During drying of binary colloidal mixtures, one colloidal particle component can segregate to the top surface. We investigate conditions where the segregation occurs through the analysis of a linearized diffusion model with Fick’s law generalized for binary colloidal mixtures. The present model is the simplest representation that includes cross-diffusion between different particle components to describe the segregation. Using the analytical solutions of this model, we classify states in terms of which the particle component segregates for the following variables: the mixture ratio of particle components, diffusion coefficients, and drying rates. The obtained state diagrams suggest how to control the segregation by designing material and operation conditions.

1.
R. E.
Trueman
,
E. L.
Domingues
,
S. N.
Emmett
,
M. W.
Murray
,
J. L.
Keddie
, and
A. F.
Routh
,
Langmuir
28
,
3420
(
2012
).
2.
D. K.
Makepeace
,
A.
Fortini
,
A.
Markov
,
P.
Locatelli
,
C.
Lindsay
,
S.
Moorhouse
,
R.
Lind
,
R. P.
Sear
, and
J. L.
Keddie
,
Soft Matter
13
,
6969
(
2017
).
3.
O.
Cusola
,
S.
Kivistö
,
S.
Vierros
,
P.
Batys
,
M.
Ago
,
B. L.
Tardy
,
L. G.
Greca
,
M. B.
Roncero
,
M.
Sammalkorpi
, and
O. J.
Rojas
,
Langmuir
34
,
5759
(
2018
).
4.
C. M.
Cardinal
,
Y. D.
Jung
,
K. H.
Ahn
, and
L. F.
Francis
,
AIChE J.
56
,
2769
(
2010
).
5.
A.
Fortini
,
I.
Martín-Fabiani
,
J. L.
De La Haye
,
P.-Y.
Dugas
,
M.
Lansalot
,
F.
D’Agosto
,
E.
Bourgeat-Lami
,
J. L.
Keddie
, and
R. P.
Sear
,
Phys. Rev. Lett.
116
,
118301
(
2016
).
6.
M. P.
Howard
,
A.
Nikoubashman
, and
A. Z.
Panagiotopoulos
,
Langmuir
33
,
3685
(
2017
).
7.
Y.
Tang
,
G. S.
Grest
, and
S.
Cheng
,
Langmuir
34
,
7161
(
2018
).
8.
R.
Tatsumi
,
T.
Iwao
,
O.
Koike
,
Y.
Yamaguchi
, and
Y.
Tsuji
,
Appl. Phys. Lett.
112
,
053702
(
2018
).
9.
A.
Statt
,
M. P.
Howard
, and
A. Z.
Panagiotopoulos
,
J. Chem. Phys.
149
,
024902
(
2018
).
10.
Y.
Tang
,
G. S.
Grest
, and
S.
Cheng
,
J. Chem. Phys.
150
,
224901
(
2019
).
11.
R. E.
Trueman
,
E. L.
Domingues
,
S. N.
Emmett
,
M. W.
Murray
, and
A. F.
Routh
,
J. Colloid Interface Sci.
377
,
207
(
2012
).
12.
J.
Zhou
,
Y.
Jiang
, and
M.
Doi
,
Phys. Rev. Lett.
118
,
108002
(
2017
).
13.
H.
Luo
,
C. M.
Cardinal
,
L. E.
Scriven
, and
L. F.
Francis
,
Langmuir
24
,
5552
(
2008
).
14.
S.
Lim
,
K. H.
Ahn
, and
M.
Yamamura
,
Langmuir
29
,
8233
(
2013
).
15.
T.
Tashima
and
M.
Yamamura
,
J. Coat. Technol. Res.
14
,
965
(
2017
).
16.
J. L.
Anderson
and
D. C.
Prieve
,
Sep. Purif. Methods
13
,
67
(
1984
).
17.
R. P.
Sear
and
P. B.
Warren
,
Phys. Rev. E
96
,
062602
(
2017
).
18.
R. P.
Sear
,
J. Chem. Phys.
148
,
134909
(
2018
).
19.
R.
Taylor
and
R.
Krishna
,
Multicomponent Mass Transfer
(
Wiley
,
New York
,
1993
).
20.
W. B.
Russel
,
D. A.
Saville
, and
W. R.
Schowalter
,
Colloidal Dispersions
(
Cambridge University Press
,
Cambridge
,
1989
).
21.
T.
Okuzono
,
K.
Ozawa
, and
M.
Doi
,
Phys. Rev. Lett.
97
,
136103
(
2006
).
22.
J. S.
Vrentas
and
C. M.
Vrentas
,
Ind. Eng. Chem. Res.
44
,
1112
(
2005
).
23.
S.
Torquato
,
T. M.
Truskett
, and
P. G.
Debenedetti
,
Phys. Rev. Lett.
84
,
2064
(
2000
).
24.
D. G.
Miller
,
V.
Vitagliano
, and
R.
Sartorio
,
J. Phys. Chem.
90
,
1509
(
1986
).
25.
M.
Mason
and
W.
Weaver
,
Phys. Rev.
23
,
412
(
1924
).
26.
F. T.
Lindstrom
,
R.
Haque
,
V. H.
Freed
, and
L.
Boersma
,
Environ. Sci. Technol.
1
,
561
(
1967
).
27.
N. D.
Gershon
and
A.
Nir
,
Water Resour. Res.
5
,
830
, (
1969
).
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