Thermo-osmosis

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As thermal osmosis (English: thermal osmosis ) the mass transport is in the Sciences membranes under the influence of a temperature gradient referred to. In contrast to osmosis under isothermal conditions, material transport also occurs here in single-substance systems. Thermo-osmosis is a special case of thermophoresis (or thermal diffusion ) and can include liquids and gases. In mining , the term refers to the movement of water from a warmer to a colder area of ​​the earth . The terms thermal osmosis and thermal transpiration are often used synonymously.

Discovery story

First description by Reynolds

In 1897 the British described physicist Osborne Reynolds a phenomenon that he called thermal transpiration (ger .: thermal transpiration hereinafter). He understood it to mean the flow of a gas through a porous plate, caused by a temperature difference between its two sides. If the gas pressure on both sides was originally the same, the gas moves from the colder to the warmer side. This increases the gas pressure there on the warmer side, provided the plate is fixed and cannot move. The thermal equilibrium is reached when the pressures to each other are in the same proportion as the square of the absolute temperature.

The effect described by Reynolds contradicts immediate intuition . It is caused by tangential forces between the gas molecules and the pore walls of the plate. The gas behaves similarly to superfluid helium (no viscosity ), which flows very quickly to the warmer region when a capillary is immersed in the container. This fountain effect was first described in 1938.

Thermo-osmosis in liquids

The proof that thermo-osmosis occurs in liquids came from the French physicist and Nobel Prize winner Gabriel Lippmann in 1907 .

Basics

Thermo-osmotic permeability

The mass transport in thermo-osmosis can be described for a single-substance system by the following flow equation:

Here, J 1 to the material flow of the component 1 in mol · s -1 , B the thermoosmotische permeability in mol · K -1 · m -1 · s -1 , q of the cross section of the membrane surface area in m², δ the thickness of the membrane in m and Δ T the temperature difference in K .

Thermo-osmosis creates a pressure difference between the two phases (initially at the same pressure); the side to which the material is transported has the higher pressure. The pressure difference now applied between the two phases leads to permeation in the opposite direction and finally to the disappearance of the flow of matter ( J 1 = 0) as soon as a steady state is established:

This stationary pressure difference is called the thermo-osmotic pressure difference . Here, A the isothermal permeability of the membrane in mol · kg -1 · s, which describes the mass transfer due to a pressure difference:

with the pressure difference Δ p in Pa .

Sign and temperature dependence

The thermo-osmotic permeability can assume positive or negative values, depending on the material component and type of membrane, and the pressure on the warmer or colder side of the system will increase accordingly. In systems where gas is divided by a rubber membrane, carbon dioxide flows to the warmer side ( B  > 0: positive thermo-osmotic permeability), while hydrogen increases the pressure on the colder side ( B  <0: negative thermo-osmotic permeability). If the system consists of water and a cellophane membrane ( Cellophane-600 ), the thermo-osmotic permeability decreases steadily with increasing temperature until the sign is reversed at around 56 °  C and its values ​​are negative at higher temperatures. Values ​​in the range from 6.5 · 10 −10  mol · K −1 · m −1 · s −1 (at 10.7 ° C) to −11.7 · 10 −10  mol · K −1 · m −1 · s −1 (at 90.0 ° C).

Proportionality to the heat of transfer

The transfer heat Q * and the thermo-osmotic permeability are proportional to each other in the steady state:

,

where Q * is the heat of transfer in J · mol −1 and the partial molar volume in m 3 · mol −1 . The heat of transfer generally has the same sign as the thermo-osmotic permeability. In the system of water and cellophane-600 it shows, like this one, a sign reversal at 56 ° C; values ​​of 11.9 J mol −1 (at 10.7 ° C) to −5.7 J mol −1 (at 90.0 ° C) were measured for the heat of transfer .

Osmotic temperature

If there is a system with more than one substance component, the thermo-osmotic pressure difference can lead to a stationary concentration difference between the two phases:

Here D is the osmotic diffusion coefficient in m 2 s −1 , which characterizes the flow equation for the isothermal- isobaric mass transport across a membrane:

with the substance quantity difference Δ x 1 of component 1 in mol · m −3

The stationary temperature difference Δ T in this case is called the osmotic temperature .

Osmotic thermal effect

If a membrane shows thermo-osmosis for a material component (its thermo-osmotic permeability is therefore not equal to 0), heat is transported at originally the same temperature of the two phases, if the effect of a pressure or concentration difference causes material transport across the membrane. This phenomenon is called the osmotic thermal effect; it has been proven experimentally in liquid helium and is also known as the mechanocaloric effect ; it is the reverse of the fountain effect .

Biological importance

Historical discussion

The importance of thermo-osmosis for biological systems was discussed by Spanner in 1954: He estimated the heat of transfer of water via plant cell membranes to be approx. 4,060 J · mol −1 ; assuming standard values ​​for the mean temperature and the molar volume of water, a temperature difference of 0.01 K would produce a stationary pressure difference of 134 kPa. However , it was not known whether a 10 nm thick membrane can maintain such a temperature gradient of 1,000 K per mm . On the other hand, since numerous energy-consuming or energy-producing reactions take place in a cell , it could not be ruled out that thermo-osmosis plays a role in membrane transport across biological membranes.

Thermo-osmotic oxygen transport in plants

Oxygen transport due to thermo-osmosis has been proven in plants that take root in a low-oxygen environment, such as the yellow pond rose or the black alder .

literature

Individual evidence

  1. M. Aubert thermo-osmosis. In: Ann. Chim. Physique. 1912, 26 (8), p. 145.
  2. a b Christoph Steinert: Thermo-osmosis in liquids . Dissertation at the Technical University of Aachen, 1958, DNB 480000727 .
  3. definition in Webster's Online Dictionary (Engl.) ( Memento of 2 December 2008 at the Internet Archive )
  4. Wolfgang Große: The mechanism of thermal transpiration (= thermal osmosis) . In: Aquatic Botany . tape 54 , no. 2-3 , 1996, pp. 101-110 , doi : 10.1016 / 0304-3770 (96) 01038-8 .
  5. ^ Osborne Reynolds: Note on thermal transpiration. 1879 In: Papers on Mechanical and Physical Subjects. Vol. 1 (1869-1882).
  6. ^ Phill Gibbs: How does a light mill work? 1996 at Usenet Physics FAQ
  7. ^ JF Allen, H. Jones: Superfluidity II - the fountain effect. In: Nature. 141 (1938), pp. 243f.
  8. G. Lippmann In: Compt. rend. Acad. Sci. 145, 104 (1907)
  9. ^ KG Denbigh: Thermo-osmosis of Gases through a Membrane. In: Nature. 163 (1949), p. 60.
  10. KG Denbigh, G. Raumann: Thermo-osmosis of gas through a membrane. In: Nature. 165 (1950), pp. 199f.
  11. KG Denbigh, G. Raumann In: Proc. Royal Soc. (A) 210, 377, 518 (1951).
  12. ^ A b Hans Joachim de Greiff: Thermo-osmosis and permeation of liquids through cellophane membranes . Dissertation at the Technical University of Aachen, 1971.
  13. DC Spanner In: Symp. Soc. Exptl. Biol. 8 (1954), 76.
  14. Peter Schröder: Thermo-osmotic oxygen transport in Nuphar lutea L. and alnus glutinosa Gaertn. and its importance for anaerobic living. Inaugural dissertation; University of Cologne. 1986.