106 M.J. Lewis ejection(see also Chapter 3)and the flow rate of permeate or permeate flux, hereafter abbreviated to'flux'. The flux will probably be measured in gallons/ min or litres/ hour, but it is usually presented in terms of volume per unit time per unit area(I m h -) Expressed this way it allows a ready comparison of the performance of different mem brane configurations with different surface areas. Flux values may be as low as 5 or as high as 450 I m-h. The flux is one of the major factors influencing the viability of many processe UF processes have been subject to a number of modelling processes, in an attempt to predict flux rates and rejection values from the physical properties of the solution, the membrane characteristics and the hydrodynamics of the flow situation, in order to opti mise the performance of the process 4.3.1 Transport phenomena and concentration polarisation Ultrafiltration is usually regarded as a sieving process and in this sense the mechanisms are simpler than for RO. However, it is important to remember that for pressure-driven membrane processes, the separation takes place not in the bulk of solution, but in a very small region close to the membrane, known as the boundary layer, as well as over the membrane itself. This gives rise to the phenomenon of concentration polarisation over the boundary layer.(Note that in streamline flow the whole of the fluid will behave as a oundary layer) Concentration polarisation occurs whenever a component is rejected by the membrane As a result there is an increase in the concentration of that component at the membrane surface, and a concentration gradient over the boundary layer. This increase in concentra tion offers a very significant additional resistance, and for macromolecules may also give se to the formation of a gelled or fouling layer on the surface of the membrane(see Fig 3.4). It is interesting to note that the boundary layer does not establish itself immediately at the point where the fluid first contacts the membrane. Rather it takes some distance fo it to be fully established. This distance taken for it to be fully established has been defined as the entry length, and the process of establishment is illustrated for a tubular membrane in Fig. 4.4. Howell et al.( 1990)have analysed flux conditions over the entry length and have concluded that the flux and wall concentrations change quite consider ably over the developing boundary layer, although changes were less marked for a fouled membrane. There would also be less likelihood of operating in the pressure-independent Membrane d Retentate Boundary layer Membrane Permeate Fig. 4.4. Development of the concentration polarisation or boundary layer106 M. J. Lewis rejection (see also Chapter 3) and the flow rate of permeate or permeate flux, hereafter abbreviated to 'flux'. The flux will probably be measured in gallons/min or litres/hour, but it is usually presented in terms of volume per unit time per unit area (1 m-2 h-l). Expressed this way it allows a ready comparison of the performance of different mem￾brane configurations with different surface areas. Flux values may be as low as 5 or as high as 450 1 m-* h-'. The flux is one of the major factors influencing the viability of many processes. UF processes have been subject to a number of modelling processes, in an attempt to predict flux rates and rejection values from the physical properties of the solution, the membrane characteristics and the hydrodynamics of the flow situation, in order to opti￾mise the performance of the process. 4.3.1 Transport phenomena and concentration polarisation Ultrafiltration is usually regarded as a sieving process and in this sense the mechanisms are simpler than for RO. However, it is important to remember that for pressure-driven membrane processes, the separation takes place not in the bulk of solution, but in a very small region close to the membrane, known as the boundary layer, as well as over the membrane itself. This gives rise to the phenomenon of concentration polarisation over the boundary layer. (Note that in streamline flow the whole of the fluid will behave as a boundary layer.) Concentration polarisation occurs whenever a component is rejected by the membrane. As a result, there is an increase in the concentration of that component at the membrane surface, and a concentration gradient over the boundary layer. This increase in concentra￾tion offers a very significant additional resistance, and for macromolecules may also give rise to the formation of a gelled or fouling layer on the surface of the membrane (see Fig. 3.4). It is interesting to note that the boundary layer does not establish itself immediately at the point where the fluid first contacts the membrane. Rather it takes some distance for it to be fully established. This distance taken for it to be fully established has been defined as the entry length, and the process of establishment is illustrated for a tubular membrane in Fig. 4.4. Howell et al. (1990) have analysed flux conditions over the entry length and have concluded that the flux and wall concentrations change quite consider￾ably over the developing boundary layer, although changes were less marked for a fouled membrane. There would also be less likelihood of operating in the pressure-independent Permeate Membrane Feed inlet --+- Retentate Boundary layer Membrane Permeate Fig. 4 4. Development of the concentration polansation or boundary layer