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 (D_Ae) 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 (k_c) of about 1.0 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 (c_A∞ ≈ 0). The molecular diffusion coefficient of the pesticide in the water (DAB) is 1.5 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, N_A(R,t), at this time, in units of mg/cm²s?

Transcribed Image Text:

Groundwater flow [o]d[0] O Pesticide-filled polymer capsules (1.0 cm diameter) buried in loose soil Water flow (Voo) Cao= 2.0 mg/cm3 DA= 5x 10-7 cm²/s DAB = 1.5x 100 cm²/s Kc = 1.0 x 10-6 cm²/s CA 20