A spherical pellet containing pure solid A is suspended in a flowing liquid stream at 20°C. The initial diameter of the pellet is 1.0 cm, and the bulk liquid velocity is 10.0 cm/s. Component A is soluble in the liquid, and as time progresses, the diameter of pellet decreases. The dissolved solute concentration in the bulk liquid is fixed at 1.0 × 10^–4 gmole/cm³. All relevant physical properties of the system are provided below. This process represents a “pseudo steady-state” convective mass-transfer system.
a. Estimate the film (convective) mass-transfer coefficient at the initial pellet diameter of 1.0 cm.
b. What is the dissolution rate of the pellet at the initial diameter of 1.0 cm?
c. How long will it take for the pellet to shrink to 0.5 cm diameter? Remember, when the diameter decreases, Re and Sh will change.
Potentially useful data: r_A,solid = 2.0 g/cm³, the density of the solid A; M_A = 110 g/gmole, the molecular weight of solute A; c*_AL = 7 × 10^–4 gmole/cm³, the equilibrium solubility of solute A in the liquid at the liquid–solid interface; v = 9.95 × 10^-3 cm²/s, the kinematic viscosity of the bulk fluid at 20°C; D_AB = 1.2 × 10^–5 cm²/s, the diffusion coefficient of solute A in  liquid at 20°C.