Flow from a Spherical Source with Water Content Dependent Diffusivity

Leakage of moisture from underground buried sources can occur in nature because of cracking or deterioration of confining surfaces. Leaking moisture can be radioactive or contaminated and may endanger public health. In disposal of such substances underground, consideration must be given to the extent of dispersal of moisture from wet containers in case of accidents. The movement of moisture from a spherical buried source into partially saturated surroundings is described by a nonlinear partial differential equation. Complexity of the equation prevents obtaining an explicit solution of the problem; however, an approximate solution has been extracted by the method of weighted residuals. The technique calls for representing the solution with a polynomial in space variable that has its coefficients as unknown functions of time, to be determined from the conditions and by satisfying the equation over the range of space variable in an averaging sense. This procedure accepts any kind of diffusivity function including numerical values obtained from experiments. The method is simple in its application and produces results that compare well with the known solution.