Estimation of the diffusion coefficients of adsorbed and non-adsorbed solutes in soil

A method is proposed which follows Darrah's experimental procedure and takes advantage of a mathematical solution provided by Carslaw & Jaeger to estimate the diffusion coefficients of adsorbed and non-adsorbed solutes in soil. The method requires only the values of the concentration of the solute at the input face of a uniform column of soil, C^s, and of the total amount, Q_t, that has entered the soil after a specified time during which the surface of the block is in contact with a thin porous pad containing a known initial amount of solute, Q₀, at concentration C₀, expressed in the same units as C^s. In the C^s/C₀ vs. Q_t/Q₀ space there is a unique relationship between the effective diffusion coefficient, D_e, of the solute in the soil and the contact conductance for this solute, h, between the pad and the soil surface. The proposed procedure is firstly to determine D_e, and h for a non-adsorbed solute in the experimental soil using the experimental values of C^s/C₀ and Q/_Q for that solute. This value of D_e, gives the diffusion impedance factor for the solute in the soil, f, which is assumed also to apply to adsorbed solutes. A first estimate of the effective diffusion coefficient of an adsorbed solute, ¹D_ea, is then made using f and the diffusion coefficient of the free solute in water, D_L, obtained from the literature (i.e. ¹D_ea= D_Lf). Only if the solute is weakly adsorbed will the values of C^s/C₀, and Q_t/Q₀ lie in C^s/C₀, vs. Q_t/Q₀, space as defined by ¹D_ea and the contact conductance, h. Instead a second space relating C^s/C₀ and Q_t/Q₀, is now constructed from nominated values of h and D_e, where D_e, is defined in terms of ¹D_ea, the adsorption coefficient, F , and the volumetric moisture content of the soil, θ. The position of the experimental values of C^s/C₀, and Q_t/Q₀ within this new space defines h and the actual D_e, and F of the solute as it diffuses and is adsorbed in the soil. The advantages and limitations of the method are discussed. In particular, the method assumes that the adsorption process is linear and reversible.