Concentration waves in dilute bubble/liquid mixtures

L. van Wijngaarden, C. Kapteyn

Research output: Contribution to journalArticleAcademicpeer-review

47 Citations (Scopus)
57 Downloads (Pure)

Abstract

In this paper we consider a uniform gas bubble-liquid mixture rising under buoyancy. When the gas volume flux is decreased, while keeping bubble size constant, a smooth transition is formed between the region of lower concentration by volume and the region of initial concentration. This transition travels through the mixture as a permanent wave. We start by discussing the mechanisms which make possible such a permanent wave. The first is its tendency to steepen at the low concentration side. At the root of this is the decrease of the uniform rise velocity, under buoyancy, with increasing concentration. Associated with the motion of the bubbles is the liquid impulse. It is shown that this increases with increasing concentration, producing a reactive force on the bubbles which counteracts buoyancy and reduces the force available to overcome friction. In the transition a balance between these two effects occurs. The internal structure following from this balance is analysed in detail and it is shown that under certain conditions all its properties can be derived from knowledge of the average rise velocities of bubbles in uniform mixtures as a function of concentration. Measurements on these are reported subsequently, followed by a discussion of our experiments on transitions of the kind mentioned in which velocity, thickness etc. of the waves have been measured. The data are compared with the results of the analysis. Order-of-magnitude agreement is found but there are differences as well, requiring further research.
Original languageEnglish
Pages (from-to)111-137
Number of pages27
JournalJournal of fluid mechanics
Volume0
Issue number212
DOIs
Publication statusPublished - 1990

Fingerprint

Buoyancy
Bubbles (in fluids)
bubbles
buoyancy
Liquids
liquids
low concentrations
Gases
Friction
Fluxes
gases
travel
impulses
tendencies
friction
Experiments

Cite this

van Wijngaarden, L. ; Kapteyn, C. / Concentration waves in dilute bubble/liquid mixtures. In: Journal of fluid mechanics. 1990 ; Vol. 0, No. 212. pp. 111-137.
@article{9b202f5acdd14e6a90d9a1a7026abd48,
title = "Concentration waves in dilute bubble/liquid mixtures",
abstract = "In this paper we consider a uniform gas bubble-liquid mixture rising under buoyancy. When the gas volume flux is decreased, while keeping bubble size constant, a smooth transition is formed between the region of lower concentration by volume and the region of initial concentration. This transition travels through the mixture as a permanent wave. We start by discussing the mechanisms which make possible such a permanent wave. The first is its tendency to steepen at the low concentration side. At the root of this is the decrease of the uniform rise velocity, under buoyancy, with increasing concentration. Associated with the motion of the bubbles is the liquid impulse. It is shown that this increases with increasing concentration, producing a reactive force on the bubbles which counteracts buoyancy and reduces the force available to overcome friction. In the transition a balance between these two effects occurs. The internal structure following from this balance is analysed in detail and it is shown that under certain conditions all its properties can be derived from knowledge of the average rise velocities of bubbles in uniform mixtures as a function of concentration. Measurements on these are reported subsequently, followed by a discussion of our experiments on transitions of the kind mentioned in which velocity, thickness etc. of the waves have been measured. The data are compared with the results of the analysis. Order-of-magnitude agreement is found but there are differences as well, requiring further research.",
author = "{van Wijngaarden}, L. and C. Kapteyn",
year = "1990",
doi = "10.1017/S0022112090001896",
language = "English",
volume = "0",
pages = "111--137",
journal = "Journal of fluid mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",
number = "212",

}

Concentration waves in dilute bubble/liquid mixtures. / van Wijngaarden, L.; Kapteyn, C.

In: Journal of fluid mechanics, Vol. 0, No. 212, 1990, p. 111-137.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Concentration waves in dilute bubble/liquid mixtures

AU - van Wijngaarden, L.

AU - Kapteyn, C.

PY - 1990

Y1 - 1990

N2 - In this paper we consider a uniform gas bubble-liquid mixture rising under buoyancy. When the gas volume flux is decreased, while keeping bubble size constant, a smooth transition is formed between the region of lower concentration by volume and the region of initial concentration. This transition travels through the mixture as a permanent wave. We start by discussing the mechanisms which make possible such a permanent wave. The first is its tendency to steepen at the low concentration side. At the root of this is the decrease of the uniform rise velocity, under buoyancy, with increasing concentration. Associated with the motion of the bubbles is the liquid impulse. It is shown that this increases with increasing concentration, producing a reactive force on the bubbles which counteracts buoyancy and reduces the force available to overcome friction. In the transition a balance between these two effects occurs. The internal structure following from this balance is analysed in detail and it is shown that under certain conditions all its properties can be derived from knowledge of the average rise velocities of bubbles in uniform mixtures as a function of concentration. Measurements on these are reported subsequently, followed by a discussion of our experiments on transitions of the kind mentioned in which velocity, thickness etc. of the waves have been measured. The data are compared with the results of the analysis. Order-of-magnitude agreement is found but there are differences as well, requiring further research.

AB - In this paper we consider a uniform gas bubble-liquid mixture rising under buoyancy. When the gas volume flux is decreased, while keeping bubble size constant, a smooth transition is formed between the region of lower concentration by volume and the region of initial concentration. This transition travels through the mixture as a permanent wave. We start by discussing the mechanisms which make possible such a permanent wave. The first is its tendency to steepen at the low concentration side. At the root of this is the decrease of the uniform rise velocity, under buoyancy, with increasing concentration. Associated with the motion of the bubbles is the liquid impulse. It is shown that this increases with increasing concentration, producing a reactive force on the bubbles which counteracts buoyancy and reduces the force available to overcome friction. In the transition a balance between these two effects occurs. The internal structure following from this balance is analysed in detail and it is shown that under certain conditions all its properties can be derived from knowledge of the average rise velocities of bubbles in uniform mixtures as a function of concentration. Measurements on these are reported subsequently, followed by a discussion of our experiments on transitions of the kind mentioned in which velocity, thickness etc. of the waves have been measured. The data are compared with the results of the analysis. Order-of-magnitude agreement is found but there are differences as well, requiring further research.

U2 - 10.1017/S0022112090001896

DO - 10.1017/S0022112090001896

M3 - Article

VL - 0

SP - 111

EP - 137

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

SN - 0022-1120

IS - 212

ER -