Rayleigh limit

Gas- borne drops can only hold a certain maximum number of charges of the same name . This charge limit is called the Rayleigh limit or Rayleigh limit (after John Strutt, 3rd Baron Rayleigh ) and depends on the size and surface tension of the droplets:

${\displaystyle q=8\cdot \pi \cdot {\sqrt {\varepsilon _{0}\cdot \gamma \cdot r^{3}}}}$

Here is

• ${\displaystyle \varepsilon _{0}}$the permittivity of the vacuum
• ${\displaystyle \gamma }$the surface tension of the liquid
• ${\displaystyle r}$ the drop radius.

If a liquid evaporates , the droplet size is reduced and the surface charge density increases. Due to the repulsive forces of the charges of the same name, the drop becomes unstable and breaks up into smaller fragments. Their resulting total surface area is higher than that of the individual drop. If one assumes that the charges are statistically evenly distributed over the fragments, then the resulting surface charge density is also lower and the Rayleigh limit is thus again fallen below.

If the ambient conditions are appropriate, this decay process can continue to such an extent that ultimately only ions remain. This effect is z. B. used in electrospray ionization (ESI) to analyze liquids by mass spectrometry .

Individual evidence

1. ^ John William Strutt, 3rd Baron Rayleigh : On the Equilibrium of Liquid Conducting. Masses charged with electricity. In: Phil. Mag. 5, No. 14, 1882, pp. 184-186.
2. ↑ Daniel C. Taflin, Timothy L. Ward, E. James Davis: Electrified droplet fission and the Rayleigh limit . In: Langmuir . tape 5 , no. 2 , March 1, 1989, ISSN  0743-7463 , p. 376-384 , doi : 10.1021 / la00086a016 .