A Free Streamline Model for a Rising Bubble.

Abstract

The motion of a two dimensional bubble rising at a constant velocity in an unbounded fluid is solved by series truncation. It is assumed there is a wake of stagnant liquid extending to infinity below the bubble. Both the effects of gravity g and surface tension T are taken into account. It is shown that the problem is characterized by a continuum of solutions for T = 0 and by a discrete set of solutions when T > 0. In addition a unique solution is obtained in the limit as the surface tension approaches zero. The corresponding profile of the bubble is found to be in good agreement with experimental data. The present paper describes example of such flow. Consider the motion of a two dimensional bubble rising at a constant velocity in an unbounded fluid. It is assumed there is a wake of stagnant liquid extending to infinity below the bubble. Both the effects of gravity and surface tension are taken into account. It is found that this problem is also characterized by a continuum of solutions when surface tension is neglected and by a discrete set of solutions when surface tension is taken into account. Moreover it is shown that a unique solution is obtained in the limit as the surface tension tends to zero. The corresponding profile of the bubble is found to be in good agreement with experimental data.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1986
Accession Number
ADA167535

Entities

People

  • Jean-marc Vanden-broeck

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Agreements
  • Analytic Functions
  • Classification
  • Contracts
  • Differential Equations
  • Equations
  • Experimental Data
  • Flow
  • Froude Number
  • Geometry
  • Lepidoptera
  • Mathematics
  • North Carolina
  • Surface Tension
  • Two Dimensional
  • United States
  • Wisconsin

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Materials Science and Engineering.
  • Underwater engineering and Marine Technology.