December 17, 2010
Biotransport Phenomena
Final Exam
35 points
1. 5 points
A rotating disc 1 cm in diameter is coated on one side with a drug that bears a fluorescent
tag that allows for determining its concentration in solution. The spinning disc system is
placed in 100 cm3 of pure water at 37 oC and the disc is spun at 25 RPM’s. After 60
minutes the concentration of the drug in the water was found to equal 0.075 g L-1. After a
long period of time the drug concentration in the solution was equal to 3.0 g L-1. From
this information estimate the diffusivity of the drug in water in cm2 sec-1. Assume the
viscosity and density of the water at these conditions are 0.76 cP and 1 g cm-3
respectively.
2. 5 points
Water at 70 oF enters a pump through a 3 inch schedule 40 pipe at atmospheric pressure
and is being pumped at a rate of 100 gallons per minute (1 gallon = 3.7853 L) through a
pipe system made up of 500 feet of three inch schedule 40 steel pipe (internal diameter =
3.068 inches). The pipe circuit includes 4 - 90 degree elbows. The total change in
elevation from the pump entrance to the discharge of the water into the atmosphere is
equal to 400 feet. Find the horsepower (HP) required for the pump assuming the pump
efficiency is 70%. The viscosity of water under these conditions is 0.96 cP and the
density of water is 1 g cm-3.
3. 5 points
Water containing a solute is flowing through a 1 cm diameter tube which is 50 cm in
length at an average velocity of 1 cm sec-1. The temperature of the water is 37 oC The
walls of the tube are coated with an enzyme that makes the solute disappear instantly.
The solute enters the tube at a concentration of 0.1 M and the solute has a molecular
weight of 300 g mol-1. Estimate the fraction of the solute that leaves the tube. Assume the
viscosity and density of the water at these conditions are 0.76 cP and 1 g cm-3
respectively.
4. 5 points
A perfusion bioreactor is being designed to contain hepatocytes for the treatment of liver
failure. The bioreactor will consist of microflow channels with the hepatocytes encased
within a gel-like material that coats the surfaces of the microflow channel. Assume the
cell fraction of the hepatocytes in the gel-like layer is 0.35 and that the pO2 of the
perfusion fluid flowing through the microflow channel is 95 mmHg. The gel itself has a
negligible effect on the diffusivity of oxygen. The hepatocytes consume oxygen at the
rate of 35 M sec-1. What is the maximum thickness of the gel-like layer of hepatocytes?
5. 5 points
A blood oxygenator for a small child needs to deliver 0.5 moles per hour of oxygen to the
blood. Assuming the blood enters the oxygenator at a pO2 of 40 mmHg and leaves at 95
mmHg estimate the required flowrate of blood (L min-1) through this oxygenator.
6. 5 points
Estimate the permeability of a spherically-shaped molecule that has a molecular weight
of 42,000 g mol-1 through a microporous polycarbonate membrane. Assume that the
molecule enters the pores of the membrane from a well-stirred bulk solution that is at 37
o
C. The membrane pores are cylindrical and have a diameter or 32 nm an overall length
of 325 microns. The membrane itself is 250 microns in thickness. The pores comprise
42% of the membrane volume.
7. 5 points
Write the letter in the space next to the equation that defines the term on the left side. L is
a characteristic length.
k L
a. Reynolds number
____ m
D
b. Peclet number
____
V L

c. Schmidt number
____


d. Kinematic viscosity
____

D
e. Sherwood number
____
VL
D