To solve Eqs. (3) and (4) J(X,Y) is defined as a function of the concentration difference using a local mass transfer coefficient for both phases. These definitions lead to an analytical solution of Eqs. (3) and (4) that divided the overall extraction curve into 3 regions: CER, FER and diffusion controlled period. By introducing Eqs. (5), despite the uniformity of solute in the solid phase, the Sovova’s model, divide the total amount of solute (O) into two fraction: the easily accessible fraction or the most superficial one (P) and the difficult accessible fraction or inside un-ruptured cells one (K):

; ; (7)

The solutions for Eqs. (3) and (4) are:

CER period, t < t CER

(8)

FER period, t CER ≤ t ≤ t FER

(9)

Diffusion controlled period, t ≥ t FER

(10)

The following restrictions are applied to Eqs. (8), (9) and (10):

Z, parameter of fast extraction period

(11)

t CER, constant extraction rate period

(12)

t FER, falling extraction rate period

(13)

W, mass transfer parameter in the solid phase

(14)

z W, dimensionless coordinate