As described in Problem 7.77, the second step in tissue engineering is to seed the top surface of the scaffold with human cells that subsequently grow into the pores of the scaffold. A seeding method that has been proposed is to use a droplet generator similar to that of Problem 7.77 to generate Dp = 50μm diameter drops. The material in the droplet generator is slurry consisting of a mixture of host liquid and human liver cells. The host liquid has properties similar to water, and the liver cells are spherical with a diameter of Dlc = 20μm and density Plc = 2400 kg/m3. Droplets are injected into atmospheric air with a relative humidity and temperature of ϕ = 0.50 and T∞ = 25°C, respectively. The particles are injected with an initial temperature of Ti = 25°C.

(a) It is desirable for each drop to contain one liver cell. Determine the volume fraction, J, of liver cells in the slurry and the terminal velocity for a drop containing one liver cell.

(b) The droplet containing one liver cell is injected at its terminal velocity. Determine the time of flight for a distance between the ejector nozzle and the scaffold of L = 4 mm.

(c) Determine the initial evaporation rate from the droplet.

(d) The tissue engineer is concerned that evaporation will change the mass of the droplet and, in turn will affect its time of flight and the precision with which the seeds can be placed on the scaffold. Estimate the maximum change in mass due to evaporation during the time of flight. Compare the variation of mass due to evaporation to the variation associated with there being one to three liver cells per droplet. Does evaporation or the liver cell population per droplet influence the variability of the droplet mass most significantly?