Colloidal droplets are used in a variety of practical applications. Some of these applications require particles of different sizes. These include medical diagnostic methods, the creation of photonic crystals, the formation of supraparticles, and the production of membranes for biotechnology. A series of earlier experiments had shown the possibility of particle separation near the contact line, depending upon their size. A mathematical model has been developed to describe this process. Bi-dispersed colloidal droplets evaporating on a hydrophilic substrate are taken into consideration. A particle monolayer is formed near the periphery of such droplets due to the small value of the contact angle. The shape of the resulting deposit is associated with the coffee ring effect. The model takes into account both particle diffusion and transfers caused by capillary flow due to liquid evaporation. Monte Carlo simulations of such particle dynamics have been performed at several values of the particle concentration in the colloidal solution. The numerical results agree with the experimental observations, in which small particles accumulate nearer to the contact line than do the large particles. However, the particles do not actually reach the contact line but accumulate at a small distance from it. The reason for this is the surface tension acting on the particles in areas, where the thickness of the liquid layer is comparable to the particle size. Indeed, the same mechanism affects the observed separation of the small and large particles.

1.
D. J.
Harris
,
J. C.
Conrad
, and
J. A.
Lewis
, “
Evaporative lithographic patterning of binary colloidal films
,”
Philos. Trans. R. Soc. A
367
,
5157
5165
(
2009
).
2.
A.
Utgenannt
,
J. L.
Keddie
,
O. L.
Muskens
, and
A. G.
Kanaras
, “
Directed organization of gold nanoparticles in polymer coatings through infrared-assisted evaporative lithography
,”
Chem. Commun.
49
,
4253
4255
(
2013
).
3.
K. S.
Kolegov
and
L. Y.
Barash
, “
Applying droplets and films in evaporative lithography
,”
Adv. Colloid Interface Sci.
285
,
102271
(
2020
).
4.
M. A.
Al-Muzaiqer
,
K. S.
Kolegov
,
N. A.
Ivanova
, and
V. M.
Fliagin
, “
Nonuniform heating of a substrate in evaporative lithography
,”
Phys. Fluids
33
,
092101
(
2021
).
5.
J. R.
Trantum
,
D. W.
Wright
, and
F. R.
Haselton
, “
Biomarker-mediated disruption of coffee-ring formation as a low resource diagnostic indicator
,”
Langmuir
28
,
2187
2193
(
2012
).
6.
V. S.
Rathaur
,
S.
Kumar
,
P. K.
Panigrahi
, and
S.
Panda
, “
Investigating the effect of antibody–antigen reactions on the internal convection in a sessile droplet via microparticle image velocimetry and DLVO analysis
,”
Langmuir
36
,
8826
8838
(
2020
).
7.
W.
Liu
,
J.
Midya
,
M.
Kappl
,
H.-J.
Butt
, and
A.
Nikoubashman
, “
Segregation in drying binary colloidal droplets
,”
ACS Nano
13
,
4972
4979
(
2019
).
8.
T. E.
Gartner
,
C. M.
Heil
, and
A.
Jayaraman
, “
Surface composition and ordering of binary nanoparticle mixtures in spherical confinement
,”
Mol. Syst. Des. Eng.
5
,
864
875
(
2020
).
9.
J.
Kim
,
W.
Shim
,
S.-M.
Jo
, and
S.
Wooh
, “
Evaporation driven synthesis of supraparticles on liquid repellent surfaces
,”
J. Ind. Eng. Chem.
95
,
170
181
(
2021
).
10.
L. T.
Raju
,
O.
Koshkina
,
H.
Tan
,
A.
Riedinger
,
K.
Landfester
,
D.
Lohse
, and
X.
Zhang
, “
Particle size determines the shape of supraparticles in self-lubricating ternary droplets
,”
ACS Nano
15
,
4256
4267
(
2021
).
11.
T.
Wang
and
J. L.
Keddie
, “
Design and fabrication of colloidal polymer nanocomposites
,”
Adv. Colloid Interface Sci.
147–148
,
319
332
(
2009
).
12.
Y.
Dong
,
N.
Busatto
,
P. J.
Roth
, and
I.
Martin-Fabiani
, “
Colloidal assembly of polydisperse particle blends during drying
,”
Soft Matter
16
,
8453
8461
(
2020
).
13.
B. Q.
Kim
,
Y.
Qiang
,
K. T.
Turner
,
S. Q.
Choi
, and
D.
Lee
, “
Heterostructured polymer-infiltrated nanoparticle films with cavities via capillary rise infiltration
,”
Adv. Mater. Interfaces
8
,
2001421
(
2021
).
14.
S.
Choi
,
S.
Stassi
,
A. P.
Pisano
, and
T. I.
Zohdi
, “
Coffee-ring effect-based three dimensional patterning of micro/nanoparticle assembly with a single droplet
,”
Langmuir
26
,
11690
11698
(
2010
).
15.
A. S.
Nunes
,
S. K. P.
Velu
,
I.
Kasianiuk
,
D.
Kasyanyuk
,
A.
Callegari
,
G.
Volpe
,
M. M. T.
da Gama
,
G.
Volpe
, and
N. A. M.
Araújo
, “
Ordering of binary colloidal crystals by random potentials
,”
Soft Matter
16
,
4267
4273
(
2020
).
16.
J.
Nozawa
,
S.
Uda
,
A.
Toyotama
,
J.
Yamanaka
,
H.
Niinomi
, and
J.
Okada
, “
Heteroepitaxial fabrication of binary colloidal crystals by a balance of interparticle interaction and lattice spacing
,”
J. Colloid Interface Sci.
608
,
873
881
(
2022
).
17.
S.
Das
,
E.-S. M.
Duraia
,
O. D.
Velev
,
M. D.
Amiri
, and
G. W.
Beall
, “
Formation of periodic size-segregated stripe pattern via directed self-assembly of binary colloids and its mechanism
,”
Appl. Surf. Sci.
435
,
512
520
(
2018
).
18.
J.-R.
Li
and
J. C.
Garno
, “
Nanostructures of octadecyltrisiloxane self-assembled monolayers produced on Au(111) using particle lithography
,”
ACS Appl. Mater. Interfaces
1
,
969
976
(
2009
).
19.
J.-R.
Li
,
K. L.
Lusker
,
J.-J.
Yu
, and
J. C.
Garno
, “
Engineering the spatial selectivity of surfaces at the nanoscale using particle lithography combined with vapor deposition of organosilanes
,”
ACS Nano
3
,
2023
2035
(
2009
).
20.
J.
Chen
,
W.-S.
Liao
,
X.
Chen
,
T.
Yang
,
S. E.
Wark
,
D. H.
Son
,
J. D.
Batteas
, and
P. S.
Cremer
, “
Evaporation-induced assembly of quantum dots into nanorings
,”
ACS Nano
3
,
173
180
(
2009
).
21.
A.
Utgenannt
,
R.
Maspero
,
A.
Fortini
,
R.
Turner
,
M.
Florescu
,
C.
Jeynes
,
A. G.
Kanaras
,
O. L.
Muskens
,
R. P.
Sear
, and
J. L.
Keddie
, “
Fast assembly of gold nanoparticles in large-area 2D nanogrids using a one-step, near-infrared radiation-assisted evaporation process
,”
ACS Nano
10
,
2232
2242
(
2016
).
22.
K. N.
Al-Milaji
and
H.
Zhao
, “
Probing the colloidal particle dynamics in drying sessile droplets
,”
Langmuir
35
,
2209
2220
(
2019
).
23.
Á.
Detrich
,
A.
Deák
,
E.
Hild
,
A. L.
Kovács
, and
Z.
Hórvölgyi
, “
Langmuir and Langmuir-Blodgett films of bidisperse silica nanoparticles
,”
Langmuir
26
,
2694
2699
(
2010
).
24.
N.
Vogel
,
L.
de Viguerie
,
U.
Jonas
,
C. K.
Weiss
, and
K.
Landfester
, “
Wafer-scale fabrication of ordered binary colloidal monolayers with adjustable stoichiometries
,”
Adv. Funct. Mater.
21
,
3064
3073
(
2011
).
25.
V.
Sharma
,
Q.
Yan
,
C. C.
Wong
,
W. C.
Carter
, and
Y.-M.
Chiang
, “
Controlled and rapid ordering of oppositely charged colloidal particles
,”
J. Colloid Interface Sci.
333
,
230
236
(
2009
).
26.
V.
Lotito
and
T.
Zambelli
, “
Self-assembly of single-sized and binary colloidal particles at air/water interface by surface confinement and water discharge
,”
Langmuir
32
,
9582
9590
(
2016
).
27.
K.
Inoue
and
S.
Inasawa
, “
Positive and negative birefringence in packed films of binary spherical colloidal particles
,”
RSC Adv.
10
,
2566
2574
(
2020
).
28.
D.
Guo
,
Y.
Li
,
X.
Zheng
,
F.
Li
,
S.
Chen
,
M.
Li
,
Q.
Yang
,
H.
Li
, and
Y.
Song
, “
Programmed coassembly of one-dimensional binary superstructures by liquid soft confinement
,”
J. Am. Chem. Soc.
140
,
18
21
(
2018
).
29.
M.
Schulz
,
R. W.
Smith
,
R. P.
Sear
,
R.
Brinkhuis
, and
J. L.
Keddie
, “
Diffusiophoresis-driven stratification of polymers in colloidal films
,”
ACS Macro Lett.
9
,
1286
1291
(
2020
).
30.
J. H.
Jeong
,
Y. K.
Lee
, and
K. H.
Ahn
, “
Stratification mechanism in the bidisperse colloidal film drying process: Evolution and decomposition of normal stress correlated with microstructure
,”
Langmuir
37
,
13712
(
2021
).
31.
A.
Samanta
and
R.
Bordes
, “
On the effect of particle surface chemistry in film stratification and morphology regulation
,”
Soft Matter
16
,
6371
6378
(
2020
).
32.
A. K.
Atmuri
,
S. R.
Bhatia
, and
A. F.
Routh
, “
Autostratification in drying colloidal dispersions: Effect of particle interactions
,”
Langmuir
28
,
2652
2658
(
2012
).
33.
B.
He
,
I.
Martin-Fabiani
,
R.
Roth
,
G. I.
Tóth
, and
A. J.
Archer
, “
Dynamical density functional theory for the drying and stratification of binary colloidal dispersions
,”
Langmuir
37
,
1399
1409
(
2021
).
34.
Y.
Tang
,
G. S.
Grest
, and
S.
Cheng
, “
Stratification of drying particle suspensions: Comparison of implicit and explicit solvent simulations
,”
J. Chem. Phys.
150
,
224901
(
2019
).
35.
J.
Zhou
,
Y.
Jiang
, and
M.
Doi
, “
Cross interaction drives stratification in drying film of binary colloidal mixtures
,”
Phys. Rev. Lett.
118
,
108002
(
2017
).
36.
J.
Zhou
,
X.
Man
,
Y.
Jiang
, and
M.
Doi
, “
Structure formation in soft-matter solutions induced by solvent evaporation
,”
Adv. Mater.
29
,
1703769
(
2017
).
37.
M.
Schulz
and
J. L.
Keddie
, “
A critical and quantitative review of the stratification of particles during the drying of colloidal films
,”
Soft Matter
14
,
6181
6197
(
2018
).
38.
M.
Yu
,
C. L.
Floch-Fouéré
,
L.
Pauchard
,
F.
Boissel
,
N.
Fu
,
X. D.
Chen
,
A.
Saint-Jalmes
,
R.
Jeantet
, and
L.
Lanotte
, “
Skin layer stratification in drying droplets of dairy colloids
,”
Colloids Surf., A
620
,
126560
(
2021
).
39.
P.
Kumnorkaew
and
J. F.
Gilchrist
, “
Effect of nanoparticle concentration on the convective deposition of binary suspensions
,”
Langmuir
25
,
6070
6075
(
2009
).
40.
V. H.
Chhasatia
and
Y.
Sun
, “
Interaction of bi-dispersed particles with contact line in an evaporating colloidal drop
,”
Soft Matter
7
,
10135
(
2011
).
41.
S.
Das
,
P. R.
Waghmare
,
M.
Fan
,
N. S. K.
Gunda
,
S. S.
Roy
, and
S. K.
Mitra
, “
Dynamics of liquid droplets in an evaporating drop: Liquid droplet ‘coffee stain’ effect
,”
RSC Adv.
2
,
8390
(
2012
).
42.
N. R.
Devlin
,
K.
Loehr
, and
M. T.
Harris
, “
The separation of two different sized particles in an evaporating droplet
,”
AIChE J.
61
,
3547
3556
(
2015
).
43.
J.
Yi
,
H.
Jeong
, and
J.
Park
, “
Modulation of nanoparticle separation by initial contact angle in coffee ring effect
,”
Micro Nano Syst. Lett.
6
,
17
(
2018
).
44.
G.
Singh
,
S.
Pillai
,
A.
Arpanaei
, and
P.
Kingshott
, “
Electrostatic and capillary force directed tunable 3D binary micro- and nanoparticle assemblies on surfaces
,”
Nanotechnology
22
,
225601
(
2011
).
45.
G.
Singh
,
V.
Gohri
,
S.
Pillai
,
A.
Arpanaei
,
M.
Foss
, and
P.
Kingshott
, “
Large-area protein patterns generated by ordered binary colloidal assemblies as templates
,”
ACS Nano
5
,
3542
3551
(
2011
).
46.
G.
Singh
,
S.
Pillai
,
A.
Arpanaei
, and
P.
Kingshott
, “
Highly ordered mixed protein patterns over large areas from self-assembly of binary colloids
,”
Adv. Mater.
23
,
1519
1523
(
2011
).
47.
G.
Singh
,
H. J.
Griesser
,
K.
Bremmell
, and
P.
Kingshott
, “
Highly ordered nanometer-scale chemical and protein patterns by binary colloidal crystal lithography combined with plasma polymerization
,”
Adv. Funct. Mater.
21
,
540
546
(
2011
).
48.
G.
Singh
,
S.
Pillai
,
A.
Arpanaei
, and
P.
Kingshott
, “
Layer-by-layer growth of multicomponent colloidal crystals over large areas
,”
Adv. Funct. Mater.
21
,
2556
2563
(
2011
).
49.
M.
Parsa
,
S.
Harmand
,
K.
Sefiane
,
M.
Bigerelle
, and
R.
Deltombe
, “
Effect of substrate temperature on pattern formation of bidispersed particles from volatile drops
,”
J. Phys. Chem. B
121
,
11002
11017
(
2017
).
50.
N. D.
Patil
,
R.
Bhardwaj
, and
A.
Sharma
, “
Self-sorting of bidispersed colloidal particles near contact line of an evaporating sessile droplet
,”
Langmuir
34
,
12058
12070
(
2018
).
51.
T.-S.
Wong
,
T.-H.
Chen
,
X.
Shen
, and
C.-M.
Ho
, “
Nanochromatography driven by the coffee ring effect
,”
Anal. Chem.
83
,
1871
1873
(
2011
).
52.
C.
Monteux
and
F.
Lequeux
, “
Packing and sorting colloids at the contact line of a drying drop
,”
Langmuir
27
,
2917
2922
(
2011
).
53.
R.
Iqbal
,
B.
Majhy
,
A. Q.
Shen
, and
A. K.
Sen
, “
Evaporation and morphological patterns of bi-dispersed colloidal droplets on hydrophilic and hydrophobic surfaces
,”
Soft Matter
14
,
9901
9909
(
2018
).
54.
G.
Marinaro
,
C.
Riekel
, and
F.
Gentile
, “
Size-exclusion particle separation driven by micro-flows in a quasi-spherical droplet: Modelling and experimental results
,”
Micromachines
12
,
185
(
2021
).
55.
G.
Upadhyay
and
R.
Bhardwaj
, “
Colloidal deposits via capillary bridge evaporation and particle sorting thereof
,”
Langmuir
37
,
12071
12088
(
2021
).
56.
T.-Y.
Hu
,
C.
Wang
,
K.-C.
Yang
, and
L.-J.
Chen
, “
Gravity effect of silica and polystyrene particles on deposition pattern control and particle size distribution on hydrophobic surfaces
,”
J. Ind. Eng. Chem.
(published online
2021
).
57.
K. S.
Kolegov
and
L. Y.
Barash
, “
Joint effect of advection, diffusion, and capillary attraction on the spatial structure of particle depositions from evaporating droplets
,”
Phys. Rev. E
100
,
033304
(
2019
).
58.
P. A.
Zolotarev
and
K. S.
Kolegov
, “
Average cluster size inside sediment left after droplet desiccation
,”
J. Phys.: Conf. Ser.
1740
,
012029
(
2021
).
59.
R. G.
Larson
, “
Transport and deposition patterns in drying sessile droplets
,”
AIChE J.
60
,
1538
1571
(
2014
).
60.
Z.
Li
,
Q.
Fan
, and
Y.
Yin
, “
Colloidal self-assembly approaches to smart nanostructured materials
,”
Chem. Rev.
(published online
2021
).
61.
F.
Ortega
,
H.
Ritacco
, and
R. G.
Rubio
, “
Interfacial microrheology: Particle tracking and related techniques
,”
Curr. Opin. Colloid Interface Sci.
15
,
237
245
(
2010
).
62.
O. S.
Deshmukh
,
D.
van den Ende
,
M. C.
Stuart
,
F.
Mugele
, and
M. H. G.
Duits
, “
Hard and soft colloids at fluid interfaces: Adsorption, interactions, assembly & rheology
,”
Adv. Colloid Interface Sci.
222
,
215
227
(
2015
).
63.
V.
Lotito
and
T.
Zambelli
, “
A journey through the landscapes of small particles in binary colloidal assemblies: Unveiling structural transitions from isolated particles to clusters upon variation in composition
,”
Nanomaterials
9
,
921
(
2019
).
64.
V.
Lotito
and
T.
Zambelli
, “
Pattern detection in colloidal assembly: A mosaic of analysis techniques
,”
Adv. Colloid Interface Sci.
284
,
102252
(
2020
).
65.
J.-Y.
Jung
,
Y. W.
Kim
, and
J. Y.
Yoo
, “
Behavior of particles in an evaporating didisperse colloid droplet on a hydrophilic surface
,”
Anal. Chem.
81
,
8256
8259
(
2009
).
66.
J.
yeul Jung
,
Y. W.
Kim
,
J. Y.
Yoo
,
J.
Koo
, and
Y. T.
Kang
, “
Forces acting on a single particle in an evaporating sessile droplet on a hydrophilic surface
,”
Anal. Chem.
82
,
784
788
(
2010
).
67.
P.
Lebedev-Stepanov
and
K.
Vlasov
, “
Simulation of self-assembly in an evaporating droplet of colloidal solution by dissipative particle dynamics
,”
Colloids Surf., A
432
,
132
138
(
2013
).

Supplementary Material

You do not currently have access to this content.