Reaction-controlled leaching

The shrinking particle model
Original particle with radius = r0
Not reacted core with radius = r

In case the chemical reaction at the surface is much slower than the diffusion of reagents through the diffusion layer, the leaching becomes reaction controlled. This also implies that the concentration of reagents at the surface becomes equal to the concentration in the bulk, i.e. Ci = C.

With the assumptions that the particles to be leached are spherical and of equal size and that the concentration of the reagent is constant during leaching, the following expression can be derived:

$1-(1-\alpha)^{1/3} = \frac{k \cdot C \cdot t}{r_0 \cdot \rho}$
Where:
α = fraction leached
k = rate constant
C = concentration of reagent
t = time of leaching
r0 = initial radius of particle
ρ= density of particle

This is also referred to as the shrinking particle model where the initial radius of the leached particles gradually decreases. As is evident from the equation, the leaching rate is inversely proportional to the radius of the particle. The rate constant may be determined by plotting the left hand side against time in a diagram.

Schematic of leaching according to the shrinking particle model.