Skip to main content Accessibility help

Thermocapillary migration of a bidisperse suspension of bubbles

  • Y. Wang (a1), R. Mauri (a2) and A. Acrivos (a1)


We consider the thermocapillary motion of a well-mixed suspension of non-conducting spherical bubbles of negligible viscosity in a viscous conducting liquid under conditions of vanishingly small Reynolds and Marangoni numbers. Recently, Acrivos, Jeffrey & Saville (1990) showed that when all the bubbles are of identical size, the ensemble-averaged migration velocity $\bar{U}_{1}$ of a test bubble of radius a1 within the suspension equals $U^{(0)}_1[1-\frac{3}{2}c_1+O(c^2_1)]$, where c1 is the volume fraction of the bubbles and U1(0) is the thermocapillary velocity of single bubble given by Young, Goldstein & Block (1959). Here we extend this result to a bi-disperse suspension containing bubbles of radii a1 and a2 ≡ λa1 in which case $\bar{U}_1 = U^{(0)}_1[1-\frac{3}{2}c_1 - S(\lambda)c_2+\ldots]$, where c1 and c2 are the corresponding volume fractions of the two sets of bubbles. Values for S(Λ) are presented for some typical size ratios Λ, and asymptotic expressions for S(Λ) are derived for Λ → 0 and for Λ → ∞.



Hide All
Acrivos, A. & Chang, E. 1986 The transport properties of non-dilute suspensions. Renormalization via an effective continuum method. In Physics and Chemistry of Porous Media II (ed. J. R. Banavar, J. Koplik & K. W. Winkler), pp. 129142. AIP Conf. Proc. 154. New York: AIP.
Acrivos, A., Jeffrey, D. J. & Saville, D. A. 1990 Particle migration in suspensions by thermocapillary or electrophoretic motion. J. Fluid Mech. 212, 95110.
Anderson, J. L. 1958 Droplet interactions in thermocapillary motion. Intl J. Multiphase Flow 11, 813824.
Chang, E. & Acrivos, A. 1986 Rate of heat conduction from a heated sphere to a matrix containing passive spheres of a different conductivity. J. Appl. Phys. 59, 33753382.
Chang, E. & Acrivos, A. 1987 Conduction of heat from a planar wall with uniform surface temperature to a monodispersed suspension of spheres. J. Appl. Phys. 62, 771776.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Jeffrey, D. J. 1973 Conduction through a random suspension of spheres. Proc. R. Soc. Lond. A 335, 355367.
Jeffrey, D. J. & Onishi, Y. 1984 Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J. Fluid Mech. 139, 261290.
Keh, H. J. & Chen, S. H. 1990 The axisymmetric thermocapillary motion of two fluid droplets. Intl J. Multiphase Flow 16, 515527.
Keh, H. J. & Chen, L. S. 1992 Droplet interactions in axisymmetric thermocapillary motion. J. Colloid Interface Sci. 151, 116.
Keh, H. J. & Chen, L. S. 1993 Droplet interactions in thermocapillary migration. Chem. Engng Sci. (to be published).
Meyyappan, M. & Subramanian, R. S. 1984 The thermocapillary motion of two bubbles oriented arbitrarily relative to a thermal gradient. J. Colloid Interface Sci. 97, 291294.
Meyyappan, M., Wilcox, W. R. & Subramanian, R. S. 1983 The slow axisymmetric motion of two bubbles in a thermal gradient. J. Colloid Interface Sci. 94, 243257.
Rallison, J. M. 1978 Note on the Fáxen relations for a particle in Stokes flow. J. Fluid Mech. 88, 529533.
Satrape, J. V. 1992 Interactions and collisions of bubbles in the thermocapillary motion. Phys. Fluids A 4, 18831900.
Subramanian, R. S. 1985 The Stokes force on a droplet in an unbounded fluid medium due to capillary effects. J. Fluid Mech. 153, 389400.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.
Thovert, J. F. & Acrivos, A. 1989 The effective thermal conductivity of a random polydisperse suspension of spheres to order C2. Chem. Engng Commun. 82, 177191.
Young, N. O., Goldstein, J. S. & Block, M. J. 1959 The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 6, 350356.
MathJax is a JavaScript display engine for mathematics. For more information see

Thermocapillary migration of a bidisperse suspension of bubbles

  • Y. Wang (a1), R. Mauri (a2) and A. Acrivos (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed