How a multicellular cluster of neutrophils sediment faster

Question

Assignment:

Problem Description:

A single human neutrophil (one of white blood cells) is placed on top of a 100 μm-deep microfluidic well filled with human blood plasma.

Density of neutrophil, p_p = 1090 [kg m ^-3]; radius of neutrophil, R = 6 [p_m]; density of blood plasma, p_m = 1020 [kg m^-3]; dynamic viscosity of blood plasma, η= 1.25.10 ^-3 [Pa-s].

1. Derive, while making reasonable simplifying assumptions, the analytical expression for the time it would take the neutrophil to sediment to the bottom of the well. (You must produce a step-by-step derivation of the analytical expression, and calculate the numerical answer to receive full credit.)

2. Would a multicellular cluster of 5 neutrophils sediment faster or slower than a single cell? By how much? (You must give a numerical answer to receive credit.)

3. Under what conditions the neutrophil would never rich the bottom of the well? (You will receive 2 points for every condition named correctly.)