Membrane And Cake Resistances Biology Essay

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Dead end membrane filtration is a batch process that can separate liquid and suspended solids effectively. Membrane filtration is widely used in water purifications and chemical industries in order to eliminate out the foreign matters in liquid. Membrane and cake resistances as well as filtration behaviour on macromolecular system are investigated through dead end filtration. In this experiment, 0.22 micron GVWP Millipore PVDF membrane was used. Water was used to determine the membrane resistance while the yeast cells were used to determine the cake resistance and fouling model. Pressure of 50 kPa was applied from gas cylinder and magnetic stirrer was set to 300 rpm. The data was collected and analysed by LabView software. Based on the data from water testings, the steady state membrane resistance was 8.55*1010 ±3.38*108 m-1. The steady state flux of water testings was 6.5*10-4 m/s. Flux was decreasing over the concentrations of yeast solution. Two types of fouling model were found in this experiment: pore constriction and cake filtration. Sedimentation of yeast cells before starting experiment also caused the initial cake resistances became negative value or negative filter medium. On top of that, filtration pressure was increasing proportionally to height of cake. Since constant pressure was used, flux was decreasing as height of cake was increasing as a function of time. In order to reduce the operating cost, membrane can be cleaned with backward flush or chemical cleaning as long as the membrane structure has not been destroyed by the foreign matters.

Table of Contents


Nowadays, water shortage becomes more serious and concerned by the world leaders. Water pollution is a main cause to water shortage. Polluted water may consist of industrial wastes and toxic substances as well as not suitable for drinking water. In order to overcome this problem, membrane filtration may be an effective and economical method. Membrane is a physical barrier and has many micro or nanometre pore diameter. Tiny pore diameter can eliminate the mineral salts and microorganisms from polluted water. Because of this, colourless and clean water is produced. The example for this case is NEWater in Singapore. The production of NEWater consists of four barriers and three stages. The source for making NEWater is from sewage and purifying through dual-membrane.

In this experiment, dead end membrane filtration was chosen to carry out the experiment. A 0.22 micron GVWP Millipore PVDF membrane was used. Feed was forced by a pressure to flow through the membrane. If the yeast solution was used, the yeast would accumulate on the membrane and form a cake. The dead end membrane filtration in this experiment was carried out as batch process due to all the suspended particles would deposit on membrane and grow cake. Size of yeast cells was much bigger than the diameter of membrane pore. Thus, the yeast cells could not pass through the membrane while the water would be collected as filtrate. Some of yeast cells might clog the pores on membrane and this could decrease filtration capacity. In fact, the dead end membrane filtration is a very good ways to concentrate the compounds.

The aim of this experiment was to determine the membrane and cake resistances and compare the results to porous media theory. This experiment also could investigate the filtration behaviour and macromolecular systems. This could be verified by using water and different concentrations of yeast solution (3, 4 and 6 g/L) testings. Water was used to determine the membrane resistance while yeast solution was used to determine the cake resistance as function of time. The types of membrane and yeast were kept constant.

Theory/ Literature

3.1 Membrane Resistance (Rm)

The membrane resistance is calculated by using equation below:


3.2 Cake Resistance (Rc)

Since the same membrane was used on all testings, the membrane resistance was constant. The cake resistance could be calculated as follow:


3.3 Hagen Poseuille Equation

This equation can calculate the theoretical flux on the membrane by assuming the ducts are cylindrical and uniform. This equation also assumes the membrane surface has number of cylindrical pores which on parallel. The equation is shown as below:


3.4 Specific Cake Resistance (α)

Specific cake resistance depends on pressure and is a parameter in this experiment. Specific cake resistance measures the filterability of the suspension solids and determines the speed of filtration. The equation is shown as below:


3.5 Fouling model (n)

When the constant pressure is used, the fouling model on membrane can be determined by plotting ln (d2τ/dV2) against ln (dτ /dV). The equation is shown as below:


where n=0 is cake filtration, n=1 is intermediate blockage, n=1.5 is pore constriction and n=2 is complete pore blockage.


Viscosity of water was 8.9*10-4 N.s/m2 at 25oC.

Viscosity of yeast was same with viscosity of water at 25oC.

Tortuosity (Ï„) was 1.

Yeast solution was well mixed.

The membrane was cleaned and no contaminated.

TranMembrane Pressure (TMP) was same as pressure applied from nitrogen gas cylinder.

Filtrate collected was water only and density was 1000 kg/m3.

Cake mass formed per unit volume of filtrate was 1.

Area of filter was 0.0014 m2.

Incompressible cake formation.

Error was mainly contributed from pressure gauge. The error of pressure gauge 0.1.


At the beginning of experiment, the cell and reservoir were inspected and cleaned. LabView software was turned on and the loop was set to 5 seconds. Microfiltration membrane (0.22 micron GVWP Millipore PVDF membrane) was cut into correctly sized circle stencilled from the cell. The membrane was soaked with water for a few seconds. Then, the membrane was assembled in cell and tightened with wrench. The reservoir was filled with water and connected to nitrogen gas cylinder through a tube. The cell was placed on stand and the beaker was placed on electronic balance and the balance was set to zero. The experiment set up was shown as Figure 1. After the permeate valves was closed, the pressure was increased to 50 kPa based on the largest pressure gauge scale. The LabView software was simultaneously starting to collect and analyse data. Each testing was carried out for five minutes. When finishing the testing, the valve on gas cylinder was turned off and the reservoir pressure was reduced be opening the reservoir fitting. The water testing on membrane was repeated for four times.

For yeast testing on membrane, the different concentrations were used. 3 g/L of yeast cells was dissolving in Milli-Q water. A new membrane was fitted on the cell; the cell feed and reservoir were filled with yeast mixture. The stirrers in cell and reservoir were set to 300 rpm. 50 kPa of nitrogen pressure was used and the result was recorded as function of time. The procedures for other concentrations of yeast solution were same with 3g/L of yeast cells. The membranes for water and yeast testing were kept on separate evaporating dishes. The types of testing carried out and concentrations of yeast used were tabulated in Table 1.

Figure : Experiment Set Up


Types/ Concentration of yeast

Pressure used (kPa)











Yeast (3g)


Yeast (4 g)


Yeast (6 g)

Table : Types of testing


According to Merck Millipore, the pore radius for 0.22 micron GVWP Millipore PVDF membrane was 2.2*10-7 m. The thickness of this membrane was 1.25*10-4 m and porosity was 70%. The membrane was hydrophilic.

Since the TranMembrane Pressure was the same for all testings, the theoretical flux from Equation (3) was constant in water and yeast solution experiment. The theoretical flux was 0.0019 m/s. The steady state membrane resistance at 50 kPa was calculated as 8.55*1010 ±3.38*108 m-1. The steady state flux on water testings was 6.5*10-4 m/s. For water testing, the membrane resistances for each trial were plotted as function of time and shown in Figure 2 under Appendix.

The average cake resistances on 3g, 4g and 6g of yeast were calculated as 5.18*1011±2.48*109 m-1, 2.73*1011±7.23*109 m-1 and 3.3*1011±6.66*108 m-1. The cake resistances on different concentrations of yeast solution were plotted as function of time and shown as Figure 3 under Appendix. Flux against time and cake resistance against flux were shown as Figure 4 and 5. These figures showed that flux was depending on the cake resistance as function of time.

The specific cake resistances for 3g, 4g and 6g of yeast were 6.92*106 m/kg, 5.55*106 m/kg and 8.76*106 m/kg. These results were calculated from gradients in Figure 6.

In this experiment, fouling model applied. 3g and 4g of yeast had pore constriction fouling models while 6g of yeast had cake filtration fouling model. These were done with using Figure 7 and 8.

From the experiment, the performance of filtration was decreasing over time. Flow rate of filtrate gradual decreased and could be observed from the reading on electronic balance. The surface of membrane was deposited with a lot of yeast cells.


6.1 Flux

Flux depended on resistance of membrane and cake. Resistance was inversely proportional to flux based on Equation (1) and (2). The resistance was mainly come from clogging on membrane pores and height of cake. When the resistance increased, the liquid permeated through the membrane was decreasing and the flux decreased too. For yeast solution, the flux was decreasing when the concentration of yeast solution became more saturated. As more saturated yeast solution was used, yeast cells would deposit much quickly on the membrane. The deposited yeast cells would form cake and increase its height. Some of yeast cells might block the pores on membrane. Thus, the resistance of cake occurred and decreased the flux rate.

6.2 Membrane Resistance

Water testing was used to determine the membrane resistance due to it did not contain any macromolecules. From the results on water testing, the average membrane resistance was decreasing over each testing. This might due to the cell was not cleaned enough and had been contaminated from previous users. The Milli-Q Water was highly purity and did not contain any suspended matter. Moreover, the accumulation of water in complexity membrane structure also might cause minor effect on the membrane resistance. The membrane used was hydrophilic which would absorb water. The absorbed water might affect the pore diameter on the membrane which might cause the membrane to expand and swollen. After a few water testings, the membrane resistance became steady due to the contamination had been washed away.

6.3 Cake Resistance

Based on the result of each yeast solution testing, the initial cake resistance was found negative value or negative filter resistance. Due to the yeast cells were quite heavier, they might start sedimentation before filtration starting. The cake resistance could not be accurately measured by using above equations once the sedimentation occurred. Because of this error, the cake resistance was inaccurately measured when using saturated yeast solution.

6.4 Specific Cake Resistance

According to Jenny Ní Mhurchú BE (2008), specific cake resistance could be determined from the gradient of t/V against V under constant pressure. Specific cake resistance could determine the efficiency of filtration. Due to specific cake resistance depended on too many variables, it could be simplified and replaced with total applied pressure. This pressure was mainly influence the specific cake resistance if the cake resistance was dominant in whole experiment.

6.5 Fouling Model

According to Cristiana Luminita (2012), Equation (5) was used to determine the fouling model. The gradients from Figure 8 were used to calculate the n values which able to find out the fouling model. From fouling model, the pore constriction was defined as fouling occurred in membrane internal pores. It was assumed that radius of pore was decreasing by adhesion material and straight through pores. The cake filtration was defined as sedimentation of solid on membrane and created filtration resistance. Based on the result, 6g of yeast solution was cake filtration. This might due to the high concentration of yeast cells deposited on membrane and inefficient of magnetic stirrer. This problem caused the flux to decrease due to water require more pressure to permeate through the cake compared to pore constriction. For 3g and 4g of yeast, they had pore constrictions. Some of yeast cells might stuck in pore and unable to move. This phenomenon was known as clogging. This had decreased the porosity of membrane and affected the filtrate flow.

6.6 Membrane Performance

Due to the size of yeast cells was much larger than diameter of membrane pore, most the yeast cells were left on membrane and clogging the membrane pores. Filtrate needed more energy to permeate through the membrane when the membrane surface was clogged. Under constant applied pressure, the flow rate of filtrate would decrease due to they did not have extra energy to permeate through the clogged membrane. In order to reuse the membrane and increase the efficiency, clogged membrane could be cleaned with backward flush or chemical cleaning. Besides that, membrane could be affected by three fouling factors: feed characteristics, membrane properties and hydrodynamic environment encountered by the membrane. According Herbert H.P. Fang (2005), permeation flux of PVDF membrane was fully recovered after sonication. Sonication could effectively remove the cake on PVDF membrane. Based on Natural Organics Removal using Membranes, the pure water flux for 0.22 micron GVWP Millipore PVDF membrane was 2.21*10-3 ±8.06*10-5 m/s. The water flux from this experiment was much smaller than the value from Natural Organics Removal using Membranes. This might due to the different area of membrane was used. The Natural Organics Removal using Membranes used 1.52*10-3 m2 while this experiment used 1.4*10-3 m2.

6.7 Explanations on Assumption

Viscosity of yeast solution was assumed to viscosity of water. This was due to most of the yeast cells deposited on membrane and the filtrate would be water only. The reading from mass balance was measuring the mass of filtrate (water). Thus, it would easier to assume that viscosity of yeast solution was same with water. On top of that, the tortuosity was assumed as 1 and used in Equation (3). Tortuosity was defined as ratio of membrane porosity and effective pore length. Without microscopy assistance (Scanning Electron Microscope), microstructure of membrane could not be determined. On top of that, the new membrane was assumed as cleaned and not contaminated. Hands could not touch or hold the membrane due to hands might contain some micro foreign matters and accidentally rub off the micro structure on membrane surface. Tranmembrane pressure (TMP) was assumed to pressure applied from gas cylinder. It was defined as the average pressure between feed and membrane sides. TMP involved feed, retentate and filtrate pressures. In order to simplify the calculation, it could be assumed TMP was same with pressure from gas cylinder. In order to calculate specific cake resistance, cake mass formed per unit volume of filtrate was assumed as 1. This was due to this experiment shortage of data on mass fraction of solids in suspension and in cake. The cake was assumed as incompressible. Under constant applied pressure, the pressure resistance increased proportionally to cake height and thus flux decreased over time.

6.8 Error Analysis

Error calculations and statistical analysis were applied from a book whose authors were Hibbert, D.B & Gooding J.J (2006). All the errors were in 95% confidence interval. Specifications of membrane and properties of water did not contain any error due to they were measured under standard conditions.


In a nutshell, dead end membrane filtration is a good method to eliminate water out if desired product is collected from membrane surface. Although it is very expensive and requires high applied pressure to maintain filtration performance, it is able to produce high quality and concentrated product. From water and yeast solution testings, membrane and cake resistance could be estimated. This experiment also could investigate filtration behaviour and macromolecular system based on data collection. The filtrate volume as a function of time was used to investigate the fouling model on membrane. In this experiment, the cake was incompressible due to flux decreasing over time.


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