The Weather of the Month

Physics of liquid jets

“…where the dot denotes a time derivative and primes spatial derivatives. Equation ( 41) replaces (30), obtained from the radial expansion method. Equations ( 29), (41) are identical to the 'Cosserat' equations as given in [129], based directly on one-dimensional fields [106][107][108], to which mechanical and thermodynamic principles are applied.…”

“…Its precise structure is somewhat arbitrary since it depends on the choice of basis function w(r, z). If one orders the terms in (41) according to the slenderness parameter , one recovers (30).…”

“…Although it was known from the beginning of the 20th century that many natural phenomena give rise to a multiplicity of drop sizes, in particular as applied to rain (see the remarkable observations of Bentley (1904) [30]), the quantitative study of sprays only started in the 1950s. This was motivated by the wide use of liquid propulsion for cars and aircraft, and concomitantly the development of appropriate measurement tools [31], as we review in section 5.…”

“…In [96] a detailed comparison with full Navier-Stokes simulations was carried out, demonstrating excellent agreement over a wide range of parameters. A comparison with experiment is shown in figure 18 for a dripping faucet, adding the acceleration of gravity g to the rhs of (30). Indeed, a number of detailed studies of the bifurcation diagram and the chaotic states of a dripping faucet [97,122,124,125] are based largely on this one-dimensional description, a full simulation being much too costly.…”

“…Since the most unstable wavelength is about 9h 0 , the long-wavelength model ( 29), (30) should describe the linear instability well, provided the full curvature (12) is kept. The latter is necessary to describe the cut-off at short wavelengths, so for ν = 0 one obtains from (30)…”