טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentHaimovitz Ory
SubjectNonlinear Dynamics of a Thin Liquid Film on an Axially
Oscillating Cylindrical Surface
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Alexander Oron
Full Thesis textFull thesis text - English Version


Abstract

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=Ac 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 Ac depends on the Womersly number N , Weber number W, the geometrical parameter H and the size of the periodic domain L in the form Ac=0.10 N-1 W-0.038 H 0.33 (1)-1.30 L1.30 The bifurcation of the undisturbed state of the forced system is numerically found to be supercritical.