Effective rheology of bubbles moving in a capillary tube

Santanu Sinha, Alex Hansen, Dick Bedeaux, and Signe Kjelstrup

Phys. Rev. E 87, 025001 – Published 14 February 2013

Abstract

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train, considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.

Received 4 September 2012

DOI:https://doi.org/10.1103/PhysRevE.87.025001

Authors & Affiliations

Santanu Sinha^1,*, Alex Hansen^1,†, Dick Bedeaux^2,‡, and Signe Kjelstrup^2,§

¹Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
²Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

^*Santanu.Sinha@ntnu.no
^†Alex.Hansen@ntnu.no
^‡Dick.Bedeaux@chem.ntnu.no
^§Signe.Kjelstrup@ntnu.no

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Issue

Vol. 87, Iss. 2 — February 2013

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics