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The straightforward third perturbation solution is derived for a time harmonic disturbance applied at the nozzle. The problem formulation sets two boundary conditions at the nozzle and downstream radiation conditions. Numerical results are presented for parameters appropriate to ink-jet printers that show the jet radius near the breakup point. In a certain frequency range good quantitiative agreement with experiment is obtained for satellite drop behavior as regards forward or backward merging with the main drops.
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David B. Bogy (1979) studied this question.
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