| We present a new numerical method, termed the embedding method, to solve a system of nonlinear diffusion-reaction partial differential equations that describes the enzyme kinetics and transport occurring within a sessile axisymmetric hydrogel drop. Michaelis-Menten kinetics is used to model the reaction mechanism leading enzyme-mediated substrate to product conversion.; The embedding method combines ideas from finite differences, especially the alternating direction implicit (ADI) on a Cartesian grid, and the volume-fraction-based front-capturing method, which accounts for interface calculations of multi-phase problem and modification to apply correct boundary conditions. The method has been implemented in two-dimensions as well as in axisymmetric three-dimensions. The major advantage of this method is that it can handle problems on zonal boundary or multi-media interfaces using a regular structured-block mesh without exactly conforming to the geometry. The major aspect of this method is its simplicity of implementation and efficiency of programming.; Validations of the method are given by comparing steady-state solutions against these obtained with the shooting method and by comparing simulations against those of a finite volume method on an unstructured, body-fitted grid. Software with a graphical interface is developed, and it enables visualization and animation of the numerical results. |
