Ordinary Integro-differential Equation Research Articles

The paper establishes the series solution of problems of infiltration from cylindrical and spherical cavities. The leading term is the fundamental horizontal absorption solution. The second term, representing linearly additive interactions of gravity and m-dimensionality (m = 2, 3), follows at once from known solutions for one-dimensional infiltration and for m-dimensional absorption. The third term is evaluated by solution of an ordinary linear integrodifferential equation. Higher terms involve circumferential flow components, and partial equations must be solved to evaluate them. For small enough times these higher terms are negligible. Physically, this implies that flow is essentially radial at such times; mathematically, that, taken no further than the third term, the solution applies indifferently to infiltration from cavities and from semicircular furrows (m = 2) and hemispherical basins (m = 3). The relation between this solution and the linearized and delta-function approximations is explored. The practical implications for sorptivity determinations based on short-time infiltration from furrows and basins are examined.