You need to estimate an overall mass transfer coefficient for solute adsorption from an aqeuous solution of density 1.3 g/cm^3 into hydrogel beads .03 cm in diameter. The coefficient sought Ky is defined by:
where N1 has the units of g/(cm^2*sec), and the y’s have units of solute mass fraction in the water. The mass transfer coefficient ks in the solution is 10^-3 cm/sec; that within the beads is given by
where d is the particle diameter and D is the diffusion coefficient, equal here to 3*10^-6 cm^2/sec. Because the beads are of hydrogel, the partition coefficient is one. Estimate Ky in the units given.