7/31/2019 HW#2 August 13, 2012

1/1

Department of Biochemical Engineering & Biotechnology

BEL416: Membrane Applications in Bioprocessing

Home Work Sheet #2August 14, 2012

1. Calculate the water flux (in LMH) through a microfiltration membrane (NMWCO=80,000) with a mean pore diameter of 5.4 nm, pore density of 2.4x1011 pores/cm2 and

skin thickness of 0.4m at an applied pressure of 125 kPa at 27C. Water viscosity is 1cp.

2 (a). Actual bubble point pressures are frequently found to be much lower than

theoretically calculated bubble points for membranes. Explain the reason.

2 (b). Calculate the diameter of the pore of the membrane, which has a bubble point

pressure of 75 psig when the test was carried out with water at 20C with a surface

tension of 70 dyne/cm. The membrane is highly wettable and the contact angle can be

assumed to be zero. Is this diameter of the largest/smallest/average pore?

3 (a). A membrane had a pore density of 8x 109

pores per square centimeter of the surface

area. The mean diameter of the pores was same as the diameter obtained in the previousquestion. The thickness of the membrane skin was 1x 10 -5 cm. Calculate the maximum

and minimum flux that could be obtained when using the membrane to filter a microbial

cell solution with a viscosity of 1.5 cp. The pressure across the membrane is maintained

using a nitrogen gas cylinder, which can provide upto 100 kPa pressure above theatmospheric pressure. If the initial feed had a concentration of 8x109 cells/mL, and the

final permeate had a concentration of 55 cells/mL, calculate the Log Reduction Value.

3 (b). The flux calculated from Hagen-Poiseuille model show greater discrepancy from

the experimentally observed values with decreasing pore size. State some possible

reasons.

3 (c). What do you mean by Integrity testing of membranes? How is it done?

4. During Ultra filtration of skim milk having a protein concentration of (CB) 2.4% w/v,in a Hollow Fiber unit (PM 50), a polarized gel layer was formed at the surface of the

membrane. The concentration of the protein in the gel layer (CG) was 16% w/v and the

concentration of the protein in the permeate (CP) was 0.3%. Resistance values for skimmilk for the unit used determined to be:Membrane Resistance (RM)=0.16 KPa /LMH; Fouling Resistance (RF)=0.7 KPa /LMH; Resistance due to

CP (RG)=3.7 kPa /LMH; The average trans membrane pressure used was 114 kPa.

(a) Using The Resistance Model, calculate the value of the Flux that would be obtainedusing this module. (b) Calculate the number of hollow fibers required to obtain the flux

using the Mass transfer model, for a cross flow rate (Q) of 40 L/min.

Given: Density () = 1.03 g/cm3, Viscosity () = 0.8 cP, Diffusivity (D) = 7x 10 -7 cm2/sec,

Diameter of Hollow Fibre (d) = 0.11 cm, Length of Fibre = 63.5 cms

*******