On homogeneous substrates, droplets can slide due to external driving forces, such as gravity, whereas in the presence of wettability gradients, sliding occurs without external forces since this gradient gives rise to an internal driving force. Here, we study via molecular dynamics simulations the more complex behavior when droplets are driven under the combined influence of an external and internal driving force. For comparison, the limiting cases of a single driving force are studied as well. During a large part of the sliding process over the borderline of both substrates, separating both wettabilities, the velocity is nearly constant. When expressing it as the product of the effective mobility and the effective force, the effective mobility mainly depends on the mobility of the initial substrate, experienced by the receding contact line. This observation can be reconciled with the properties of the flow pattern, indicating that the desorption of particles at the receding contact line is the time-limiting step. The effective force is the sum of the external force and a renormalized internal force. This renormalization can be interpreted as stronger dissipation effects when driving occurs via wettability gradients.
REFERENCES
1.
T. M.
Squires
and S. R.
Quake
, “Microfluidics: Fluid physics at the nanoliter scale
,” Rev. Mod. Phys.
77
, 977
–1026
(2005
).2.
B. S.
Yilbas
, G.
Hassan
, A.
Al-Sharafi
, H.
Ali
, N.
Al-Aqeeli
, and A.
Al-Sarkhi
, “Water droplet dynamics on a hydrophobic surface in relation to the self-cleaning of environmental dust
,” Sci. Rep.
8
, 2984
(2018
).3.
G.
Hassan
, B. S.
Yilbas
, A.
Al-Sharafi
, and H.
Al-Qahtani
, “Self-cleaning of a hydrophobic surface by a rolling water droplet
,” Sci. Rep.
9
, 5744
(2019
).4.
S.
Lin
, B.
Li
, Y.
Xu
, A. A.
Mehrizi
, and L.
Chen
, “Effective strategies for droplet transport on solid surfaces
,” Adv. Mater. Interfaces
8
, 2001441
(2021
).5.
S.
Ravi Annapragada
, J. Y.
Murthy
, and S. V.
Garimella
, “Prediction of droplet dynamics on an incline
,” Int. J. Heat Mass Transfer
55
, 1466
–1474
(2012
).6.
T.
Podgorski
, J.-M.
Flesselles
, and L.
Limat
, “Corners, cusps, and pearls in running drops
,” Phys. Rev. Lett.
87
, 036102
(2001
).7.
M.
Sakai
, H.
Kono
, A.
Nakajima
, X.
Zhang
, H.
Sakai
, M.
Abe
, and A.
Fujishima
, “Sliding of water droplets on the superhydrophobic surface with ZnO nanorods
,” Langmuir
25
, 14182
–14186
(2009
), part of Special Issue: Langmuir 25th Year: Wetting and Superhydrophobicity.8.
P.
Hao
, C.
Lv
, Z.
Yao
, and F.
He
, “Sliding behavior of water droplet on superhydrophobic surface
,” Europhys. Lett.
90
, 66003
(2010
).9.
P.
Olin
, S. B.
Lindström
, T.
Pettersson
, and L.
Wågberg
, “Water drop friction on superhydrophobic surfaces
,” Langmuir
29
, 9079
–9089
(2013
).10.
H.
Wang
, C.
Liu
, H.
Zhan
, and Y.
Liu
, “Droplet asymmetric bouncing on inclined superhydrophobic surfaces
,” ACS Omega
4
, 12238
–12243
(2019
).11.
M.
Backholm
, D.
Molpeceres
, M.
Vuckovac
, H.
Nurmi
, M. J.
Hokkanen
, V.
Jokinen
, J. V. I.
Timonen
, and R. H. A.
Ras
, “Water droplet friction and rolling dynamics on superhydrophobic surfaces
,” Commun. Mater.
1
, 64
(2020
).12.
M.
Sakai
, J.-H.
Song
, N.
Yoshida
, S.
Suzuki
, Y.
Kameshima
, and A.
Nakajima
, “Direct observation of internal fluidity in a water droplet during sliding on hydrophobic surfaces
,” Langmuir
22
, 4906
–4909
(2006
).13.
S.
Suzuki
, A.
Nakajima
, M.
Sakai
, Y.
Sakurada
, N.
Yoshida
, A.
Hashimoto
, Y.
Kameshima
, and K.
Okada
, “Slipping and rolling ratio of sliding acceleration for a water droplet sliding on fluoroalkylsilane coatings of different roughness
,” Chem. Lett.
37
, 58
–59
(2008
).14.
G.
Ahmed
, M.
Sellier
, Y. C.
Lee
, M.
Jermy
, and M.
Taylor
, “Modeling the spreading and sliding of power-law droplets
,” Colloids Surf., A
432
, 2
–7
(2013
), part of Special Issue: Wetting and Evaporation: Droplets of Pure and Complex Fluids.15.
C.
Shen
, C.
Yu
, and Y.
Chen
, “Spreading dynamics of droplet on an inclined surface
,” Theor. Comput. Fluid Dyn.
30
, 237
–252
(2016
).16.
S. D.
Hong
, M. Y.
Ha
, and S.
Balachandar
, “Static and dynamic contact angles of water droplet on a solid surface using molecular dynamics simulation
,” J. Colloid Interface Sci.
339
, 187
–195
(2009
).17.
H.
Li
, T.
Yan
, K. A.
Fichthorn
, and S.
Yu
, “Dynamic contact angles and mechanisms of motion of water droplets moving on nanopillared superhydrophobic surfaces: A molecular dynamics simulation study
,” Langmuir
34
, 9917
–9926
(2018
).18.
J.
Servantie
and M.
Müller
, “Statics and dynamics of a cylindrical droplet under an external body force
,” J. Chem. Phys.
128
, 014709
(2008
).19.
H.
Linke
, B. J.
Alemán
, L. D.
Melling
, M. J.
Taormina
, M. J.
Francis
, C. C.
Dow-Hygelund
, V.
Narayanan
, R. P.
Taylor
, and A.
Stout
, “Self-propelled leidenfrost droplets
,” Phys. Rev. Lett.
96
, 154502
(2006
).20.
M. K.
Chaudhury
and G. M.
Whitesides
, “How to make water run uphill
,” Science
256
, 1539
–1541
(1992
).21.
S.-K.
Fan
, H.
Yang
, T.-T.
Wang
, and W.
Hsu
, “Asymmetric electrowetting—Moving droplets by a square wave
,” Lab Chip
7
, 1330
–1335
(2007
).22.
K.
Ichimura
, S.-K.
Oh
, and M.
Nakagawa
, “Light-driven motion of liquids on a photoresponsive surface
,” Science
288
, 1624
–1626
(2000
).23.
H. P.
Greenspan
, “On the motion of a small viscous droplet that wets a surface
,” J. Fluid Mech.
84
, 125
–143
(1978
).24.
R. S.
Subramanian
, N.
Moumen
, and J. B.
McLaughlin
, “Motion of a drop on a solid surface due to a wettability gradient
,” Langmuir
21
, 11844
–11849
(2005
).25.
Q.
Liu
and B.
Xu
, “A unified mechanics model of wettability gradient-driven motion of water droplet on solid surfaces
,” Extreme Mech. Lett.
9
, 304
–309
(2016
).26.
S.
Wang
, C.
Wang
, Z.
Peng
, and S.
Chen
, “Moving behavior of nanodroplets on wedge-shaped functional surfaces
,” J. Phys. Chem. C
123
, 1798
–1805
(2019
).27.
Q.
Liu
and B.
Xu
, “Actuating water droplets on graphene via surface wettability gradients
,” Langmuir
31
, 9070
–9075
(2015
).28.
B.
Xu
, S.
Wang
, and Z.
Chen
, “Molecular dynamics study of self-propelled droplet on different surfaces
,” Chem. Phys. Lett.
782
, 139029
(2021
).29.
A.
Mahmood
, S.
Chen
, L.
Chen
, C.
Chen
, D.
Liu
, D.
Weng
, and J.
Wang
, “Spontaneous propulsion of a water nanodroplet induced by a wettability gradient: A molecular dynamics simulation study
,” Phys. Chem. Chem. Phys.
22
, 4805
–4814
(2020
).30.
C.
Hinduja
, A.
Laroche
, S.
Shumaly
, Y.
Wang
, D.
Vollmer
, H.-J.
Butt
, and R.
Berger
, “Scanning drop friction force microscopy
,” Langmuir
38
, 14635
–14643
(2022
).31.
J. A.
Anderson
, J.
Glaser
, and S. C.
Glotzer
, “HOOMD-blue: A python package for high-performance molecular dynamics and hard particle Monte Carlo simulations
,” Comput. Mater. Sci.
173
, 109363
(2020
).32.
P. J.
Hoogerbrugge
, and J. M. V. A.
Koelman
, “Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics
,” Europhys. Lett.
19
, 155
–160
(1992
).33.
J. M. V. A.
Koelman
and P. J.
Hoogerbrugge
, “Dynamic simulations of hard-sphere suspensions under steady shear
,” Europhys. Lett.
21
, 363
–368
(1993
).34.
P.
Español
and P.
Warren
, “Statistical mechanics of dissipative particle dynamics
,” Europhys. Lett.
30
, 191
–196
(1995
).35.
R. D.
Groot
and P. B.
Warren
, “Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation
,” J. Chem. Phys.
107
, 4423
–4435
(1997
).36.
C. L.
Phillips
, J. A.
Anderson
, and S. C.
Glotzer
, “Pseudo-random number generation for Brownian dynamics and dissipative particle dynamics simulations on GPU devices
,” J. Comput. Phys.
230
, 7191
–7201
(2011
).37.
T.
Ingebrigtsen
and S.
Toxvaerd
, “Contact angles of Lennard-Jones liquids and droplets on planar surfaces
,” J. Phys. Chem. C
111
, 8518
–8523
(2007
).38.
J. H.
Weijs
, A.
Marchand
, B.
Andreotti
, D.
Lohse
, and J. H.
Snoeijer
, “Origin of line tension for a Lennard-Jones nanodroplet
,” Phys. Fluids
23
, 022001
(2011
).39.
M.
Kanduč
, “Going beyond the standard line tension: Size-dependent contact angles of water nanodroplets
,” J. Chem. Phys.
147
, 174701
(2017
).40.
T.
Young
III, “An essay on the cohesion of fluids
,” Philos. Trans. R. Soc. London
95
, 65
–87
(1805
).41.
P. G.
de Gennes
, “Wetting: Statics and dynamics
,” Rev. Mod. Phys.
57
, 827
–863
(1985
).42.
K.
Meier
, A.
Laesecke
, and S.
Kabelac
, “Transport coefficients of the Lennard-Jones model fluid. II Self-diffusion
,” J. Chem. Phys.
121
, 9526
–9535
(2004
).43.
T. D.
Blake
and J. M.
Haynes
, “Kinetics of liquidliquid displacement
,” J. Colloid Interface Sci.
30
, 421
–423
(1969
).44.
L.
Topp
, L.
Haddick
, D.
Mählmann
, and A.
Heuer
(2023
). “Data supplement for ‘wettability gradient driven droplets with an applied external force
,’” Zenodo, Dataset. https://doi.org/10.5281/zenodo.7640342© 2023 Author(s). Published under an exclusive license by AIP Publishing.
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