Table 3.

Mathematical models for drug release.

Model	Mathematical equation	Release mechanism	Codes
Zero order kinetic model	Cr = C0 − k0. t	Diffusion Mechanism	ZoM
First order kinetic model	lnCr =  ln C0 − k1. t	Fick's first law, diffusion mechanism	FoM
Higuchi Model	$\frac{{\mathrm{C}}_{\mathrm{r}}}{{\mathrm{C}}_{\infty }}={\mathrm{k}}_{\mathrm{H}}.\sqrt{\mathrm{t}}$	Diffusion medium based mechanism in Fick's first law	HM
Korsmeyer-Peppas Model	$ln\frac{{\mathrm{C}}_{\mathrm{r}}}{{\mathrm{C}}_{\infty }}=ln{\mathrm{k}}_{\mathrm{KP}}+\mathrm{n}.\mathrm{lnt}$	Semi empirical model, diffusion-based mechanism	KPM

C_r is concentration of urea release in time t (mg/L); C₀ is the initial concentration of urea in the solution (most times, C₀ = 0) (mg/L); k₀ is the zero order release constant expressed in units of concentration/time (mg/(L.min)); t is time (min); k₁ is the first order release constant (1/min); C_∞ is concentration of fertilizer release in equilibrium (mg/L); k_H is Higuchi release rate constant (1/$\sqrt{min}$); k_KP is Korsmeyer-Peppas release rate constant; n is release exponent which is indicative of the transport mechanism (M_t/M_∞ < 0.6 should only be used.