Interfacial waves in core-annular flow

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Abstract
In this paper we present experiments and an analysis of interfacial waves in core—annular flow; these waves are important for the flow to be stable. The observed wave velocity is about equal to the speed of the fluids near the interface, and the wavelength is 1–10 times the thickness of the annulus. These results are predicted by our analysis, which is valid provided the Reynolds number of the fluid in the annulus, and the ratio of the viscosities of the fluids in the core and the annulus, are large. The theory gives the growth rate of a wave as a function of this ratio, the Reynolds number, the surface tension and the wavenumber. For parameter values of interest, the growth rate is positive for a range wavenumbers which we compare with the experiments. Qualitative agreement between theory and experiment is excellent; quantitative comparison reveals discrepancies for which a possible explanation is the neglect of nonlinear terms.