Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-29T12:56:23.905Z Has data issue: false hasContentIssue false
  • English
  • Français

Growth and collapse of translating compound multiphase drops: analysis of fluid mechanics and heat transfer

Published online by Cambridge University Press:  21 April 2006

H. N. O~uz  and
S. S. Sadhal
H. N. O~uz
Affiliation:
Department of Mechanical Engineering, 1, Los Angeles, CA 90089-1453, USA
S. S. Sadhal
Affiliation:
Department of Mechanical Engineering, 1, Los Angeles, CA 90089-1453, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The time history is examined of the motion of a compound multiphase drop formed by a vapour bubble completely covered by its liquid phase in another immiscible liquid. The compound drop is growing or collapsing owing to change of phase while it is translating under buoyant forces. In the limit of large surface-tension forces the interfaces are spherical. An exact analytical solution for the fluid-mechanical part of the problem can be obtained. The heat-transfer treatment of the problem, however, requires numerical solution if we are to include convective terms along with time dependence. The drag component induced by radial velocity contributes to the total drag on the bubble in eccentric configuration. This drag force is towards the centre of the drop in the case of growth and has an effect of restoring concentricity. However, it is found that, in the case of growth, the compound drop, in general, cannot maintain its configuration of two non-intersecting eccentric spheres. On the other hand, in the case of collapse the bubble stays inside the drop if the collapse velocity is high enough. The complete analysis exhibits some interesting flow patterns relating to compound drops and bubbles. The time-dependent Nusselt number for a single bubble generally decreases with time but it may have a strong dependence on the compound-drop configuration, as well as the conductivities of the participating liquids. The radial convection opposes heat transfer but it has to compete with translatory convection, which is usually overwhelming in the case of growth.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 105 - 136
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Goren, S. L. & O'Neill, M. E.1971 On the hydrodynamic resistance to a particle of a dilute suspension when in the neighborhood of a large obstacle. Chem. Engng Sci. 26, 325–338.Google Scholar
Haber, S., Hetsroni, G. & Solan, A. 1973 On the low Reynolds number motion of two droplets. Intl J. Multiphase Flow 1, 57–71.Google Scholar
Hayakawa, T. & Shigeta, M. 1974 Terminal velocity of two-phase droplet. J. Chem. Engng Japan 7, 140–142.Google Scholar
Isenberg, J. & Sideman, S. 1970 Direct contact heat transfer with change of phase: bubble condensation in immiscible liquids. Int J. Heat Mass Transfer 13, 997–1011.Google Scholar
Jacobs, H. R. & Major, B. H. 1982 The effect of noncondensible gases on bubble condensation in an immiscible liquid. Trans. ASME C: J. Heat Transfer 104, 487–492.Google Scholar
Jeffery, G. B. 1912 On a form of the solution of Laplace's equation suitable for problems relating two spheres. Proc. R. Soc. Lond. A 87, 115.Google Scholar
Johnson, R. E. & Sadhal, S. S. 1985 Fluid mechanics of compound multiphase drops and bubbles. Ann. Rev. Fluid Mech. 17, 289–320.Google Scholar
Lerner, Y. & Letan, R. 1985 Dynamics of condensing bubbles: effects of injection frequency. 22nd National Heat Transfer Conference, Denver, Colorado, August 4–7, 1985, paper no. 85-HT-47.
Meyyapan, M., Wilcox, W. R. & Subramanian, R. S. 1981 Thermocapillary migration of a bubble normal to a plane surface. J. Colloid Interface Sci. 83, 199–208.Google Scholar
O'Neill, M. E.1964 A slow motion of a viscous fluid caused by a slowly moving solid sphere. Mathematica 11, 67–74.Google Scholar
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Ann. Rev. Fluid Mech. 9, 145–185.Google Scholar
Prosperetti, A. & Plesset, M. S. 1978 Vapour-bubble growth in a superheated liquid. J. Fluid Mech. 85, 349–368.Google Scholar
Rasmussen, R. M., Levizzani, V. R. & Pruppacher, H. R. 1982 A numerical study of heat transfer through a fluid layer with recirculating flow between concentric and eccentric spheres. Pure Appl. Geophys. 120, 702–720.Google Scholar
Rushton, E. & Davies, G. A. 1973 The slow unsteady settling of two fluid spheres along their line of centers. Intl J. Multiphase Flow 4, 357–381.Google Scholar
Rushton, E. & Davies, G. A. 1978 The slow motion of two spherical particles along their line of centers. Intl J. Multiphase Flow 9, 337–342.Google Scholar
Sadhal, S. S. & O>uz, H. N. 1985 Stokes flow past compound multiphase drops: the case of completely engulfed drops/bubbles. J. Fluid Mech. 160, 511–529.Google Scholar
Selecki, A. & Gradon, L. 1976 Equation of motion of an expanding vapour drop in an immiscible liquid medium. Intl J. Heat Mass Transfer 19, 51–59.Google Scholar
Sideman, S. & Hirsch, G. 1965 Direct contact heat transfer with change of phase: condensation of single vapour bubbles in an immiscible liquid medium. Preliminary studies. AIChE J. 11, 1019–1025.Google Scholar
Sideman, S. & Taitel, Y. 1964 Direct contact heat transfer with change of phase: evaporation of drops in an immiscible liquid medium. Intl J. Heat Mass Transfer 7, 1273–1289.Google Scholar
Stimson, M. & Jeffery, G. B. 1926 The motion of two spheres in a viscous fluid. Proc. R. Soc. Lond. A 111, 110–116.Google Scholar
Stokes, G. G. 1851 On the effect of the internal friction of fluid on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 8–106.Google Scholar
Tochitani, Y., Mori, Y. H. & Komotori, K. 1977a Vaporization of single drops in an immiscible liquid. Part I. Forms and motions of vaporizing drops. Wärme Stoffübertrag. 10, 51–59.Google Scholar
Tochitani, Y., Nakagawa, T., Mori, Y. H. & Komotori, K. 1977b Vaporization of single liquid drops in an immiscible liquid. Part II. Heat transfer characteristics. Wärme Stoffübertrag. 10 71–79.Google Scholar