Cylindrical capillary waves

As mentioned above, only few comparisons of different techniques have been reported. For example, Jiang et al. (1992) studied the dilational elasticity of Triton X-100 adsorption layers with plane and cylindrical capillary wave. The results of the two measurements are given in Fig. 6.10. 

Fig. 5.21 shows a liquid jet ejected from a cylindrical capillary of diameter 2r. Prior to break-up into individual drops, the liquid jet surface oscillates with wavelength X and amplitude Ar = r - r . The surface tension can be calculated from the wave parameters of two adjacent nodes using the Bohr equation. 

In the case of capillary waves, the flat surface or interface is basically stable and the waves are the result of thermal fluctuations. However, there are interface geometries where a simple interface shape — such as a cylindrical tube of one phase in other or the surface of a cylinder of fluid or solid — is intrinsically unstable because there are other geometries of lower surface areas and hence lower interfacial free energies. A simple energetic/thermodynamic argument (see the next example) can be used to show that the free energy of an undulated cylinder with undulations whose wavelength exceeds a critical value proportional to the cylinder radius, is lower than that of the perfect cylinder. These undulations eventually lead to the breakup of the cylinder into... 

An infinitely long cylindrical Newtonian liquid jet, is disturbed with a spatially harmonic surface displacement of a cosine shape R = a — Cocoskz, where k = Ina/X, and a is determined such that the volume of the jet is kept constant when the initial amplitude is changed. Therefore, a = (1 — Co/2) - The dynamics of this jet due to capillary forces was investigated for various values of initial disturbance wave number k, and initial amplitude i o> and of the jet Ohnesorge number, Oh. 

---