We study self-propelled dynamics of a droplet due to a Marangoni effect and chemical reactions in a binary fluid with a dilute third component of chemical product which affects the interfacial energy of a droplet. The equation for the migration velocity of the center of mass of a droplet is derived in the limit of an infinitesimally thin interface. We found that there is a bifurcation from a motionless state to a propagating state of droplet by changing the strength of the Marangoni effect.
REFERENCES
1.
K.
Nagai
, Y.
Sumino
, H.
Kitahata
, and K.
Yoshikawa
, Phys. Rev. E
71
, 065301
–R
(2005
).2.
T.
Toyota
, N.
Maru
, M. M.
Hanczyc
, T.
Ikegami
, and T.
Sugawara
, J. Am. Chem. Soc.
131
, 5012
(2009
).3.
A.
Shioi
, T.
Ban
, and Y.
Morimune
, Entropy
12
, 2308
(2010
).4.
S.
Thutupalli
, R.
Seemann
, and S.
Herminghaus
, New J. Phys.
13
, 073021
(2011
).5.
H.
Kitahata
, N.
Yoshinaga
, K. H.
Nagai
, and Y.
Sumino
, Phys. Rev. E
84
, 015101
–R
(2011
).6.
K.
Furtado
, C. M.
Pooley
, and J. M.
Yeomans
, Phys. Rev. E.
78
, 046308
(2008
).7.
Y.-G.
Tao
and R.
Kapral
, J. Chem. Phys.
128
, 164518
(2008
).8.
Y.-G.
Tao
and R.
Kapral
, Soft Matter
6
, 756
(2010
).9.
M. D.
Levan
, J. Colloid Interface Sci.
83
, 11
(1981
).10.
A. Ye.
Rednikov
and Y. S.
Ryazantsev
, J. Appl. Math. Mech.
53
, 212
(1989
).11.
D.
Jasnow
and J.
Vinals
, Phys. Fluids
8
, 660
(1996
).12.
K.
John
, M.
Baer
, and U.
Thiele
, Eur. Phys. J. E
18
, 183
(2005
).13.
K.
Krischer
and A.
Mikhailov
, Phys. Rev. Lett.
73
, 3165
(1994
).14.
M.
Or-Guil
, M.
Bode
, C. P.
Schenk
, and H. G.
Purwins
, Phys. Rev. E
57
, 6432
(1998
).15.
T.
Ohta
, Physica D
151
, 61
(2001
).16.
S.-I.
Ei
, M.
Mimura
, and M.
Nagayama
, Physica D
165
, 176
(2002
).17.
Y.
Nishiura
, T.
Teramoto
, and K.
Ueda
, Chaos
15
, 047509
(2005
).18.
T.
Ohta
, T.
Ohkuma
, and K.
Shitara
, Phys. Rev. E
80
, 056203
(2009
).19.
K.
Shitara
, T.
Hiraiwa
, and T.
Ohta
, Phys. Rev. E
83
, 066208
(2011
).20.
T.
Ohta
and T.
Ohkuma
, Phys. Rev. Lett.
102
, 154101
(2009
).21.
K.
Kitahara
, Y.
Oono
, and D.
Jasnow
, Mod. Phys. Lett. B
6
, 765
(1988
).22.
D. M.
Anderson
, G. B.
McFadden
, and A. A.
Wheeler
, Annu. Rev. Fluid Mech.
30
, 139
(1998
).23.
K.
Kawasaki
and T.
Ohta
, Physica A
118
, 175
(1983
).24.
N. O.
Young
, J. S.
Goldstein
, and J. M.
Block
, J. Fluid Mech.
6
, 350
(1989
).25.
T.
Ohta
, Ann. Phys.
158
, 31
(1984
).26.
A.
Onuki
and K.
Kanatani
, Phys. Rev. E
72
, 066304
(2005
).27.
N.
Yoshinaga
, K.
Nagai
, Y.
Sumino
, and H.
Kitahata
(unpublished).© 2012 American Institute of Physics.
2012
American Institute of Physics
You do not currently have access to this content.