Numerical Solution of Oxygen Diffusion Problem in Spherical Cell

This study addresses the diffusion of oxygen in a spherical geometry with simultaneous absorption at a constant rate. The analytical method assumes a polynomial representation of the oxygen concentration profile, leading to a system of differential equations through mathematical manipulation. A numerical scheme is then employed to solve this system, linking the moving boundary and its velocity to determine the unknown functions within the assumed polynomial. An approximate analytical solution is obtained and compared with other methods, demonstrating very good agreement. This approach provides a novel method for addressing oxygen diffusion in spherical geometries, combining analytical techniques with numerical computations to efficiently solve for oxygen concentration profiles and moving boundary dynamics.