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