Krogh model is a
scientific model
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted ...
of
mass transfer
Mass transfer is the net movement of mass from one location (usually meaning stream, phase, fraction or component) to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtration, ...
explaining the concentration of
molecular oxygen
There are several known allotropes of oxygen. The most familiar is molecular oxygen (O2), present at significant levels in Earth's atmosphere and also known as dioxygen or triplet oxygen. Another is the highly reactive ozone (O3). Others are:
* ...
through a
cylindrical capillary tube
Capillary action (sometimes called capillarity, capillary motion, capillary rise, capillary effect, or wicking) is the process of a liquid flowing in a narrow space without the assistance of, or even in opposition to, any external forces li ...
as a function of a changing position over the capillary tube's length. It was first conceptualized by
August Krogh
Schack August Steenberg Krogh (15 November 1874 – 13 September 1949) was a Danish professor at the department of zoophysiology at the University of Copenhagen from 1916 to 1945. He contributed a number of fundamental discoveries within severa ...
in 1919 with the help of
Agner Krarup Erlang
Agner Krarup Erlang (1 January 1878 – 3 February 1929) was a Denmark, Danish mathematician, statistician and engineer, who invented the fields of teletraffic engineering, traffic engineering and queueing theory.
By the time of his relatively ...
to describe oxygen supply in living tissues from human
blood vessel
The blood vessels are the components of the circulatory system that transport blood throughout the human body. These vessels transport blood cells, nutrients, and oxygen to the tissues of the body. They also take waste and carbon dioxide away ...
s.
Its applicability has been extended to various academic fields, and has been successful explaining drug diffusion, water transport, and ice formation in tissues.
Mathematical modeling
Krogh model is derived by applying
Fick's laws of diffusion and the
law of conservation of mass over a radial
interval
Limitations
Although Krogh model is a good approximation, it underestimates oxygen consumption
because the cylinder model does not include all the tissue surrounding the capillary.
Notes
References
*
*{{citation, last1=Wei, first1=James, last2=Anderson, first2=John, year=1995, title=Advances in chemical engineering, Volume 19, isbn=978-0120085194, url=https://books.google.com/books?id=U2ExzucYUJIC&q=Advances+in+chemical+engineering+19
Diffusion
Scientific models
Mathematics in medicine