Volume-averaged liquid density, transport

Leonard et al. (2006) modeled liquid transport in the (fully saturated) gel by a diffusion approach for the volume-averaged liquid density,... 

The diffusion model is not very satisfactory from a physical point of view since liquid transport is known to be convective. Therefore, Jomaa et al. made an effort to develop a more fundamental description by volume averaging of the heat and mass balances in the deforming saturated gel (Caceres et al., 2007). For the evolution of the volume-average liquid density, or equivalently the local porosity ip = q /q, they obtained... 

In the usual macroscopic analysis of transfer phenomena, fluids are considered as continuous media and macroscopic properties are assumed to vary continuously in time and space. The physical properties (density,. ..) and macroscopic variables (velocity, temperature,...) are averages on a sufficient number of atoms or molecules. If A 10" is a number of molecules high enough to be significant, the side length of a volume containing these N molecules is about 70 nm for a gas in standard conditions and 8 nm for a liquid. These dimensions are smallest than those of a microchannel whose characteristic dimension is between 1 to 300 pm. The transport properties (heat and mass diffusion coefficients, viscosity) depend on the molecular interactions whose effects are of the order of magnitude of the mean free path These last effects can be appreciated with the Knudsen number... 

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