M.Sc Student | Haimovitz Ory |
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Subject | Nonlinear Dynamics of a Thin Liquid Film on an Axially Oscillating Cylindrical Surface |

Department | Department of Mechanical Engineering |

Supervisor | Professor Alexander Oron |

Full Thesis text |

Investigation of the dynamics of a thin liquid film on a horizontal
circular cylinder subjected to axial harmonic oscillation was carried out.
Using the methods of long-wave theory a nonlinear evolution equation describing
the spatio-temporal dynamics of the film in terms of local film thickness
depending on both axial and azimuthal coordinates was derived. The axisymmetric
case of the evolution equation was numerically investigated. It was found that the
capillary long-time film rupture typical for film on a static cylinder can be
arrested, if the substrate is forced with a sufficiently high amplitude and/or
frequency. The threshold for the rupture prevention which delineates the
borderline between the ruptured and non-ruptured subdomains in the forcing
parameter plane is given by AN=*const* , where A and N are, respectively,
the dimensionless amplitude and frequency of forcing, whereas the value of *const*
is independent of forcing parameters. In the parameter domain where the
continuity of the film is preserved due to forcing, a typical pattern consists
of one drop in the periodic domain. A continuous transformation from the
pattern consisting of several droplets in the case of the unforced system to a
single droplet near the critical curve of A=A_{c} was found.

An approximate expression which relates the critical amplitude to the
rest of the problem parameters was derived. Using similarity analysis combined
with the numerical results it was found that the critical amplitude A_{c}
depends on the Womersly number N , Weber number *W*, the geometrical
parameter H and the size of the periodic domain L in the form A_{c}=0.10
N^{-1} W^{-0.038} H ^{0.33} (1)^{-1.30} L^{1.30}
The bifurcation of the undisturbed state of the forced system is numerically
found to be supercritical.