Coupling between liquid flow and heat flow in porous media: A connection between two classical approaches

The presented work addresses exclusively to the transport in the liquid (sub)phases occurring in porous media. By analysing the thermodynamics of the solid-liquid and liquid-gas interfaces present within a porous solid-liquid-gas system, it is shown that the forces acting on two distinct subphases of the liquid, due to the presence of a macroscopic temperature gradient, tend to balance each other. Exact counterbalance of the resulting fluxes implies that liquid flow in porous media under nonisothermal conditions is adequately described by the product of isothermal liquid diffusivity and the gradient of volumetric liquid content.It is shown on the basis of physical arguments that in the coefficient matrix, resulting from the analysis of fluxes and forces along the lines of TIP (Thermodynamics of Irreversible Processes), one coupling term vanishes if the liquid content gradient is chosen as the primary driving force. This does not imply that its cross-coefficient, causing the reduced heat flux arising under isothermal conditions from a gradient in liquid content, tends to be zero. The mechanistic Philip and De Vries formulation is reconsidered and is found to be incomplete and not capable of describing true coupling in the thermodynamic sense. Furthermore, the physical interpretation of the so-called reduced heat flux is discussed.