The mathematical method of separation of motions represents the effect of fast high-frequency oscillations by an effective averaged force or potential. Ultrasound acoustic vibrations are an example of such rapid oscillations leading to cavitation in water due to the gas phase formation (bubbles). Ultrasound cavitation is used to treat the surface of brass microparticles submerged in water. The formation of bubbles and their collapse triggers the modification of surface roughness and chemical composition. Consequently, the suspension separates into various fractions related to demonstrating biocide properties. While the exact mechanism of this process is complex, it can be explained phenomenologically by using the Onsager reciprocal relations for coupling the copper ion diffusion with the gas phase separation in water as a result of the action of the effective average vibrational force.
M. Sabbouh, A. Nikitina, E. Rogacheva, L. Kraeva, S.A. Ulasevich, E. V. Skorb, M. Nosonovsky, 2021, “Separation of motions and vibrational separation of fractions for biocide brass”, Ultrasonics Sonochemistry, 105817, https://doi.org/10.1016/j.ultsonch.2021.105817
Figure 4. a) Putative mechanisms involved in bacteria-killing: direct destruction of the membrane by Cu2+/Cu+ (black pathway); interactions between copper ions and glutathione under anaerobic conditions (blue path) and displacement of iron from iron-sulfur clusters (dark blue path), reactive oxygen species generation via hydrogen peroxide formation in the presence of Cu2+/Cu+, inactivation of key proteins/enzymes, among which are those involved in the respiratory system as well as RNA and DNA damages. b) The biocidal activity of nanostructured Cu-Zn alloy (sample 2) was estimated using E. coli. c) The diameter of the inhibition zone of prepared Cu-Zn particles (from Sabbouh et al, 2021, “Separation of motions and vibrational separation of fractions for biocide brass”, Ultrasonics Sonochemistry, 105817 Doi: 10.1016/j.ultsonch.2021.105817).
By the way, copper, brass, and bronze are know to have medical properties already from ancient mythology. I am not going into that, since copper-related mythology is not the focus of the present research (however, I will give a hint: key words Nehushtan, Caduceus, and Asclepius).
See also: Ultrasound phase separation and amazing effects of fast small-amplitude vibrations