A spherical time-release capsule was developed to release pesticide to surrounding soil, as shown in the figure below. The capsule is 1.0 cm in diameter, and is made of a polymer containing a uniform initial concentration of pesticide (species A) equal to 2.0 mg/cm3 . The effective diffusion coefficient (DAe) of the pesticide in the polymer is 5.0 x 10-7 cm2 /s. During wet periods of the year, water flows into the loose soil and slowly flows around the buried capsules, creating a boundary layer that provides a convective mass transfer coefficient (kc) of about 1.0 x 10-6 cm/s. The bulk concentration of pesticide in the flowing water is very small, and so can be considered as effectively equal to zero (cA 0). The molecular diffusion coefficient of the pesticide in water (DAB) is 1.0 x 10-6 cm2 /s (A = pesticide, B = water).

a. What is the concentration of pesticide in the center of the capsule after a time of 173.6 h?

b. What is the concentration of pesticide at the surface (r = R) of the capsule after 173.6 h, and what is the flux of pesticide out of the particle, NA(R,t), at this time, in units of mg/cm2 s?

Water flow (v.) Groundwater flow CAO = 2.0 mg/cm3 Dne = 5 x 10-7 cm/s Pesticide-filled polymer capsules (1.0 cm diameter) buried in loose soil CAS CA=0