Dynamics of contracting filaments

Revisiting the Taylor-Culick approximation: Retraction of an axisymmetric filament

“…Depending on Oh, at least 20 cells (for large Oh) and up to approximatively 80 cells (for low Oh) per initial filament radius are uniformly distributed in this region. In comparison, 16 radial elements stand along the filament radius in the simulations of Anthony et al [12]. In the outer region, r 3R 0 − 4R 0 , the grid is uniform in the axial (z) direction but the cell size increases with r. More specifically, this size doubles every time r increases by 0.5R 0 , until a maximum cell size of approximatively R 0 /2 is reached.…”

“…In real experiments, e.g., atomization of a jet, the filament has a more complex initial shape and the velocity within it is nonzero. Nevertheless this simple initial configuration, already widely used in previous investigations [10][11][12], provides a reference starting point to understand more realistic situations. Influence of the initial shape on the successive stages of the dynamics is discussed in the Appendix.…”

“…A large stream of work has focused on the corresponding breakup mechanisms. Recently, Anthony et al [12] performed an extensive numerical investigation of the retraction dynamics over a wide range of Ohnesorge number and initial aspect ratio A, and proposed a classification of the different breakup modes as a function of these two control parameters. The end-pinching mechanism [13,14] prevails at low Oh, while the classical Rayleigh-Plateau mechanism dominates at high Oh.…”

“…Still for low Oh, Hoepffner and Paré [16] observed that the filament may escape from end-pinching due to the formation and detachment of a Venturi-like flow inside the blob. This escape from pinching, which may occur at multiple times, results in a discontinuous variation of the critical aspect ratio leading to breakup as a function of Oh [12,16].…”

Jet breakup in superfluid and normal liquid He4

“…McCarthy and Molloy [33] review the importance of nozzle design, discussing how the length to diameter ratio affects the jet's initial velocity profile and subsequently the surface roughness and other features. Contracting liquid filaments breakup in a similar manner to Rayleigh jets, forming one to multiple droplets of various sizes depending on Oh l and the aspect ratio [22,[34][35][36][37]. Other topics include: the forced breakup from sinusoidal perturbations [38][39][40], inkjet printing [41], liquid jets with surrounding coaxial gas flow [42], computer modeling [43,44], jet impact on solids [15,45] and liquids [46][47][48][49], flash boiling breakup when a jet injects into an atmosphere below its own vapor pressure [50,51], cooling and fragmentation of molten metal jets [52,53], and applications such as fuel injection [54,55] and other technologies [56].…”