Constrictivity
Encyclopedia
Constrictivity is a dimensionless parameter used to describe transport processes
Transport Phenomena
Transport Phenomena is the first textbook that is about transport phenomena. It is specifically designed for chemical engineering students...

 (often molecular diffusion) in porous media
Porous medium
A porous medium is a material containing pores . The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid...

.

Constrictivity is viewed to depend on the ratio of the diameter of the diffusing particle to the pore diameter. The value of constrictivity is always less than 1. The constrictivity is defined not for a single pore, but as the parameter of the entire pore space considered.

The resistance to transport in porous media increases because the viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 of the fluid (which fills the pores) increases in the vicinity of the pore walls (see electroviscous effects
Electroviscous effects
Electroviscous effects, in chemistry of colloids and surface chemistry, according to an IUPAC definition, are the effects of the particle surface charge on viscosity of a fluid....

). This effect is important in very narrow pores and in pore narrowing their diameter to the same size as the diameter of the diffusing particles. Constrictivity must be distinguished from the effects of Knudsen diffusion
Knudsen diffusion
Knudsen diffusion is a means of diffusion that occurs in a long pore with a narrow diameter because molecules frequently collide with the pore wall.Consider the diffusion of gas molecules through very small capillary pores...

. Knudsen diffusion occurs when the particle interacts with the pore walls more than it does with other particles due to the large free path and narrow pores. Constrictivity, on the other hand, depends on the influence of the pore walls on the fluid filling the pores.

There are a number of empirical formulas used to estimate the value of constrictivity. For simple pore geometries, constrictivity can be inferred from the geometry of the porous media. In practice, the constrictivity together with the porosity
Porosity
Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0–1, or as a percentage between 0–100%...

 and tortuosity
Tortuosity
Tortuosity is a property of curve being tortuous . There have been several attempts to quantify this property. Tortuosity is commonly used to describe diffusion in porous media...

 are often used in models as purely empirical parameters to establish the effective diffusivities
Diffusivity (biology)
Diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species . Diffusivity is encountered in Fick's law and numerous other equations of physical chemistry.It is generally prescribed for a...

in porous media.

Sources

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

  • van Brakel, J., Heertjes, P. M. (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
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