This paper describes dynamic self-assembly of millimeter-sized objects rotating at two parallel fluid interfaces and interacting with one another hydrodynamically, both in the plane of the interface and between the interfaces. The nature of hydrodynamic interactions between the objects rotating on different interfaces and, consequently, the morphologies of the ordered structures that self-assemble, depend on the sizes and the three-dimensional shapes of the rotating particles. Large particles rotating on one interface (“templates”) can direct the self-assembly of smaller particles (“substrates”) on the other interface. Two examples of directed self-assembly are discussed: (i) selective dimerization of disk spinning on the lower interface under the influence of cylinders rotating on the upper interface, and (ii) assembly of “substrate” rectangles into a pattern of squares that is identical with the pattern formed by the “template” squares. General, qualitative characteristics of the vortex–vortex interactions between objects of complex shapes are discussed.

1.
A. S.
Mikhailov
and
G.
Ertl
,
Science
272
,
1596
(
1996
).
Google Scholar
Crossref
Search ADS
 
2.
M. C.
Cross
and
P. C.
Hohenberg
,
Rev. Mod. Phys.
65
,
851
(
1993
).
Google Scholar
Crossref
Search ADS
 
3.
P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability, and Fluctuations (Wiley–Interscience, New York, 1971).
4.
G. Nicolis and I. Prigogine, Exploring Complexity (Freeman, New York, 1989).
5.
F.
Kannari
,
N.
Takei
, and
M.
Shiozawa
,
Rev. Laser Eng.
28
,
479
(
2000
).
Google Scholar
Crossref
Search ADS
 
6.
P.
Alstrom
and
D.
Stassinopoulos
,
Phys. Rev. E
51
,
5027
(
1995
).
Google Scholar
Crossref
Search ADS
 
7.
B. A.
Grzybowski
,
D.
Qin
, and
G. M.
Whitesides
,
Appl. Opt.
38
,
2997
(
1999
).
Google Scholar
Crossref
Search ADS
PubMed
 
8.
B. A.
Grzybowski
,
D.
Qin
,
R.
Haag
, and
G. M.
Whitesides
,
Sens. Actuators A
A86
,
81
(
2000
).
Google Scholar
 
9.
J. J.
Yao
,
J. Micromech. Microeng.
10
,
R9
(
2000
).
Google Scholar
Crossref
Search ADS
 
10.
B. A.
Grzybowski
and
G. M.
Whitesides
,
J. Phys. Chem. B
106
,
1188
(
2002
).
Google Scholar
Crossref
Search ADS
 
11.
B. A.
Grzybowski
,
H. A.
Stone
, and
G. M.
Whitesides
,
Nature (London)
405
,
1033
(
2000
).
Google Scholar
Crossref
Search ADS
 
12.
B. A.
Grzybowski
,
X.
Jiang
,
H. A.
Stone
, and
G. M.
Whitesides
,
Phys. Rev. E
6401
,
1603
(
2001
).
Google Scholar
 
13.
B. A. Grzybowski and G. M. Whitesides, Science (in press).
14.
Kinematic viscosity of the mixture effected the stability of the aggregates. In liquids of low viscosities (v≲3 cp), the flows created by spinning disks were often turbulent, and the self-assembled aggregates were unstable. If the viscosity was too high (v≳50 cp), the magnetic torque was to small to spin the disks. Most stable structures were observed in liquids of intermediate kinematic viscosities, such as the 1:1 mixture of EG and water.
15.
The cutter was build from three translational stages. Two of the stages were stacked on top of each other and served as an xy platform, on which the tubing was placed. The third stage was free to move in the direction perpendicular to the plane of the platform, and had a fine razor blade glued to it; this blade was used to cut the tubing.
16.
B. A.
Grzybowski
,
N.
Bowden
,
F.
Arias
,
H.
Yang
, and
G. M.
Whitesides
,
J. Phys. Chem. B
105
,
404
(
2001
).
Google Scholar
Crossref
Search ADS
 
17.
R. E. Rosensweig, Ferrohydrodynamics (Dover, New York, 1997).
18.
D. J. Tritton, Physical Fluid Mechanics (Clarendon, Oxford, 1988).
19.
D.
Dijkstra
and
G. J. F. Van
Heijst
,
J. Fluid Mech.
128
,
123
(
1983
).
Google Scholar
Crossref
Search ADS
 
20.
T. H.
Havelock
,
Philos. Mag.
11
,
617
(
1931
).
Google Scholar
Crossref
Search ADS
 
21.
D. G.
Dritschel
,
J. Fluid Mech.
157
,
95
(
1985
).
Google Scholar
Crossref
Search ADS
 
This content is only available via PDF.
© 2002 American Institute of Physics.
2002
American Institute of Physics
You do not currently have access to this content.