<P> Leaching is extensively used in metal processing industries . The useful metal may occur in mixtures with very large amounts of undesirable constituents, and leaching is used to remove the metals as soluble salts . The use of acids is prevalent in the metal processing industry . Sulfates are normally used to remove metals from the solid phase . These processes result in harmful sulfate - rich environmental byproducts . Because acids solubilize metals, large - scale release of heavy - metal - rich acidic mine drainage (AMD) can thereby occur . </P> <P> As mentioned above when leaching a solid with a liquid the desired solid goes to the liquid phase while undesired solid remains . The removal of the solid as the liquid dissolves into the particle leads to a diameter of unleached core that shrinks with time . A mathematical model can be used for this process, derived using Fick's law of diffusion taking pore diffusion as rate limiting step: </P> <Dl> <Dd> t = ρ B r s 2 6 D e b M B c A b (1 − 3 (r c r s) 2 + 2 (r c r s) 3) (\ displaystyle t = (\ frac (\ rho _ (B) r_ (s) ^ (2)) (6D_ (e) bM_ (B) c_ (A_ (b)))) \ left (1 - 3 \ left ((\ frac (r_ (c)) (r_ (s))) \ right) ^ (2) + 2 \ left ((\ frac (r_ (c)) (r_ (s))) \ right) ^ (3) \ right)) </Dd> </Dl> <Dd> t = ρ B r s 2 6 D e b M B c A b (1 − 3 (r c r s) 2 + 2 (r c r s) 3) (\ displaystyle t = (\ frac (\ rho _ (B) r_ (s) ^ (2)) (6D_ (e) bM_ (B) c_ (A_ (b)))) \ left (1 - 3 \ left ((\ frac (r_ (c)) (r_ (s))) \ right) ^ (2) + 2 \ left ((\ frac (r_ (c)) (r_ (s))) \ right) ^ (3) \ right)) </Dd>

Leaching of sugar from sugar beets is done by