Wed like to estimate the average flow in the stomach by measuring the dissolution rate of a non-absorbing (inert) solute (A) present as a spherical pill. From in vitro experiments, we know that the pills dissolution is accurately described with a mass transfer coefficient kc. Assume that the pills radius stays constant R0 and that the stomach flow is dominated by convection. You may also assume that flow in and flow out of the stomach is negligible.

a. Write down a transient mole balance of species A in the stomach, assuming A is well-mixed and has a uniform concentration cA in the stomach due to the convective flow. Let cAs be the concentration at the pills surface and V be the volume of stomach to derive the dependence of cA with time.

b. For flow around the sphere, the Sherwood number Sh is given by Sh=(2k_cR0)/D_AB=2+0.6 Re^1/2 Sc^1/3 and Re=(2R0v_flow)/ where DAB is the diffusivity of A in the stomach and is the kinematic viscosity of the fluid. Solve for the flow velocity v_flow in the stomach. Now if you know the concentration of A in the stomach is cA0 at some known time t0, how could you evaluate vflow from your data?

No flow in Stomach Well mixed, CA /CAS Pill No flow out