Equations of anomalous absorption onto swelling porous media

Abstract

Absorption is a very common process which takes place on various types of materials ranging from porous media to new nano-materials and biological tissues. The majority of studies reported on absorption to date are concentrated on “rigid” porous media, which contradict the properties of real porous media which undergo swelling and shrinking changes. Here we present new absorption equations derived from a fractional diffusion-wave equation (fDWE) for absorption onto swelling porous media in a material coordinate. We show that the cumulative anomalous absorption is I( t) = St β/2 and the absorption rate i ( t ) = 1 2 β S t β / 2 − 1 , where S is the anomalous sorptivity and β the order of fractional derivative in fDWE. Using published data on cumulative absorption against time, the two adsorption parameters are determined: β = 1.2448 and S = 2.7775 cm 2/h. The value of β = 1.2448 implies that absorption onto this swelling porous media belong to the category of super-diffusion, which is a phenomenon unknown to us before. In comparison, the traditional absorption equations do not have such features. When S is determined, the anomalous diffusivity, D m , is calculated using its relation with S. We expect that the proposed new absorption equations will be valuable for explaining new phenomena and processes encountered in broader disciplines of science and engineering applications.