Structure Formation in Soft Matter by Solvent Evaporation
Masao Doi
Center of Soft Matter Physics and its ApplicationsBeihang University, Beijing, China
2018/02/28 Institute of Mathematics and its Applications, University of Minnesota
Collaborators:Beihang University: Xingkun Man, Jiajia Zhou, Fanlong MengTokyo University:Tadashi Kajiya, Masaru Kobayashi, Shunto Arai,Tohru Okuzono,
Solvent evaporation induces• Liquid flow• Deformation• Structural change (phase separation, gelation etc)
Drying is not simple
Outline
• Evaporation rate– What determines the evaporation rate
• Flow induced by evaporation– Coffee ring effect
• Structural formation – Skin formation
• Summary
Evaporation rate
Measurement of evaporation rate
2010g
2010g
h(t)
time
Evaporation rate depends on
TemperatureHumidityOriginal volumeShape of the container
h(t)
Evaporation of a droplet
R
vg s
c (T)(1 H)J D vR−
=
2g
c D ct∂
= ∇∂
2c 0∇ =
vc(R) c=
a vc( ) c c H∞ = =
s gcJ v Dr∂
=∂
Calculation of evaporation rate
θR ( )2v a
g sc cJ D v 0.65 0.135
R−
= + θ
R0JJ
1 (R / )≈
+
Kobayashi, Makino, Okuzono, MD JPSJ 2010
Experiments
L
]mm[L
]s[τ
R
RLLJJ 0 +
≈
Interference is long range
Kobayashi, Makino, Okuzono, MD JPSJ 2010
Flow induced by evaporation
Coffee ring effect
Pinning of the contact line Outward flow
Coffee ring
Calculation of the outward flow
2
2rh(r, t) H(t) 1
R(t)
= −
R
H
Assume
1H R2
= θr
h(r, t)
θ3V R
4π
= θ
( )h 1 hrv Jt r r
∂ ∂= − −
∂ ∂
2VJR
= −π
v
R Vv rR 4V
= −
v(r) 0>When contact line is pinned
The outward flow brings coffee particles to the edge, making the ring
Contact line can move
When contact line is not pinnedWhen contact line is pinned
Xingkun Man, MD PRL (2016)
Use Onsager principle for contact line motion
)x,...x,x(x f21=
A(x)
State variables specifying the non-equilibrium state
Free energy
Free energy change rate
ij i j1 (x)x x2
Φ = ζ∑
ij jj i
A(x)xx∂
ζ = −∂∑ Kinetic equation
ii i
AA xx∂
=∂∑
Minimize R A= Φ +
Energy dissipation function
effm g
x−ζ
21 x2
Φ = ζ
effA m gx=
Free energy
22 2
e44V 1A R
R 2
= γ + π θ π
R
H
r
h(r, t)
θ 2
2rh(r, t) H(t) 1
R(t)
= −
( )R
2sv sl
0
A dr2 r 1 h '= π γ + − γ + γ∫
sv sl ecosγ − γ = γ θ
A
eθ θ
R2
0
1 3dr2 r v2 h
ηΦ = π∫
Energy dissipation function(lublication approximation)
22
hydro cl1 V 12 R R R R2 4V 2
Φ = π ξ − + ξ
Dissipation function
2
2rh(r, t) H(t) 1
R(t)
= −
R Vv rR 4V
= −
hydro3 Rln
aη ξ = θ
clξ phenomenological parameter
Evolution equation
VRv(R) R4V
= −
2 2cl e
hydro
( )VR1 R4V 6 ln(R / a)
ξ γθ θ −θ+ = + ξ η
clξ →∞
cl 0ξ =
cl ( )ξ θ
Xingkun Man, MD PRL (2016)
Deposit pattern in two neighbouring droplets
Stronger pinning
Shiyuan Hu, Yuhan Wang, Xingkun Man and MD Langmuir (2017)
Structural formation in droplets
Evaporation creates inhomogeneity
D( )t z z
∂φ ∂ ∂φ = φ ∂ ∂ ∂
Drying of a film of colloidal solution
0h(t) h Jt= −
D Jz∂φ
= φ∂
D 0z∂φ
=∂
z h(t)=
z 0=
at
at
0Jh 1D
<<
0Jh 1D
>>
Okuzono, Ozawa MD PRL 2006
SkinsSkin
Skins cause problems
Dimples Cavitues
Pauchard et al (2003), Kajya et al (2006) Arai et al (20013)
Dimples and Cavities
Protein suspensions (milk)Spray drying
Cavity formation
Sadek et al Langmuir 2013
Mechanism of cavity formation
An elastic layer is created at the surface
F. Meng MD, Z. OuYang PRL (2014)
Further evaporation creates contractile stress, and negative pressure
Simulation
F. Meng et al EPJE (2015)
Skins in sessile droplet
P∆
But there are phenomena which indicates that it must be positive.
Arai Doi, EPJE 2013
SummaryCoffee ring effect
Skin and cavitation
Stratification in colloidal solutions
Molecular configuration, crystallization kinetics
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