Fatty deposits in blood vessels pose a health risk. Chemical agents added to the blood can increase the solubility of the fatty deposits in blood, thereby providing a means to dissolve the fatty...

Fatty deposits in blood vessels pose a health risk. Chemical agents added to the blood can increase the solubility of the fatty deposits in blood, thereby providing a means to dissolve the fatty deposits in situ. To explore the mass-transfer characteristics of this phenomenon, a biological engineer set up the experiment shown below. The inner walls of a smooth, 0.8 cm inner diameter tube are uniformly coated with a thin layer, 0.01 cm, of lipophilic material called fatty compound A (FA for short). A synthetic solution (B) is pumped through the tube at a

volumetric flow rate of 3.0 cm³/s. The maximum solubility of FA in this synthetic solution is 20 mg FA/cm³
solution (). At the conditions of the experiment, the kinematic viscosity of the synthetic solution is 0.02 cm²/s, the density of the synthetic solution is 1.04 g/cm³
and the diffusion coefficient is
. The density of the solid FA is 1.10 g/cm³. As the solution flows down the length of the tube, the concentration of FA changes with axial position, z, according to the material balance model:

How long should the tubing be if the desired outlet concentration of FA is 0.010 mg/cm³?