Tortuosity, definition

Vascular tortuosity predicting adverse events following carotid stenting. (See text for definition.)... 

Calculate the tortuosity for the hypothetical pore of length, L (Figure 12-2b), from the definition of t. ... 

The authors state that while the above definition is used widely, other authors have defined tortuosity as 1/T, T, and l/T as these forms are frequently encountered in expressions for ionic conductivity and mobility through tortuous membranes. Experimental measurement of liquid membrane support tortuosity is described by Bateman et al. 

Areal Porosity and Tortuosity. Areal porosity or areosity, Ap, is defined as the effective areal ratio of the open pore cross-section to the bulk space. A more strict definition of areosity was introduced by Ruth and Suman (56). However, the areosity as defined by them is not a property of the porous medium only but a property of both the porous medium and the transport strength of the fluid such as the flow strength and electric current strength. The areal porosity is undoubtedly a very useful quantity for a bundled or ensemble passage model because it represents the ratio of the total passage cross-sectional area to the total cross-sectional area of the porous medium at a given planar section. 

The tortuosity, r, of a porous medium is defined as the ratio of the distance between two fixed points and the tortuous passage followed by a fluid element of a single fluid saturated in the porous medium when traversing the two points. It may be viewed as a line porosity because, by definition, tortuosity is a one-dimensional property of the porous medium. It can be related to the formation factor, or formation conductivity factor, Ft by... 

Permeability for a Rock Formation. For natural consolidated porous medium, however, the definitions of the equivalent spherical diameter and the specific surface area per unit volume are not widely used because of its difficulty in determination and relation to other measurable quantities. Just to serve as a comparison, we give the permeability equation based on the previous passage model with the tortuosity given by equation 61 and assuming that the areal porosity equation 54 still holds. The permeability can then be given by... 

In this chapter, we introduced the characteristics of porous media from both fundamental and application points of view. We listed some relevant definitions and properties and useful models dealing with flow though porous media and reviewed the description of porous media to introduce to the reader the techniques used in modeling the porous media and the properties of the porous media and their relationship to the models. Field level characterization is actually a direct utilization of the models for transport in porous media, and our section on this may be considered as a study on the transient compressible flows. Because of the importance of the tortuosity and areal porosity, we devoted a section to discuss them. These two properties are not newly defined, but they do generate some confusion in the literature. For instance, the areal porosity was... 

Since the tortuosity is often interpreted as the increase in diffusional path length, and since the characteristic time for diffusion scales with the diffusional path length squared, an alternative definition for tortuosity is sometimes used ... 

The definition of tortuosity factor in Eq. 3.5.b-2 includes both the effect of altered diffusion path length as well as changing cross-sectional areas in constrictions for some applications, especially with two-phase fluids in porous media, it may be better to keep the two separate (e.g., Van Brakel and Heertjes [39]). This tortuosity factor should have a value of approximately 3 for loose random pore structures, but measured values of 1.5 up to 10 or more have been reported. Satterfield [40] states that many common catalyst materials have a t 2 3 to 4 he also gives further data. 

The tortuosity describes the ratio of the (average) incremental distance that an ion/molecule must travel to cover the direct distance in the direction of diffusion (Berner, 1980) and is thus the factor, which describes the increase in travel distance in the porous medium. Since the definitions of tortuosity in literature indicate small however substantial differences (an excellent overview of different procedures, equations and definitions is given by Boudreau (1997)), the definition used here is described briefly. The diffusion coefficient is corrected by the squared tortuosity. The square of the tortuosity is called tortuosity factor (Carman, 1937). This factor represents the... 

Thus by definition, the tortuosity, x, is greater than unity. 

One last useful definition is the tortuosity t. The tortuosity relates the effective diffusivity in the pores - effective to 6 molecular diffusivity in free solution, Dnjoiecuiar... 

The fractional porosity accounts for the reduction in the flux due solely to the reduced area available for diffusion. It is customary to use the fractional volume porosity, but it has been argued tht the fractional area porosity at the material s surface is more appropriate [43]. The definition given by Eq. (3) uses the tortuosity to account for all other effects that alter the binary diffusivity, and it lacks any inherent mechanistic or predictive detail. 

The diffusion data was fitted by a two-component diffusion model and an alternate classification of the two components was discussed by Perkins and Batchelor (2012) in combination with traditional definitions of water types within such systems. At intermediate moistme contents, the diffusion coefficients of both components of water were observed to decrease with deCTeasing moisture content because SBW contribution increases. The relative mass fractions of water in each component were near equal and the ratio between the two diffusion coefficients remained near constant, implying that there was interaction between the two water components under these moisture conditions. Through plane and in-plane studies show an increase in the interaction effects and tortuosity of the diffusion motion for water through the sheet compared to that within the plane of the sheet. The fiber ultrastructme had no measured effect on the diffusion behavior (Perkins and Batchelor 2012). 

We present a local structural characteristic which describes the detour of, for example, a gas flowing through a porous material, the so-called tortuosity, usually defined as the ratio of the mean effective path length of the fluid through a porous material and the material thickness. Note that a unique definition in physics is missing see also the discussion in Wang et al. [10]. 

The effect of the solid obstructing the gas transport is determined by the porosity s and tortuosity t of the GDL. Tortuosity describes the elongation of the direct transport distance x by the solid structure of the GDL, and definition of the porosity is obvious. Liquid water may occupy part of the pore space, decreasing porosity and increasing tortuosity. This effect depends on the amount of liquid water present in the GDL, which is given as the saturation s, the fraction of the pore space occupied. The effective diffusion coefficient is therefore defined as ... 

Here, Dt is the diffusion coefficient of species i in the gas phase, Em is the porosity of the membrane having thickness Sm and pore tortuosity and xsgim is the logarithmic mean mole fraction difference of the inert gas species B along the diffusion path (see definition (3.1.132)). Such an expression for k g is valid for conditions of ordinary diffusion of A through a stagnant gas film of B in the pores of the membrane. If the mean free path conditions are such that Knudsen diffusion or other convection mechanisms are valid, appropriate equations have to be used from Section 3.4.2.4. 

Such expressions are used also to describe the volumetric flow rate through deposits of particles, macromolecules, proteins, etc., on top of filters, membranes, etc. Often, a tortuosity factor, r, is used along with L in the definition (6.1.4g) of hydraulic permeability to accommodate... 

With the following definitions of the tortuosity, x, and the shape factor, F ... 

---