Experiments in Fluids

, Volume 37, Issue 2, pp 301–308

Velocity fields and streamline patterns of miscible displacements in cylindrical tubes


DOI: 10.1007/s00348-004-0824-0

Cite this article as:
Kuang, J., Petitjeans, P. & Maxworthy, T. Exp Fluids (2004) 37: 301. doi:10.1007/s00348-004-0824-0


Displacements of a viscous fluid by a miscible fluid of a lesser viscosity and density in cylindrical tubes were investigated experimentally. Details of velocity and Stokes streamline fields in vertical tubes were measured using a DPIV (digital particle image velocimetry) technique. In a reference frame moving with the fingertip, the streamline patterns around the fingertip obtained from the present measurements confirm the hypothesis of Taylor (1961) for the external patterns, and that of Petitjeans and Maxworthy (1996) for the internal patterns. As discussed in these papers, the dependent variable, m, a measure of the volume of viscous fluid left on the tube wall after the passage of the displacing finger, is a parameter that determines the flow pattern. When m>0.5 there is one stagnation point at the tip of the finger; when m<0.5 there are two stagnation points on the centerline, one at the tip and the other inside the fingertip, and a stagnation ring on the finger surface with a toroidal recirculation in the fingertip between the two stagnation points. The finger profile is obtained from the zero streamline of the streamline pattern.


Miscible fluidsFingerFingering displacementPIV/DPIVVelocity fieldStreamlineFlow patternExperiment

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Aerospace and Mechanical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Laboratoire de Physique et Mecanique des Milieux HeterogenesEcole Superieure de Physique et de Chimie IndustriellesParis Cedex 05France