Unpublished Research Paper
In this study the instability of droplets and cylindrical jets is investigated. The understanding of these processes has both academic and practical value. Instability of cylindrical jets is theoretically investigated for infinitesimal and finite, but small initial amplitudes (linear and nonlinear stability). For droplets, only linear theory is presented. It is assumed that the capillary force play a dominant role. It is determined that the viscosity exerts a damping effect. In the first section we give an introduction, after which the linear stability theory of cylindrical liquid jets is presented. In the third section the nonlinear jet stability theory is presented. In both sections the influence of the surroundings on the jet is neglected. In the fourth section we give an overview of existing linear droplet stability theories. In this case we included the effect of surrounding fluid as well as the viscosity of a droplet. The Rayleigh jet breakup phenomenon is important for droplet stability analysis since droplets are initially formed from cylindrical jets and liquid ligaments with surface distortion and the associated potential energy of the oscillations gives rise to linear/nonlinear surface mode interactions. At the end of section 4 three appendices give the most important derivations and the special functions needed. This study provide an introduction into more complex theory of nonlinear droplet oscillations and nonlinear droplet resonance in turbulent flows. Such problems will be solved by the method of asymptotic expansions and perturbation analysis, and when necessary by some existing numerical schemes. The idea is to compare the theoretical investigations with the experimental studies of the droplet breakup in homogeneous and isotropic turbulence.
Daidzic, N. E. (1992). Some stability problems in droplet formation and breakup [Unpublished manuscript]. LSTM 351/T/92, Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstr. 4, 91058, Erlangen, Germany.
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