Weakly Nonlinear Instability of a Liquid Jet in a Viscous Gas

[+] Author and Article Information
E. A. Ibrahim

Mechanical Engineering Department, Tuskegee University, Tuskegee, AL

S. P. Lin

Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY

J. Appl. Mech 59(2S), S291-S296 (Jun 01, 1992) doi:10.1115/1.2899503 History: Received July 26, 1990; Revised March 15, 1991; Online March 31, 2008


The weakly nonlinear instability of a viscous liquid jet emanated into a viscous gas contained in a coaxial vertical circular pipe is investigated as an initial-value problem. The linear stability theory predicted that the jet may become unstable either due to capillary pinching or due to interfacial stress fluctuation. The results of nonlinear stability analysis shows no tendency of supercritical stability for both of the linearly unstable modes. In fact, the nonlinear growth rate of the disturbance is faster than the exponential growth rate of the linear normal mode disturbance for the same flow parameters. Moreover, the most amplified linear normal mode disturbance evolves nonlinearly into a nonsinusoidal wave of shorter wavelength. No nonlinear instability is found for the linearly stable disturbances. Thus, while the linear theory is adequate for the prediction of the onset of jet breakup, nonlinear theory is required to describe the outcome of the jet breakup.

Copyright © 1992 by The American Society of Mechanical Engineers
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