[ ] SEMII 2012/2013

ASSIGNMENT 2

Please submit the assignment before 5pm (27th May 2013 -Monday). Late submission will not be evaluated.

1. One way to deliver a timed dosage of a drug within the human body is to ingest a capsule

and allow it to settle in the gastrointestinal system. Consider a cylindrical tablet of diameter

0.8 cm and thickness of 0.3 cm as in Figure 1 with the uniform initial concentration of the

drug is 6.89 kg/m3 dramamine was consumed. Diffusion coefficient of Dramamine in the

gastrointestinal system is 3 x 10-7 cm2/s at a body temperature of 37°C and the

concentration of the drug at the exposed surface of the capsule is maintained at zero.

Figure 1: Capsule configurations

a) Calculate the concentration of dramamine (mg/cm3) at the center of the capsule

after 48 hr if the diffusion occurs radially?

b) Calculate the concentration of dramamine (mg/cm3) at the center of the capsule

after 48 hr if the diffusion occurs radially and axially?

c) How long (hr) will it take for the concentration at the midpoint to reach 50% of its

initial concentration?

d) In your opinion, what are TWO (2) factors that can affects the rate of diffusion of the

drug in the gastrointestinal system?

2. Company X manufactures many types of ball such as football, basketball and handball as

been shown in Figure 1 and Figure 2. These balls have different diameters. In order to test

the quality of the balls, technician A needs to examine and check the balls to ensure that the

balls meet the customer requirement. From his observation, he found that the football

containing 100% of air concentration and has diameter of 69cm while the handball

containing 100% of air concentration and has diameter of 63 cm. Therefore,

D = 0.8 cm

0.3 cm

[ ] SEMII 2012/2013

Figure 1: Handball Figure 2: Football

a) Calculate the remaining air concentration at the midpoint of the football and

handball after the technician leave the ball for 3 days. The diffusion of the air in

these balls is same and can be approximated by a diffusion of DAB = 1 x 10-3 m2/h.

Assume that the equilibrium air concentration in the balls is constant.

b) Calculate the time for the football to reach 30% of air concentration.

3. A 1.5 litre stirred fermenter contains a batch culture of Lactococcus lactei bacteria at 33°C.

Air at 20°C is pumped into the vessel at 1 atm absolute pressure. The diffusivity of oxygen

(air) in the water at 37°C is 3.25 x 10-9 m2/s.

a) Calculate the maximum rate of absorption of oxygen from air bubbles having

diameter of 3 mm into water having zero concentration of dissolved oxygen.

b) Determine the maximum possible rate of oxygen uptake by suspended Lactococcus

lactei (diameter of 0.5 μm) in an agitated aqueous solution. Assume that the

bacteria have a density very close to water.

c) If 10 g of wet Lactococcus lactei with a density of 1000 kg/m3 are added to 1.5L

aqueous solution, calculate the mass transfer of oxygen in kg mol O2/s to the surface

of the bacteria. Assume that the solution is saturated with air at 1 atm absolute

pressure.