CHEM 233 Assignment 4

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Questions

1. In blood, leukocytes attack viruses and neutralize them. Leukocytes have antibodies on their surface, which recognize a specific antigen on the surface of a virus. After a virus infection has been successfully eliminated, only a few leukocytes with the specific antibody remain in  the blood, thus allowing a reasonably quick response in case the body gets re-infected by the same virus. Let us call these remaining leukocytes “sleeping” leukocytes. Assume there is one sleeping leukocyte per 50 mL of blood left when reinfection occurs. Virus particles multiply quickly before they are recognized and attacked.

a) How many virus particles will be present in 50 mL of blood when the rate at which they are detected has reached 1 virus particle/day? (Afterwards, the body produces more leukocytes with the right antibodies and the rate goes up quickly).

Hint: consider the heterocoagulation between leukocytes and virus particles. The rate at which

viruses collide with a single leukocyte is given by

Here αo is the capture efficiency (assumed to be one), G the effective shear rate in blood (assumed to be 100 s-1,) n is the number of virus particles per unit volume, a1  the radius of a leukocyte (assumed to be 3 μm) and a2 the radius of the virus (10 nm).

b). Assuming the virus has a density of 1 g/cm3, what is the corresponding concentration of virus particles (g/L)?

2. Consider an aqueous suspension of spherical particles with a radius of 50 nm and a volume fraction of 10-4.

a) What is the perikinetic coagulation rate and the coagulation half-time, assuming fast coagulation?

b) The onset of fast perikinetic coagulation was found to occur at a NaCl concentration of 0.1 M.

At 0.05 M, the coagulation rate was half the fast rate. Draw a (perikinetic) stability diagram for this suspension.

3. For the same suspension as in question 2

a) What is the orthokinetic coagulation rate and coagulation half-time at G = 10 s-1, assuming the

orthokinetic coagulation efficiency αo = 0.8? What is the orthokinetic coagulation half-time at 10,000 s-1, assuming αo = 0.2?

b) What is the Peclet number at G = 10 s-1 and 10,000 s-1?