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The purpose of the study is to understand the principles of cross-flow ultrafiltration separation process and factors that affect the mass transfer coefficient during the ultrafiltration process of macromolecules. Results show that the experimental mass transfer coefficient deviates from the theoretical mass transfer coefficient obtained using Sherwood number due to several factors. As the ultrafiltration process continues for a period of time, problems such as fouling and concentration polarization tend to occur. The presence of fouling tends to reduce the efficiency of the membrane, increase cost of cleaning of the membrane and causes the loss of productivity of the process.
The application of membrane filtration processes is one of the separation processes that have been widely used in the recent developments of industrial operations. These processes are used to separate macromolecules, organic molecules, small colloids, solvents, ions as well as fine particles . The principle of membrane separation is based on the application of a thin barrier or film between two different phases with preferential transport of some species over others. Some solutes and solvent that are able to pass through the membrane are known as permeate while other solutes that are rejected by the membrane remained in the feed side as the retentate.
There are various types of driving force for membrane separation and they are mainly pressure, concentration, temperature differences and electrical potential . In this experiment, we will concentrate on the ultrafiltration separation process. Ultrafiltration is utilized as an effective pressure driven process to remove macromolecules such as protein, small colloidal particles and other contaminants . The objective of this experiment is to determine the wall concentration and the mass transfer coefficient of the ultrafiltration of protein solution. As concentration polarization is one of the problems that lead to the declination of permeate flux of the membrane, the filtration behaviour of the cross-flow ultrafiltration system such as fouling and concentration polarization will be studied in this experiment.
In cross-flow ultrafiltration process, the solutes in the feed stream are convectively driven to the surface of the membrane and the rejected solutes are removed and recirculated to the bulk by back diffusion . This process allows the fluid to flow tangentially  to the porous membrane to prevent the accumulation of retained solutes on the surface of the membrane while the rejected solutes remain on the feed side as retentate.
Many of the macromolecules have notable osmotic pressure and this leads to the buildup of solutes which may form a gel-like layer on the membrane surface. This phenomenon tend to increase the hydraulic resistance against the permeate flux and may reduce the flux and alter the rejection of the solutes. As the retained or rejected solutes accumulate on the surface of the membrane, the concentration gradient increases and causes concentration polarization to occur. Concentration polarization reduces the activity of the solvent and reduces the solvent flow through the membrane as well as increases the potential of fouling.
Equipment and Methods
The schematic diagram of the cross-flow ultrafiltration process can be seen in Figure 2 in Appendix A. The tubing, cross-flow filtration cell with the filtration channel having dimensions of 2.5cm width, 11cm length and 3.1mm height and the feed reservoir were cleaned and free of particulates beforehand. This step was made sure before inserting the membrane into the filtration cell.
Then, the ultrafiltration membrane made of polyethersulfone  was inserted into the filtration cell using tweezers with only the very edge of the membrane being touched. The membranes may need to be soaked before being used. Any part of the membrane that will be exposed in the filtration cell was avoided being touched as well as the surface is damaged easily.
The filtration cell was configured by firstly tightening the fittings by hands and then using the wrench and they should not be over tightened. The reservoir was then filled with Milli-Q water. The permeate line of the filtration cell was placed over the beaker which was positioned on the electronic balance. The electronic balance was zeroed and the valve on the permeate line was kept closed.
Both the valves in the bypass line and in the retentate line were adjusted when the feed pump is turned on to meet the desired feed flow rate and the pressure of the feed. The valve on the permeate line was opened after the flow rate of the feed and the feed pressure were stabilized. The data acquisition program was set to measure the weight on the balance over a proper time interval.
The permeate flow was measured for 5 to 10 minutes and the membrane resistance was calculated. The value of the resistance was compared with the manufacturer's membrane resistance value. Note that step 1 to step 5 must be repeated and the current membrane must be replaced with a new piece if the value is not in a reasonable range. The Milli-Q water in the reservoir and in the pipe line is drained.
Bovine serum albumin (BSA) solution was made with 0.1M phosphate buffer solution which has a pH of 7.4 . The BSA solution must be fully dissolved and the pH values with the pH meter were double checked. The feed reservoir was then occupied with BSA solution and the permeate line with the permeate pump were clamped. The permeate line was placed over a beaker on the electronic balance and zeroing was performed again as well as keeping the permeate pump off.
The steps from adjusting the valves to making sure the feed flow rate and pressure were stabilized were repeated. The permeate pump was turned on to meet the required permeate flux while the transmembrane pressure was measured with time using the data logging system.
The rotation speed of the permeate pump was increased after 10 to 20 minutes to increase the permeate flux. The TMP profile against time was monitored. The permeate sample was collected and the BSA concentration was measured using UV spectrometer.
The previous step was repeated until TMP increase against time is visible. The flux step gap is kept constant and 20 minutes filtration time was allowed for each flux step. When the experiment ended, the used membrane was saved in beakers of clean water. The variation of permeate flow rate and permeate flux step for BSA solution are given below.
Flux step (L/m2/hr)
Flow rate of solvent (mL/min)
0 - 20
20 - 40
40 - 60
60 - 80
Table Values of each flux step with its corresponding flow rate for BSA solution.
Results and Discussion
The experiment is first carried out with Milli-Q water to determine the resistance of the membrane in the absence of fouling. Milli-Q water has very high purity with very little to negligible salt concentration and therefore when calculating the membrane resistance in the filtration equation, the osmotic pressure is zero as the feed is a pure solvent. The membrane resistance, Rm was calculated to be 7.943 x1011 m-1 using the equation J = TMP / (µRm)  where the viscosity of fluid at a temperature of 25oC is 8.94 x 10-4 Pa.s  and the TMP value can be found in Appendix B.
The cross-flow velocity is the rate of the feed flow into the filtration channel and across the membrane. The cross-flow velocity is found to be 3.64 x 10-3 m/s as the flow rate of water is given as 600 cm3/min and the cross-sectional area of the ultrafiltration membrane used is 0.00275m2. The Reynolds number in the filtration channel is 22.44 and is calculated using the Reynolds equation where the diameter is the hydraulic diameter, dh of the flat rectangular membrane of height h and width w. The sample calculation of values of cross-flow velocity, Reynolds number and hydraulic diameter, dh are detailed in Appendix C.
The Milli-Q water is then replaced with BSA solution containing macromolecules such as protein. The flow rate is started off with a value of 0.46 mL/min and the starting flux value for the BSA solution was 10 L/m2/hr. The corresponding values for the permeate flux and the flow rate of BSA solution which is found in Table 1 are used as a set point for each flux step for every 20 minutes of filtration time. The graph below represents each flux step corresponding to its transmembrane pressure (TMP) for BSA solution over a period of time.
Figure Relationship between permeate flux and the corresponding transmembrane pressure for BSA solution over a period of time
From Figure 1, it can be seen that at the early stage, the permeate flux is linearly proportional to the transmembrane pressure and as the period of time increases, the flux versus TMP curve deviated from linearity . When the flux does not increase in proportion with the increase in TMP, fouling start to occur which will then lead to the buildup of resistance at each flux step due to the increasing TMP .
The critical flux is defined as the permeate flux above which the fouling starts to occur. Operation above the critical flux value reduces the permeate flux back to its critical value as fouling occurs over time . When this happens, increasing the TMP beyond the graph in Figure 1 will only cause the permeate flux to fall back to the critical flux. This is because fouling has already occurred when the critical flux value has been exceeded . V.Chen et al.  states that the onset of fouling occurs when the flux and the solute's concentration that is required to pass through the pore increases at the wall of the membrane beyond the pore size of the membrane.
With the ultrafiltration experiment using BSA solution as compared to Milli-Q water, osmotic pressure is not negligible and can be calculated using the filtration equation. Osmotic pressure with its corresponding wall concentration, Cwall and the mass transfer coefficient, k can be calculated and tabulated in Table 2. The detailed calculation of the values obtained can be found in Appendix C.
Flux step (L/m2/hr)
Osmotic pressure (Δπ)(Pa)
Mass transfer coefficient, k
Table Results of osmotic pressure and its corresponding wall concentration and mass transfer coefficient
The theoretical value for k can be derived from Sherwood number correlation for developing flow :
where Sh = Sherwood number, Re = Reynolds number, Sc = Schmidt number, dh = hydraulic diameter and l = length of the filtration channel. The predicted value of k was found to be 2.9 x 10-6 m/s . The theoretical value of mass transfer coefficient are compared with the experimental value using the relationship of Sherwood number and it can be seen that the mass transfer coefficient calculated from the experiment has a lower value as compared to the theoretical value obtained.
Experimental techniques using suction effect on Sherwood number have been carried out by De S et al.  to predict the mass transfer coefficient, k in cross-flow ultrafiltration process. De S et al. states that the standard Sherwood number that is used to predict the theoretical k value has a variation of limitations. Sherwood number does not take into the effect of suction in the presence of a permeable membrane and concentration due to concentration polarization of the solvent . The effect of pressure which is present during the cross-flow ultrafiltration process is also neglected in Sherwood number when predicting the k value.
De S et al.  propose that presence of suction increases the mass transfer from the surface of the membrane to the bulk solution. From the graphical study of the experimental data plotted by De S et. al , it can be observed that for BSA, a macromolecule solute, the Sherwood number increases as the extend of the suction increases. The mass transfer coefficient that is predicted from the Sherwood number increases when other variables in the Sherwood correlation remain constant.
On the other hand, as the properties of the solution such as the concentration of the solvent increases, the mass transfer through the membrane decreases. This is because the concentration of solute on the membrane surface is much higher than the concentration of solute in the bulk solution. Therefore, the phenomenon of severe concentration polarization on the surface of the membrane occur which results to the addition of resistance to the flux of the solvent . This leads to the decrease in mass transfer across the membrane which eventually decreases the mass transfer coefficient.
Based on the graph plotted between the permeate flux and transmembrane pressure against time, it can be seen that the TMP increases proportionally with time. The permeate flux increases at a proportional rate at the beginning and the rate of increasing of the permeate flux tend to decrease gradually as time increases. This is because as time increases, the accumulation of the solutes on the mass transfer boundary layer tends to increase. The buildup of the dissolved particles on the membrane surface will reduce the flow of the solvent through the porous membrane.
Robert Field  states that an ultrafiltration process where there is a constant flux will yield an increase in the transmembrane pressure (TMP) as time increases. This can be seen from the plot of TMP against time found in Appendix B. The rate of TMP increase is linear in the presence of constant flux and can be represented by the straight line in graph of TMP against time which indicates the formation of cake on the membrane surface.
The filtration behaviour of the cross-flow ultrafiltration system and the mass transfer of macromolecules across the permeable membrane were studied. It can be seen that the mass transfer coefficient can be affected by various factors ranging from the suction to the physical properties of solvent. The concentration polarization and progress of fouling were also studied and shows that both of the phenomena can affect the permeate flux and decreases the performance of ultrafiltration. Fouling could also lead to the contamination of product  and damages to the membrane as a long term effect. Therefore, cleaning techniques should be implemented at an early stage to reduce the potential of fouling.