# Finite difference solution of the Cosserat fluid jet equations

## Abstract

A simultaneous finite difference solution of the nonlinear Cosserat fluid jet equations for a semi-infinite jet emanating from a circular nozzle is presented. The problem is treated as time-dependent with a small amplitude periodic excitation of the velocity at the nozzle. Solutions for the jet radius and velocity are computed up to the breakoff point where the radius becomes zero or the absolute value of the velocity exceeds a chosen maximum value. It is found that when the dimensionless frequency of the excitation, ω, satisfies ω < 1, the disturbance wave grows in amplitude as it propagates downstream until it finally breaks the jet. The breakoff point depends on the frequency and amplitude of the excitation, the jet velocity, and the viscosity of the fluid. When ω > 1 the disturbance is stable and therefore no jet breakup occurs. Even for the unstable frequencies high viscocity can appreciably dampen the growth of the disturbance. For ω < 1 and low viscosity the jet breaks up into main drops of twice the nozzle diameter and for certain conditions, small, so-called satellite drops are shown to form between the main drops. The results are compared with results from perturbation solutions of the same equations due to Bogy. © 1980.