Initial Perturbation Effects on the Instability of a Viscous Capillary Jet

        St. Radev*, M. Koleva**, M. Kaschiev**, L. Tadrist***

       *Institute of Mechanics, Bulgarian Academy of Sciences, 
        4, acad. G. Bonchev str., 1113 Sofia, Bulgaria; 
      **Institute of Mathematics and Informatics, Bulgarian Academy of Sciences,        8, acad. G. Bonchev str., 1113 Sofia, Bulgaria; 
     ***Institut Universitaire des Systemes Thermique Industriels, 
        Universite de Provence, Technopole de Chateau Gombert, 
        5, rue Enrico Fermi, 13453 Marseille Cedex 13, France


   The jet disintegration is considered as an evolution of growing in time
of spatially periodical disturbances of initially given set of harmonics, among
which one fundamental and several higher harmonics of prescribed amplitudes and
phases. The role of the number of the harmonics, as well as of their amplitudes 
and phases is studied in order to determine the initial perturbation effects on both the upward and backward satellites merging and the size of detaching main 
and satellite drops.
    For this aim a numerical solution is proposed for computing the evolution
of the jet radius and velocity in time. In computations a system of two 
one-dimensional equations is used which consists of an axial momentum equation 
similar to Trouton equation and one equation for mass conservation across the
jet. In the force balance the capillary pressure and viscous effects are 
included, while the gravity is neglected (non contracting jet).
     In the numerical method special attention is paid to keep high level 
accuracy when approaching the break-up point. It is shown that combining 
different harmonics leads to the possibility to control at some extent the jet 
disintegration.