Initial nonequilibrium distribution of temperature or surfactant concentration between suspended drops and the continuous fluid in a suspension results in an unsteady-state heat/mass transfer between the phases. Nonuniformities of temperature or solute concentration, which arise as a natural result of local geometrical inhomogeneities in the suspension, produce temperature/concentration gradients along the interfaces that, in turn, generate thermocapillary fluid motion along the interfaces and migration of drops toward or apart from each other. Asymptotic analysis of the process is carried out for large Peclet numbers of the dispersed phase. The dynamics of drops is studied and the approach time is estimated for the limiting cases of small and large Peclet numbers of the continuous phase.

1.
N. O.
Young
,
J. S.
Goldstein
, and
M. J.
Block
, “
The motion of bubbles in a vertical temperature gradient
,”
J. Fluid Mech.
6
,
350
(
1959
).
2.
R. S. Subramanian, “The motion of bubbles and drops in reduced gravity,” in Transport Processes in Bubbles, Drops, and Particles (Hemisphere, New York, 1992), pp. 1–42.
3.
G.
Wozniak
,
J.
Siekmann
, and
J.
Srulijjes
, “
Thermocapillary bubble and drop dynamics under reduced gravity—Survey and prospects
,”
Z. Flugwiss. Weltraumforsch.
12
,
137
(
1988
).
4.
M.
Meyyappan
,
W. R.
Wilcox
, and
R. S.
Subramanian
, “
The slow axisymmetric motion of two bubbles in a thermal gradient
,”
J. Colloid Interface Sci.
94
,
243
(
1983
).
5.
F.
Feuillbois
, “
Thermocapillary migration of two equal bubbles parallel to their line of centers
,”
J. Colloid Interface Sci.
131
,
267
(
1989
).
6.
M.
Meyyappan
and
R. S.
Subramanian
, “
The thermocapillary motion of two bubbles oriented arbitrarily to a thermal gradient
,”
J. Colloid Interface Sci.
97
,
291
(
1984
).
7.
A.
Acrivos
,
D. J.
Jeffrey
, and
D. A.
Saville
, “
Particle migration in suspensions by thermocapillary or electrophoretic motion
,”
J. Fluid Mech.
212
,
95
(
1990
).
8.
J. V.
Satrape
, “
Interactions and collisions of bubbles in thermocapillary motion
,”
Phys. Fluids A
4
,
1883
(
1992
).
9.
Y.
Wang
,
R.
Mauri
, and
A.
Acrivos
, “
Thermocapillary migration of a bidisperse suspension of bubbles
,”
J. Fluid Mech.
261
,
47
(
1994
).
10.
J. L.
Anderson
, “
Droplet interaction in thermocapillary motion
,”
Int. J. Multiphase Flow
11
,
813
(
1985
).
11.
H. J.
Keh
and
S. H.
Chen
, “
The axisymmetric thermocapillary motion of two fluid droplets
,”
Int. J. Multiphase Flow
16
,
515
(
1990
).
12.
H. J.
Keh
and
L. S.
Chen
, “
Droplet interaction in axisymmetric thermocapillary motion
,”
J. Colloid Interface Sci.
151
,
1
(
1992
).
13.
H. J.
Keh
and
L. S.
Chen
, “
Droplet interaction in thermocapillary motion
,”
Chem. Eng. Sci.
48
,
3565
(
1993
).
14.
H.
Wei
and
R. S.
Subramanian
, “
Thermocapillary migration of a small chain of bubbles
,”
Phys. Fluids A
5
,
1583
(
1993
).
15.
M.
Loewenberg
and
R.
Davis
, “
Near-contact thermocapillary motion of two nonconducting drops
,”
J. Fluid Mech.
256
,
107
(
1993
).
16.
A. A.
Golovin
,
A.
Nir
, and
L. P.
Pismen
, “
Spontaneous motion of two droplets caused by mass transfer
,”
Ind. Eng. Chem. Res.
34
,
3278
(
1995
).
17.
O. M.
Lavrenteva
,
A. M.
Leshansky
, and
A.
Nir
, “
Spontaneous thermocapillary interaction of drops, bubbles and particles: Unsteady convective effects at low Peclet numbers
,”
Phys. Fluids
11
,
1768
(
1999
).
18.
R.
Balasubramaniam
and
R. S.
Subramanian
, “
Axisymmetric thermal wake interaction of two bubbles in a uniform temperature gradient at large Reynolds and Marangoni numbers
,”
Phys. Fluids
11
,
2856
(
1999
).
19.
J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice–Hall, Englewood Cliffs, NJ, 1965).
20.
S.
Haber
,
G.
Hestroni
, and
A.
Solan
, “
On the low Reynolds number motion of two droplets
,”
Int. J. Multiphase Flow
1
,
57
(
1973
).
21.
A. M.
Leshansky
,
A. A.
Golovin
, and
A.
Nir
, “
Thermocapillary interaction between a solid particle and a liquid–gas interface
,”
Phys. Fluids
9
,
2818
(
1997
).
22.
A. S.
Brignell
, “
Solute extraction from an internally circulating spherical liquid drop
,”
Int. J. Heat Mass Transf.
18
,
61
(
1975
).
23.
A. D.
Polyanin
, “
Unsteady-state extraction from a falling droplet with nonlinear dependence of distribution coefficient on concentration
,”
Int. J. Heat Mass Transf.
27
,
1261
(
1984
).
24.
R. H.
Davis
,
J. A.
Schonberg
, and
J. M.
Rallison
, “
The lubrication force between two viscous drops
,”
Phys. Fluids A
1
,
77
(
1989
).
25.
M. D. A.
Cooley
and
M. E.
O’Neill
, “
On the slow motion of two spheres in contact along their line of centers through a viscous fluid
,”
Proc. Cambridge Philos. Soc.
66
,
407
(
1969
).
26.
L. D.
Reed
and
F. A.
Morrison
, “
The slow motion of two touching fluid spheres along their line of centers
,”
Int. J. Multiphase Flow
1
,
573
(
1974
).
27.
A. D.
Polyanin
, “
Method for solution of some nonlinear boundary value problems of a non-stationary diffusion controlled (thermal) boundary layer
,”
Int. J. Heat Mass Transf.
25
,
471
(
1982
).
28.
S. G.
Yiantsios
and
R. H.
Davis
, “
Close approach and deformation of two viscous drops due to gravity and van der Waals forces
,”
J. Colloid Interface Sci.
181
,
60
(
1991
).
29.
H.
Zhou
and
H. R.
Davis
, “
Axisymmetric thermocapillary migration of two deformable viscous drops
,”
J. Colloid Interface Sci.
181
,
60
(
1996
).
30.
M. A.
Rother
and
R. H.
Davis
, “
The effect of slight deformations on thermocapillary driven droplet coalescence and growth
,”
J. Colloid Interface Sci.
214
,
297
(
1999
).
31.
A. A.
Golovin
, “
Thermocapillary interaction between a solid particle and a gas bubble
,”
Int. J. Multiphase Flow
21
,
715
(
1995
).
32.
P.
Dell’Aversana
,
J. R.
Banavar
, and
J.
Koplik
, “
Suppression of coalescence by shear and temperature gradients
,”
Phys. Fluids
8
,
15
(
1996
).
33.
R.
Savino
and
R.
Monti
, “
Modelling of non-coalescing liquid drops in the presence of thermocapillary convection
,”
Meccanica
32
,
115
(
1997
).
34.
R.
Monti
and
R.
Savino
, “
Correlation between experimental results and numerical solutions of the Navier–Stokes problem noncoalescing liquid drops with Marangoni effects
,”
Phys. Fluids
9
,
260
(
1997
).
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