Pressure-activated membrane processes 67 solid constituents. In some applications it is the permeate which is the required material for example the production of 'drinking waterfrom sea-water or 'pure water brackish water. The best processes are those where both the concentrate and the permeate e fully utilised. There have been several comparisons made between evaporation and reverse osmosis in terms of capital costs, energy costs and product quality(Renner, 1991). In general terms Ro is less energy intensive and can improve product quality. Some limitations are the high capital costs, membrane replacement costs and extent of concentration, which is not as high as that obtainable by evaporation If a fluid, for example milk, is separated from water by a semi-permeable membrane (see Fig. 3.2()), there will be a flow of water from the water to the milk, in order equalise the chemical potential of the two fluids; this is termed osmosis. This flow of water can be stopped by applying a pressure to the milk. This pressure that stops the flow termed he osmotic pressure. If a pressure greater than the water will flow from the milk to the water, thereby reversing the natural process of osmosis and achieving a concentration of the milk. Therefore in reverse osmosis, the pressure applied needs to be in excess of the osmotic pressure. Osmotic pressure(r)is a olligative property, the pressure being dependent upon the number of particles and thei molecular weight. In classical terms it is determined from the Gibb's free energy InyX (3.1) whereR= gas constant, T=absolute temperature, y= activity coefficient, X mole frac tion, and Vm= partial molar volume For dilute solutions of non-ionisable materials, the Van t Hoff equation can be used 丌=RT(c/M) (3.2) where c= concentration(kg m")and M= molecular weight For ionisable salts this becomes iRT(c/M) (3.3) where i= the degree of ionisation, e. g. for NaCl, i= 2; for FeCl2, i=3. This equation predicts a linear increase in osmotic pressure with concentration. How ever, this relationship breaks down, even at relatively low concentrations, with the rela- tionship between osmotic pressure and concentration becoming non-linear. For example, the osmotic pressure of a 25% serum albumin solution was 300 t, which is about six times higher than predicted from the Van't Hoff equation. It is also affected by pH This non-linear relationship can be represented by virial type equations 兀=Ac+Bc2+Dc (3.4) where c=concentration and A, B and D are constants. The constants are presented for dextran and whey by Cheryan(1986)Pressure-activated membrane processes 67 solid constituents. In some applications it is the permeate which is the required material; for example the production of ‘drinking water’ from sea-water or ‘pure water’ from brackish water. The best processes are those where both the concentrate and the permeate are fully utilised. There have been several comparisons made between evaporation and reverse osmosis, in terms of capital costs, energy costs and product quality (Renner, 1991). In general terms RO is less energy intensive and can improve product quality. Some limitations are the high capital costs, membrane replacement costs and extent of concentration, which is not as high as that obtainable by evaporation. If a fluid, for example milk, is separated from water by a semi-permeable membrane (see Fig. 3.2(b)), there will be a flow of water from the water to the milk, in order to equalise the chemical potential of the two fluids; this is termed osmosis. This flow of water can be stopped by applying a pressure to the milk. This pressure that stops the flow is termed the osmotic pressure. If a pressure greater than the osmotic pressure is applied, the water will flow from the milk to the water, thereby reversing the natural process of osmosis and achieving a concentration of the milk. Therefore in reverse osmosis, the pressure applied needs to be in excess of the osmotic pressure. Osmotic pressure (T) is a colligative property, the pressure being dependent upon the number of particles and their molecular weight. In classical terms it is determined from the Gibb’s free energy equation: (3.1) RT ;rl=-1nyX “m where R = gas constant, T = absolute temperature, y= activity coefficient, X = mole frac￾tion, and V, = partial molar volume. For dilute solutions of non-ionisable materials, the Van’t Hoff equation can be used z = RT(C/M) (3.2) where c = concentration (kg m-3) and M = molecular weight. For ionisable salts this becomes ;rl = iRT(c/M) (3.3) where i = the degree of ionisation, e.g. for NaC1, i = 2; for FeC12, i = 3. This equation predicts a linear increase in osmotic pressure with concentration. How￾ever, this relationship breaks down, even at relatively low concentrations, with the rela￾tionship between osmotic pressure and concentration becoming non-linear. For example, the osmotic pressure of a 25% serum albumin solution was 300 2, which is about six times higher than predicted from the Van’t Hoff equation. It is also affected by pH. This non-linear relationship can be represented by Virial type equations: ;rl = Ac+ Bc2 + Dc3 (3.4) where c = concentration and A, B and D are constants. The constants are presented for dextran and whey by Cheryan (1986)