Question

(b) (15 points) Water (species A) slowly absorbs and diffuses into a cylindrical polymer rod (species B) of length L and radius R. The rod is narrow and long enough that diffusion occurs primarily in the radial direction r over time t (diffusion in the axial direction through the two ends of the rod can be ignored). There is no reaction of water with the polymer, while the diffusion of water in the polymer can be related by the diffusion coefficient DAB. Due to limited water solubility in the polymer, diffusion can be considered to be through a stationary medium, while the concentration at the cylinder surface is at the solubility limit of cAs. Initially, there is no absorbed water in the polymer. Derive the differential equation for this mass transfer process that relates the concentration of water with position and time in the polymer. Write down the corresponding initial and boundary conditions. Note: You do NOT need to solve or integrate the differential equation; you also do NOT need to write down the assumptions. NO credit will be given for writing down assumptions, or solving/integrating the derived differential equation.

Answer 1

Water ar Jot Jr L from water balance Jo = - Das Schal Jor ar = -DAR OC a london generation + DAB CA. 270L/ In-out + Accumulation -DAG Och all = 2117dr.l. 2a at ar Etdr Y during by dr a.2017. - DAR CA 2004/ ar redy 27/LaCA at dr DAR OZCA raca at ar² Id CA g ar² LOCA DAB at Ang