A spherical drug capsule dispenses Dicyclomine (an irritable bowel syndrome drug) to the body’s gastrointestinal tract over time. Initially, 2.00 mg of Dicyclomine (mAo) is loaded into the 0.50-cm-diameter capsule. In the bulk fluid surrounding the capsule, the Dicyclomine has a residual constant concentration (c_A∞) of 0.20 mg/cm³. The solubility of Dicyclomine in the capsule polymer is the same as that in the surrounding fluid, which approximates the properties of liquid water. The molecular diffusion coefficient of Dicyclomine in water is 1.0 × 10^-5 cm²/s, whereas the effective diffusion coefficient of Dicyclomine in the capsule matrix material is 4.0 × 10^-6 cm²/s. At 37°C, the density and viscosity of liquid water are 1.0 g/cm³ and 0.0070 g/cms, respectively. Fluid movement inside the intestinal tract as has “mass-transfer Biot number” of nominally 5.0, and is defined by B_i = k_cR/D_Ae, where D_Ae is the effective diffusion coefficient associated with the solid surface in contact with the fluid, and R is the radius of the spherical capsule.

a. What is the concentration of Dicyclomine remaining in the center of the spherical capsule after a time of 4.34 hr (15,625 s)

b. What is the estimated Biot number if the velocity of the bulk fluid is 0.50 cm/s? Does the diffusion process within the drug capsule have any convective mass-transfer resistances associated with it?