrane into the higher concentration compartment. This is osmosis and occurs because of difference of chemical potential of water between the two compartments. If the solution level is elevated, the flow of water through the membrane to the higher concentration side drops. This extra pressure due to the elevated level of the solution is called osmotic pressure(∏). An application of an extra pressure higher than osmotic pressure, chemical potential of water in solutions side becomes more than that of pure water. Under such a condition, flow of water occurs from solution side to the pure water side which is called reverse osmosis. The membrane pore size range is from 0.1 nm-1 nm. The separation mechanism is solution-diffusion. The feed might be salt solutions, sea water and the pressure difference applied is around 10-100 bar. The rejected species are mainly low molecular weight solutes and permeated species is mainly water. The feed water to the RO unit must be preheated to remove suspended and dissolved membrane fouling agents.

Uses

Desalination of sea water, brackish water, treatment of wastewater.