Tortuosity

The tortuosity τ (lat. Tortuosus "wound") characterizes the degree of tortuosity of the transport routes in the pores of porous materials. It is used to describe various physical transport processes and, in addition to porosity and permeability, is a parameter for describing the properties of porous materials.

Tortuosity is defined by the square of the ratio of the mean effective length of the transport path through a porous layer to the thickness of the layer: ${\ displaystyle l _ {\ mathrm {eff}}}$ ${\ displaystyle l}$

{\ displaystyle \ tau = \ left ({\ frac {l _ {\ mathrm {eff}}} {l}} \ right) ^ {2}}

Sometimes the simple ratio of the two lengths is also referred to as tortuosity.

An alternative, physically more sensible definition of tortuosity is based on the mean value of the angle between the pore direction and the direction of transport in a section through the porous medium: ${\ displaystyle \ theta}$

{\ displaystyle \ tau = \ left ({\ frac {1} {\ cos {\ theta}}} \ right) ^ {2}}

From theoretical considerations, values of 2 or 3 result for pore space models with cylindrical, non-connected pores. In natural pore spaces, the values differ from this in some cases significantly.

The transportation processes that tortuosity is used for include:

electrical current (electrical tortuosity),
Flow of fluids (hydraulic tortuosity),
Diffusion .

The tortuosity of a particular porous material can be different for different transport processes. In a porous material filled with conductive water, for example, the effective length of the streamlines for electric current is not necessarily exactly as great as that of the streamlines for the flow of water.

The concept of tortuosity is used in geo- and petrophysics , where the flow of water and oil through porous rock layers is investigated, and in acoustics , where tortuosity plays a role in the characterization of the absorption effect of porous sound absorbers.

literature

P. Grathwohl: Diffusion in natural porous media: Contaminant transport, sorption / desorption and dissolution kinetics . Kluwer Academic Publishers, 1998, ISBN 0-7923-8102-5

J. van Brakel and PM Heertjes (1974). Analysis of diffusion in macroporous media in terms of a porosity, a tortuosity and a constrictivity factor. Int. J. Heat Mass Transfer 17: 1093-1103.

L. Schildkrauth (1961). Tortuosities and Turtoises. A Comparativistic Companion to Fluid Dynamics in Porous Media Int. J. Appl. Por. 14 (2): 231-274.

Epstein, N. (1989). On tortuosity and the tortuosity factor in flow and diffusion through porous media. Chem. Eng. Sci. 44 (3): 777-779.