Transport of Water in a Biconstituent Elastic Medium

Abstract

A phenomenological equation is established for water transport in a biconstituent, isotropic, isothermal elastic medium. The equation includes a term related to the water content gradient and a term related to the deformation gradient. It is shown that in the case of an infinite plate, the transport law can be similar to Fick’s law in which water flux is proportional to the water content gradient alone. The apparent transport coefficient then depends on the hygroscopic and rheological coefficients of the medium. Experimental analysis of the evolution of water content profiles of agar gel plates validates this transport law and makes it possible to deduce the variation in apparent transport coefficient according to water content. Transport coefficients associated with water content and deformation gradients and applicable to any geometrical features are deduced.