The linear stability of a spherical drop migrating due to thermocapillarity and buoyancy in an unbounded fluid is investigated. The scope of the analysis is confined to axisymmetric perturbations of drop shape and conditions of negligible Reynolds number and Peclet number for which the basic flow is given by the solution of Young etal. [J. Fluid Mech. 6, 350 (1959)]. The spherical drop is found to be unstable when the capillary number exceeds a critical value that depends on the dynamic Bond number, the viscosity ratio, and the thermal conductivity ratio.

1.
N. O.
Young
,
J. S.
Goldstein
, and
M. J.
Block
,
J. Fluid Mech.
6
,
350
(
1959
).
2.
J.
Hadamard
,
C. R. Acad. Sci.
152
,
1735
(
1911
).
3.
D.
Rybczynsky
,
Bull. Acad. Sci. Cracovie Ser. A
1
,
40
(
1911
).
4.
T. D.
Taylor
and
A.
Acrivos
,
J. Fluid Mech.
18
,
466
(
1964
).
5.
M.
Kojima
,
E. J.
Hinch
, and
A.
Acrivos
,
Phys. Fluids
27
,
19
(
1984
).
6.
C. J.
Koh
and
L. G.
Leal
,
Phys. Fluids A
1
,
1309
(
1989
).
7.
C.
Pozrikidis
,
J. Fluid Mech.
210
,
1
(
1990
).
8.
J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1965).
This content is only available via PDF.
You do not currently have access to this content.