Controlled release of urea, mass transfer from a sphere and a single opening on a coated sphere into a quiescent liquid

grantor: University of TorontoA continuous weighing technique was developed for measuring the transfer of urea (carbamide, a fertilizer) from a single opening on a coated sphere into a stagnant liquid. Hollow polymer spheres of a 3.8 cm diameter were used as non-permeable shells enclosing a saturated urea solution (57wt% at 303K). Urea release was determined from changes in particle weight with time. Coated solid urea spheres were also used. Mass transfer rates were measured for various Rayleigh numbers from 1.8 * 107 to 6.8 * 1010. For the opening oriented vertically upward in water, natural convection enhanced the release rate by 1.8 times compared to diffusion only. However, when liquid viscosity was increased above 1.0 Pa.s, using a carboxymethylcellulose solution, the effect of natural convection on the release became insignificant. The mass flux of urea diffusion through a single opening was 6.2 times that for pure diffusion from an uncoated sphere over the same area. For other opening orientations (45°, 90°, 135° and 180° to the upward vertical), natural convection provided the main mechanism for urea transfer in both water and CMC solutions. The average mass transfer rate (for all angular positions of the opening) for a coated solid urea sphere was 5.7 times lower than that for a sphere filled with the saturated urea solution. Models for urea diffusion through a vertically upward opening were developed. The models agree well with the experimental data. From local natural convection mass transfer rates for various angular positions of the opening, the average Sherwood number was estimated. A correlation for the average Sherwood number with the Rayleigh number was obtained. The average Sherwood numbers for smaller particles of a 2.0 cm diameter align well with the correlation. Uncoated urea spheres were also used so that mass transfer occurred over the whole surface. Both concentration boundary layer build-up and natural convection were observed visually. Local Sherwood numbers were obtained from the change of the particle shape, and the average transfer rates were estimated from particle weight loss. These were in good agreement with literature data and correlations. The Sherwood number correlation obtained predicts urea transfer from a 2 mm uncoated particle well. Electrochemical measurements using a sectioned sphere were also carried out with the ferricyanicle-ferrocyanide solution. Both local and average transfer rates were much higher than those for pure diffusion. This was due to natural convection in the bulk liquid. However, the transient transfer was in good agreement with a theoretical prediction for convective mass transfer to a sphere. The data and the models obtained in the present study provide a fundamental understanding of controlled release of a substrate through a single opening on a coated sphere in a stagnant liquid. They were also shown to be potentially applicable in predicting urea transfer rates from sulfur-coated urea (SCU).Ph.D