AEM Home page> People > Faculty > Daniel D. Joseph> Archive on Irrotational Motions of Viscous and Viscoelastic Fluids

Ellipsoidal model of the rise of a Taylor bubble in a round tube

By T. FUNADA1, D. D. JOSEPH2, T. MAEHARA1, AND S. YAMASHITA1

1Department of Digital Engineering, Numazu College of Technology, 3600 Ooka, Numazu, Shizuoka, 410-8501, Japan
2Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St. SE, Minneapolis, MN 55455, USA

(Received March, 2004 and in revised form ??)

Abstract

The rise velocity of long gas bubbles (Taylor bubbles) in round tubes is modeled by an ovary ellipsoidal cap bubble rising in an irrotational flow of a viscous liquid. The analysis leads to an expression for the rise velocity which depends on the aspect ratio of the model ellipsoid and the Reynolds and Eotvos numbers. The aspect ratio of the best ellipsoid is selected to give the same rise velocity as the Taylor bubble at given values of the Eotvos and Reynolds numbers. The analysis leads to a prediction of the shape of the ovary ellipsoid which rises with same velocity as the Taylor bubble.