porosity

The porosity is a dimensionless measurement and represents the ratio of the volume of the void to the total volume of a substance or mixture of substances. It serves as a classifying measure for the voids actually present. The size is used in the field of materials and construction technology as well as in the geosciences . The porosity has a great influence on the density of a material as well as on the resistance when flowing through a bed ( Darcy's law ).

Originally due to natural conditions and usually undesirable especially in the production of sophisticated cast products, there is now an artificially created, insofar desired porosity, primarily in the service of the production of lightweight building materials. Metal foam and lightweight concrete are examples of porosity, which as such is not the subject of this article.

definition

The porosity is defined as 1 minus the quotient of the bulk density (of a solid ) or bulk density (of a pile ) and the true density : ${\displaystyle \Phi }$

${\displaystyle \Phi =1-{\frac {\rho }{\rho _{0}}}}$

As a percentage it is calculated as follows:

${\displaystyle \Phi =\left(1-{\frac {\rho }{\rho _{0}}}\right)\times 100\,\%}$

Alternatively, the porosity can be defined as the ratio of void volume to total volume with a net volume state of the solid: ${\displaystyle V_{H}}$ ${\displaystyle V=V_{H}+V_{F}}$ ${\displaystyle V_{F}}$

${\displaystyle \Phi ={\frac {V_{H}}{V}}={\frac {V_{H}}{V_{H}+V_{F}}}}$

In soil mechanics , the number of pores is also used as a key figure (ratio of void volume to solid volume ). ${\displaystyle V_{H}}$ ${\displaystyle V_{F}}$

Open and closed porosity

The total porosity of a substance is made up of the sum of the cavities that are connected to one another and to the environment ( open porosity , useful porosity) and the cavities that are not connected to one another ( cemented , closed or dead-end porosity ).

High open porosity is the term used for open-pored material or, ideally, a honeycomb structure ; pure closed -pore properties are called foam .

Typical values

The following geometrically determinable total porosities of an arrangement of massive spheres of equal size can be regarded as typical:

• For an ordered, cubic closest (face-centered) packing of spheres as well as for an ordered, hexagonal closest packing of spheres , it is Φ = 0.26
• for the body-centered cubic packing of the spheres it is Φ = 0.32.

These values ​​result directly from the packing density , which results in a degree of space filling of 74% for the cubic and hexagonal closest packing of spheres. Kepler postulated that this is the greatest value that a sphere packing can assume. This so-called Kepler conjecture could only be confirmed by computer-aided evidence; it was added by David Hilbert in 1900 as the 18th problem in his list of 23 mathematical problems .

With a body-centered cubic lattice (like tungsten - bcc) the value is only 0.68 and a primitive cubic lattice (like alpha polonium - sc) only 0.52.

For any packing of spheres made of a material that is not internally porous (solid spheres), the following rough estimate applies:

${\displaystyle \Phi \approx {\frac {\pi }{\text{Koordinationszahl}}}\cong 0{,}4\ldots 0{,}45}$

Appearance of porosity

Construction engineering

Asphalt layer with a high pore volume

In civil engineering, the term porosity refers to the voids in a bed or pile. Porosity and bulk density are related. The porosity is defined as the ratio of the void volume V _hollow to the total volume of the pile V _tot . Commonly used is the letter ε or P _W , while the already introduced bereits is less common.

The following definition is common:

${\displaystyle \varepsilon ={\frac {V_{\mathit {H}}}{V_{\mathrm {ges} }}}={\frac {V_{\mathit {H}}}{V_{\mathit {H}}+V_{s}}}}$

The total volume V _ges sets itself from the solids volume V _s (corresponding to pure volume V _F ) and the cavity volume V _H together.

Materials engineering

In materials engineering, porous materials are classified according to the size of the pores :

• microporous : pores <2 nm
• Mesoporous : pore size between 2 and 50 nm
• macroporous : pores> 50 nm

For gray cast iron parts, but also those that are cast from copper alloys in sand molds, there are u. A. a very characteristic pore shape known as pin-holes (“pinhole porosity”). It can be visible on the surface or just below it. These are reactions of the melt with the moisture of the molding material or the cores used, but also with the binders of the same. Hydrogen pin-holes and hydrogen-nitrogen pin-holes are possible. Another type of porosity is found in cast aluminum in sand and mold. The solidification of the metal in the mold can lead to porosity as the cooling increases, because the hydrogen solubility of aluminum and aluminum alloys decreases depending on the temperature, but the released hydrogen is prevented from escaping and thus leads to undesirable porosity with a considerable influence on the strength properties. Degassing measures as part of a melt treatment can help. Die-cast aluminum is less prone to porosity due to its very rapid mold filling and solidification. Porosity caused by air trapped in the casting process is avoided by using a vacuum casting process (VACURAL).

earth sciences

Soil constituents Solid, water and air

In geology , hydrogeology and soil science , porosity describes the ratio of the volume of all cavities in a porous soil or rock to its external volume. It is therefore a measure of how much space the actual soil or rock fills within a certain volume due to its grain size or fissures or which cavities it leaves behind in it. The pores or capillaries are usually filled with air and / or water . The porosity is usually given in percent or as a fraction (fractions of 1 = 100%) and is designated with the formula letter Φ.

The porosity of rocks describes the volume of voids that can be taken up by mobile, migratory media such as water and gases. Occasionally, the synonymous term “ degree of impermeability” is used for the porosity of rocks . There are also the rock- technical values ​​of the number of pores (symbol ) and proportion of pores (symbol ). ${\displaystyle e}$ ${\displaystyle n}$

When considering the weathering resistance of natural stone, one starts with the open porosity ( π _wi ). It only describes those pore spaces in which liquids and gases are involved in exchange processes.

Sediments and sedimentary rocks have a porosity of around 10 to 40%, while metamorphites and igneous rocks only around 1 to 2%. Typical, real measured total porosities are:

• Sandstone : 5 to 40%, typically 30% (depending on grain size distribution, type of binding agent and consolidation)
• Limestone or dolomite : 5 to 25% (depending on dissolution processes through groundwater and weathering)
• Mudstone : 20 to 45% (due to the small diameter of the pores, however, no storage rock)
• Slate : less than 10%
• Loose sand and gravel: up to over 40%

Classification of porosities in the deposit assessment

classification	Porosities
Negligible	Φ <4%
Low	4 <Φ <10%
Well	10 <Φ <20%
Excellent	Φ> 20%

In the oil / natural gas industry , mining geology and geothermal energy , the effective porosity plays a major role, since fluids (water, oil or gas) can only flow through the interconnected pores . In connection with the storage properties of a rock, the term usable porosity is also used in hydrogeology .

Web links

• geotechnical porosity
• Quantitative description of a porous medium (script "Hydrogeology", Chapter 4, University of Kassel) (PDF file; 0.63 MB)

Individual evidence

1. ↑ "An evaluation concept for computed tomographically determined porosities in cast parts with regard to their effect on the local stress resistance of the component", Rüdiger Bahr and colleagues, Giesserei Rundschau des VÖG, Vienna, 60th year, issue 5/6, p. 106.
2. ^ Helmut Polster, Christa Buwert, Peter Herrmann: Sanierungsgrundlagen Plattenbau. Test procedure . Published by the Institute for the Preservation and Modernization of Buildings eV (IEMB). Fraunhofer Information Center for Space and Construction, Stuttgart. Version: January 1995. IRB-Verlag, Stuttgart 1995, ISBN 3-8167-4137-1 .
3. ↑ ^ Jump up to: from Hales, Thomas; Adams, Mark; Bauer, Gertrud; Dang, Tat Dat; Harrison, John; Hoang, Le Truong; Kaliszyk, Cezary; Magron, Victor; McLaughlin, Sean; Nguyen, Tat Thang; Nguyen, Quang Truong; Nipkow, Tobias; Obua, Steven; Pleso, Joseph; Tail, Jason; Solovyev, Alexey; Ta, Thi Hoai An; Tran, Nam Trung; Trieu, Thi Diep; Urban, Josef; Vu, Ky; Zumkeller, Roland (29 May 2017). "A Formal Proof of the Kepler Conjecture". Forum of Mathematics, Pi. 5: e2. doi: 10.1017 / fmp.2017.1 . Retrieved June 16, 2017.
4. ↑ to this pinholes. In: Ernst Brunhuber (founder): Foundry Lexicon . 17th edition, completely revised and edited by Stephan Hasse. Schiele & Schön, Berlin 1997, ISBN 3-7949-0606-3 .
5. ↑ B. Oberdorfer, D. Habe, E. Kaschnitz Determination of the porosity in aluminum castings by means of CT and its influence on the strength properties . Lecture at the VÖG conference 2014 in Bad Ischl, published in VÖG Giesserei-Rundschau, vol. 61, issue 5/6, p. 138.
6. ↑ Arnd Pesch: Natural stones . 2nd, revised edition. German publishing house for basic industry, Leipzig 1983, p. 64-65 .
7. ^ R. Allan Freeze, John A. Cherry: Groundwater . Prentice-Hall, Englewood Cliffs NJ 1979, ISBN 0-13-365312-9 .