Modification of square root formula for approximate estimation of diffusion coefficient of particulate adsorbents

The well known square root formula for the kinetics of adsorption by spherical particle U(t)=(6/r₀)(Dt/π)^1/2 is only valid in the early stage of adsorption (U(t) ≤0.3), where U(t) shows fractional attainment to the equilibrium. Present study shows that with a little manipulation of this formula, its application range can be extended to U(t) ≤0.95. The suggested formula U(t)=(6/r₀)(Dt/π)^1/2-(3Dt/r₀²) in addition of simplicity, has higher accuracy than both square root and Vermeulen´s formulas.