Abstract

Particle transport through Marangoni convection inside a sessile droplet can be controlled by the ultraviolet (UV) light distribution on the surface. The photosensitive solution changes the surface tension gradient on the droplet surface and can induce clockwise and counterclockwise circulations depending on the incident light distribution. In this paper, the stream function in the sessile drop has been evaluated in toroidal coordinates by solving the biharmonic equation. Multiple primary clockwise and counterclockwise circulations are observed in the droplet under various concentric UV light profiles. The downward dividing streamlines are expected to deposit the particles on the substrate, thus matching the number of deposited rings on the substrate with the number of UV light rings. Moffatt eddies appear near the contact line or centerline of the droplet depending on the UV light profile and its distance from the contact line.

References

References
1.
Högberg
,
S. M.
,
Åkerstedt
,
H. O.
,
Holmstedt
,
E.
,
Staffan Lundström
,
T.
, and
Sandström
,
T.
,
2012
, “
Time-Dependent Deposition of Micro-and Nanofibers in Straight Model Airways
,”
ASME J. Fluids Eng.
,
134
(
5
), p. 051208.10.1115/1.4006698
2.
Michaelides
,
E. E.
,
2016
, “
Wall Effects on the Brownian Movement, Thermophoresis, and Deposition of Nanoparticles in Liquids
,”
ASME J. Fluids Eng.
,
138
(
5
), p. 051303.10.1115/1.4027624
3.
Liu
,
R.
,
Vanka
,
S. P.
, and
Thomas
,
B. G.
,
2014
, “
Particle Transport and Deposition in a Turbulent Square Duct Flow With an Imposed Magnetic Field
,”
ASME J. Fluids Eng.
,
136
(
12
), p. 121201.10.1115/1.4032030
4.
Vogel
,
N.
,
Retsch
,
M.
,
Fustin
,
C. A.
,
Del Campo
,
A.
, and
Jonas
,
U.
,
2015
, “
Advances in Colloidal Assembly: The Design of Structure and Hierarchy in Two and Three Dimensions
,”
Chem. Rev.
,
115
(
13
), pp.
6265
6311
.10.1021/cr400081d
5.
Haes
,
A. J.
, and
Van Duyne
,
R. P.
,
2002
, “
A Nanoscale Optical Biosensor: Sensitivity and Selectivity of an Approach Based on the Localized Surface Plasmon Resonance Spectroscopy of Triangular Silver Nanoparticles
,”
J. Am. Chem. Soc.
,
124
(
35
), pp.
10596
10604
.10.1021/ja020393x
6.
Armstrong
,
E.
,
Khunsin
,
W.
,
Osiak
,
M.
,
Blömker
,
M.
,
Torres
,
C. M. S.
, and
O'Dwyer
,
C.
,
2014
, “
Ordered 2D Colloidal Photonic Crystals on Gold Substrates by Surfactant‐Assisted Fast‐Rate Dip Coating
,”
Small
,
10
(
10
), pp.
1895
1901
.10.1002/smll.201303616
7.
Mihi
,
A.
,
Ocaña
,
M.
, and
Míguez
,
H.
,
2006
, “
Oriented Colloidal‐Crystal Thin Films by Spin-Coating Microspheres Dispersed in Volatile Media
,”
Adv. Mater.
,
18
(
17
), pp.
2244
2249
.10.1002/adma.200600555
8.
Zhang
,
X.
,
Zhang
,
J.
,
Zhu
,
D.
,
Li
,
X.
,
Zhang
,
X.
,
Wang
,
T.
, and
Yang
,
B.
,
2010
, “
A Universal Approach to Fabricate Ordered Colloidal Crystals Arrays Based on Electrostatic Self-Assembly
,”
Langmuir
,
26
(
23
), pp.
17936
17942
.10.1021/la103778m
9.
Dziomkina
,
N. V.
,
Hempenius
,
M. A.
, and
Vancso
,
G. J.
,
2005
, “
Symmetry Control of Polymer Colloidal Monolayers and Crystals by Electrophoretic Deposition on Patterned Surfaces
,”
Adv. Mater.
,
17
(
2
), pp.
237
240
.10.1002/adma.200400830
10.
Sirotkin
,
E.
,
Apweiler
,
J. D.
, and
Ogrin
,
F. Y.
,
2010
, “
Macroscopic Ordering of Polystyrene Carboxylate-Modified Nanospheres Self-Assembled at the Water−Air Interface
,”
Langmuir
,
26
(
13
), pp.
10677
10683
.10.1021/la1009658
11.
Meng
,
X.
, and
Qiu
,
D.
,
2014
, “
Gas-Flow-Induced Reorientation to Centimeter-Sized Two-Dimensional Colloidal Single Crystal of Polystyrene Particle
,”
Langmuir
,
30
(
11
), pp.
3019
3023
.10.1021/la404944w
12.
Castillo-Orozco
,
E.
,
Kar
,
A.
, and
Kumar
,
R.
,
2017
, “
Electrospray Mode Transition of Microdroplets With Semiconductor Nanoparticle Suspension
,”
Sci. Rep.
,
7
(
1
), pp. 1–1010.1038/s41598-017-05175-6.
13.
Castillo-Orozco
,
E.
,
Kumar
,
R.
, and
Kar
,
A.
,
2019
, “
Laser Electrospray Printing of Nanoparticles on Flexible and Rigid Substrates
,”
J. Laser Appl.
,
31
(
2
), p.
022015
.10.2351/1.5079733
14.
Castillo-Orozco
,
E.
,
Kumar
,
R.
, and
Kar
,
A.
,
2019
, “
Laser-Induced Subwavelength Structures by Microdroplet Superlens
,”
Opt. Express
,
27
(
6
), pp.
8130
8142
.10.1364/OE.27.008130
15.
Varanakkottu
,
S. N.
,
Anyfantakis
,
M.
,
Morel
,
M.
,
Rudiuk
,
S.
, and
Baigl
,
D.
,
2016
, “
Light-Directed Particle Patterning by Evaporative Optical Marangoni Assembly
,”
Nano Lett.
,
16
(
1
), pp.
644
650
.10.1021/acs.nanolett.5b04377
16.
Anyfantakis
,
M.
,
Varanakkottu
,
S. N.
,
Rudiuk
,
S.
,
Morel
,
M.
, and
Baigl
,
D.
,
2017
, “
Evaporative Optical Marangoni Assembly: Tailoring the Three-Dimensional Morphology of Individual Deposits of Nanoparticles from Sessile Drops
,” ACS Appl. Mater. Interfaces, 9(42), pp.
37435
37445
.
17.
Anyfantakis
,
M.
, and
Baigl
,
D.
,
2014
, “
Dynamic Photocontrol of the Coffee-Ring Effect With Optically Tunable Particle Stickiness
,”
Angew. Chem., Int. Ed.
,
53
(
51
), pp.
14077
14081
.10.1002/anie.201406903
18.
Brown
,
P.
,
Butts
,
C. P.
, and
Eastoe
,
J.
,
2013
, “
Stimuli-Responsive Surfactants
,”
Soft Matter
,
9
(
8
), pp.
2365
2374
.10.1039/c3sm27716j
19.
Chevallier
,
E.
,
Mamane
,
A.
,
Stone
,
H. A.
,
Tribet
,
C.
,
Lequeux
,
F.
, and
Monteux
,
C.
,
2011
, “
Pumping-Out Photo-Surfactants From an Air-Water Interface Using Light
,”
Soft Matter.
,
7
(
17
), p.
7866
.10.1039/c1sm05378g
20.
Marin
,
A.
,
Liepelt
,
R.
,
Rossi
,
M.
, and
Kähler
,
C. J.
,
2016
, “
Surfactant-Driven Flow Transitions in Evaporating Droplets
,”
Soft Matter.
,
12
(
5
), pp.
1593
1600
.10.1039/C5SM02354H
21.
Diddens
,
C.
,
Tan
,
H.
,
Lv
,
P.
,
Versluis
,
M.
,
Kuerten
,
J. G. M.
,
Zhang
,
X.
, and
Lohse
,
D.
,
2017
, “
Evaporating Pure, Binary and Ternary Droplets: Thermal Effects and Axial Symmetry Breaking
,”
J. Fluid Mech.
,
823
, pp.
470
497
.10.1017/jfm.2017.312
22.
Ristenpart
,
W. D.
,
Kim
,
P. G.
,
Domingues
,
C.
,
Wan
,
J.
, and
Stone
,
H. A.
,
2007
, “
Influence of Substrate Conductivity on Circulation Reversal in Evaporating Drops
,”
Phys. Rev. Lett.
,
99
(
23
), p. 234502.10.1103/PhysRevLett.99.234502
23.
Tam
,
D.
,
von Arnim
,
V.
,
McKinley
,
G. H.
, and
Hosoi
,
A. E.
,
2009
, “
Marangoni Convection in Droplets on Superhydrophobic Surfaces
,”
J. Fluid Mech.
,
624
pp.
101
123
.10.1017/S0022112008005053
24.
Li
,
T.
,
Kar
,
A.
, and
Kumar
,
R.
,
2019
, “
Marangoni Circulation by UV Light Modulation on Sessile Drop for Particle Agglomeration
,”
J. Fluid Mech.
,
873
, pp.
72
88
.10.1017/jfm.2019.373
25.
Li
,
T.
,
Kar
,
A.
, and
Kumar
,
R.
,
2020
, “
Concentration Distribution of Photosensitive Liquid in a Droplet Under Ultraviolet Light
,”
ASME J. Fluids Eng.
,
142
(
2
), p. 021301.10.1115/1.4044442
26.
Strasser
,
W.
,
2010
, “
Cyclone-Ejector Coupling and Optimisation
,”
Prog. Comput. Fluid Dyn.
,
10
(
1
), pp.
19
31
.10.1504/PCFD.2010.030423
27.
Moffatt
,
H. K.
,
1964
, “
Viscous and Resistive Eddies Near a Sharp Corner
,”
J. Fluid Mech.
,
18
(
1
), pp.
1
18
.10.1017/S0022112064000015
28.
Biswas
,
S.
, and
Kalita
,
J. C.
,
2018
, “
Moffatt Eddies in the Driven Cavity: A Quantification Study by an HOC Approach
,”
Comput. Math. Appl.
,
76
(
3
), pp.
471
487
.10.1016/j.camwa.2018.04.030
29.
Masoud
,
H.
, and
Felske
,
J. D.
,
2009
, “
Analytical Solution for Stokes Flow Inside an Evaporating Sessile Drop: Spherical and Cylindrical Cap Shapes
,”
Phys. Fluids
,
21
(
4
), p.
042102
.10.1063/1.3112002
30.
Happel
,
J.
, and
Brenner
,
H.
,
2012
,
Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media
, Vol.
1
,
Springer Science & Business Media
, Dordrecht, The Netherlands.
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