Representative elementary volume: REV

Volume averaging is a technique in which the fundamental equations are spatially averaged over a representative elementary volume (REV) of porous media.f ° This approach has provided insight into the relationship between fundamental physics and larger-scale behavior but is rarely used for studying transport in specific media in a deterministic sense. 

Numerical models have also been applied to simulate macrodispersion in spatially variable ksat fields (e.g., Thompson Gelhar, 1990 Moissis Wheeler, 1990 Wheatcraft et al., 1991). This Darcian approach requires averaging of flow over some Representative Elementary Volume (REV). 

For dealing with variability of soil properties at the larger scale, a continuum approach is implemented. Thereby a representative elementary volume (REV) is considered to exist and material properties related to flow and transport are defined at the centre of this REV. Thermodynamic principles related to conservation of mass and momentum are further applied on the REV to obtain governing flow and transport equations. The... 

Two homogenization scales were obtained by two teams using the same Crack Tensor theory, and the validity of representative elementary volume (REV) and its relationship to the size of finite element are unresolved, and remain an open problem. 

Electrokinetic Flow in Porous Media, Fig. 1 Schematic illustration of (a) representative elementary volume (REV), (b) porosity, and (c) tortuosity. The length scale of the REV is much larger than the pore scale but considerably smaller than the length scale of the macroscopic flow domain... 

We apply the concept of the representative elementary volume (REV) within a volume AE for averaging variables, which will be discussed in Sect. 5.1. Suppose that for a mixture solution with -components of species, an amount of substance of species a is given as ria mole. Then the volume molar fraction coa and the mass density are defined as follows ... 

Let us consider a volume AV, referred to as the representative elementary volume (REV), and with A/ being the size of the porous body for averaging any independent variable within this volume. Figure 5.1 schematically shows how to decide on the REV. If AVy is the volume of voids in the REV, the porosity is defined by... 

Figure 14.7. Porous medium, (a) Representation at the scale of a representative elementary volume (REV) of a size greater than the scale of a pore, (b) Representation by a network of capillary tubes...

More specifically, the conventional approach to describe this situation is to introduce a so-called representative elementary volume (REV). The size of an REV has to be small on the scale of the electrode thickness, and large on the scale of microscopic variations in electrode structure and composition. Fluctuations on the scale of the double layer thickness, that is, below 1 nm, are averaged out. The electrochemical properties of an REV are defined by local values of metal and electrolyte phase potentials. These potentials are continuous functions of spatial coordinates. 

We first assume that there are no micro-cracks in the domain. The distance between osteons is determinated with d = 0jjm. Thanks to the periodical condition, only one Representative Elementary Volume (REV) (see Fig. 2) is needed to be modeled. Fig. 2 depicts the response of fluid velocity field when applying a frequency of loading fo = IHz and a strain rate = 0.0035that were taken... 

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