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 in the figure.

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). The length of the tubing containing the FA layer is 50 cm. A synthetic solution is pumped through the tube at a volumetric flow rate of 35:0 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 cm³/s and the density of the synthetic solution is 1:04 g/cm³. The density of the solid FA is 1:10 g/cm³.

a. Develop a material balance to predict the concentration of FA in the solution exiting the tube.

b. Experiments were conducted with the test unit shown above, with a measured dissolved concentration of FA in the synthetic solution exiting the tube of 0.1 mg FA/cm³. This concentration was constant over time. From this data, using your model, back out the molecular diffusion coefficient of FA in the solution.