ONE-DIMENSIONAL MODELS FOR SLENDER AXISYMMETRICAL VISCOUS-LIQUID JETS

A one-dimensional analysis of slender axisymmetric viscous liquid jets is considered. A set of one-dimensional models is derived by substitu ting a truncated Taylor series in the radial coordinate into the Navie r-Stokes equations and boundary conditions at the interface. The relat ive error, defined as the order of magnitude of the neglected terms di vided by the order of the retained ones, is small if the dimensionless wave number k is small enough. The Lee slice model is generalized to take into account viscosity, the relative error being k2. A new model having a parabolic radial dependence for the axial velocity is develop ed, with a relative error k4. The Cosserat model comes from the introd uction of the mean axial velocity into the previous one, but an incons istency arises from neglecting some viscous terms of the same order as those retained. A new model for the mean axial velocity is derived. I t conserves the same inertial contribution but avoids the above-mentio ned problem by estimating the involved terms instead of neglecting the m. Therefore the relative error is k4 for any value of viscosity. Line ar stability analysis is performed for the infinite jet. Results are c ompared with the exact linear solution given by Lord Rayleigh. The mai n features predicted in the derivation of the one-dimensional models m anifest themselves in the linear case.