Lifetime of a soluble solid particle in a stagnant medium: approximate analytical modelling involving fractional (half-time) derivatives

Approximate analytical solutions concerning lifetime of soluble solid particles in an unbounded stagnant medium have been developed by simple application of fractional half-time derivative in the Riemann-Liouville sense to express the relationship between the net surface mass flux and the concentration at the interface. The solutions start with the initial formulation of Rice and Do on the time-depletion of the radius of a spherical particle expressed through terms including the solubility parameter as the only key parameter controlling the process of dissolution. The two approximate developed solutions use different scaling and dimensionless variables: The 1^st solution is developed by an introduction of a similarity variable [xxx] while the 2^nd solution applies the classical scaling using the initial sphere radius as a length scale that leads to dimensionless radius r = R/R₀ and time τ = Dt/R₀². Both solutions provide approximate relationships close to that of Rice and Do.