General solution of hydraulic diffusivity from sorptivity test

A general approach to solving hydraulic diffusivity from sorptivity test is established and verified in this paper. The diffusion equation governing capillary water absorption is first converted into normalized ordinary differential and integral forms via Boltzmann transformation, which are then directly solved by the method of weighted residuals. By this method, the approximate solution of Boltzmann variable is determined for any distribution law of diffusivity. The relationship between sorptivity and diffusivity is further analytically established. Itʹs found that initial diffusivity is proportional to square of the ratio of sorptivity to the water content difference between saturated and initial states. Ignoring the water vapor diffusion leads to the underestimation of derived water content profile and diffusivity. The Boltzmann variable and diffusivity calculated by the proposed method are verified by experimental data. Finally, the relationship between coefficients of general solution for diffusion equation and shape parameter for exponential diffusivity is also derived.