One of the most important features of mathematical modeling in drug delivery processes is its capability to predict change of performance of a drug by manipulating the parameters. Therefore a substantial reduction in the number of experiments can be made which results in some economical gains. Parameters include initial concentration of drug in the solid and liquid phase, radius of the solid drug carrier and diffusivity of drug in the solid, equilibrium constant of solid-liquid inter phase and kinetic rate constant of the drug in the liquid phase. There are many proposed models in the literature which focus on either diffusion or dissolution mechanism. In this paper a mathematical model has been developed which takes into account both diffusion and reaction. It is believed that both mechanisms are important in controlling the release of drug (lidocaine) from a spherical reservoir (biodegradable PLGA nano spheres). The proposed model combines both mechanisms in the form of a conjugate boundary layer problem. The partial differential equations obtained from Fick's second law for a spherical drug particle and from material balance of the drug in the liquid phase and the boundary conditions governing these equations are converted into non-dimensional form and solved using Laplace Transform method and the Residue theorem to carry out the inversion. The Eigen- values are found using Mathematica. The advantage of this model is it could potentially provide both the length of time needed for the drug to reach its effective concentration once it is placed in the compartment and length of time the drug concentration will stay above an effective concentration before a second dose of drug needs to be administered. Also this model is an improvement over diffusion only systems where a chemical is expected to be assimilated.