Manifestation of Acceleration of Mass Flow Effects in Dissolving Pill Problem

The dissolving pill problem is solved in all three dimensions after taking into account the acceleration of mass flow effects in the constitutive law for mass diffusion and relaxation. The method of relativistic transformation of coordinates is used. A trifurcated solution results. A Bessel composite function of the third order and first kind in one regime and modified Bessel composite function of the third order and first kind solution in another regime was derived. A third inertial regime of null transfer was also identified. The non-Fick diffusion equation can be derived from free electron theory after taking into account the acceleration effects. The solution to the second order damped wave hyperbolic PDE is within the bounds of second law of thermodynamics.