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![Page 1: Particles as surfactants and antifoams N. D. Denkov and S. Tcholakova Department of Chemical Engineering, Faculty of Chemistry, Sofia University, Sofia,](https://reader036.fdocuments.us/reader036/viewer/2022062519/56649d985503460f94a82c15/html5/thumbnails/1.jpg)
Particles as surfactants and antifoams
Particles as surfactants and antifoams
N. D. Denkov and S. Tcholakova
Department of Chemical Engineering,
Faculty of Chemistry, Sofia University, Sofia, Bulgaria
Discussion at COST D43 Training School
“Fluids and Solid Interfaces”
Sofia, Bulgaria, 12–15 April, 2011
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Problem 1 Energy of particle adsorption
Problem 1 Energy of particle adsorption
2 20 0 2 1 122 sinA i i i i S SE A A a a h a
20 0 1 124i i SA a S
2 1 12 cosS S cosh a
0 0A i i i iE A A
2 21 2 122 2 sini i S SA a a h a a h S a
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Particle adsorption energy = - a212(1-cos)2
a, nm EA, J EA/kT
1 - 9.410-20 - 23
10 - 9.410-18 - 2300
100 - 9.410-16 -230000
12 = 30 mN/m; = 90
2 1 12 cos 0S S
2 2 212 122 1 cos cos sinAE a a
EDISER1-2
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Particle size, nm
0.1 1 10 100 1000
-EA/k
T
10-1
100
101
102
103
104
105
106
107
108
Adsorption energy vs particle size
EA>> kBT for a > 1 nm
12 = 30 mN/m; = 90
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Adsorption energy for particles with different contact angles
, deg ER1-2/kT EDIS/kT EA/kT EA, J
10 68.78 -69.28 - 0.5 - 2.210-21
90 0 -2300 - 2300 - 9.410-18
150 -7430 -575 -8005 - 3.310-17
12 = 30 mN/m; a = 10 nm
2 1 29.54 mN/mS S
2 1 25.98 mN/mS S
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Adsorption energy vs contact angle
Contact angle, deg
0 20 40 60 80 100 120 140 160 180
-EA/k
T
0
2000
4000
6000
8000
1000012 = 30 mN/m; a = 10 nm
Significant effect of contact angle on the energy of adsorption !
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Desorption energy
Desorption is favored into the phase which wets better the particle!
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Desorption energy vs contact angle
, deg ED, J ED/kT
10 2.210-21 0.5
90 9.410-18 2300
150 1.610-19 41
12 = 30 mN/m; a = 10 nm
21222
122 cos1cos1 aaED
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Contact angle, deg
0 20 40 60 80 100 120 140 160 180
ED/k
T
0
500
1000
1500
2000
2500
Desorption energy vs contact angle12 = 30 mN/m; a = 10 nm
Maximum ED at cos = 0 = 90
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Problem 2 Interfacial tension of particle
adsorption monolayers
Problem 2 Interfacial tension of particle
adsorption monolayers
d d
0 lnS kT
kT 0
Ideal 2-dimensional gas
Dilute adsorption layerLow surface coverage
Gibbs isotherm
Surface coverage
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Surface tension at 30 % surface coverage
Close packing of particles on interface
9069.036 2
2
a
a
min2
19069.0
Aa
Amin, nm2
, molec./m2
,
molec./m2
, mN/m
Surfactant 0.4 2.51018 0.751018 69
Particle (10 nm) 346.4 2.71015 8.21014 72
kTkT 00
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Volmer adsorption isotherm
10 kT
Surface tension at 80 % surface coverage
Amin, nm2
, molec./m2
, mN/m
Surfactant 0.4 2.51018 31
Particle (10 nm) 346.4 2.71015 72
Particles are very inefficient at reducing surface tension even at very high surface coverage
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Problem 3 Formation of complete monolayer
Problem 3 Formation of complete monolayer
Volume fraction
EMD VV DEM VV
Specific surface area
DDREMDR VAVAS
ADR VD S
Monodisperse
Polydisperse
24 RN 34 3RN R3
24 iiRN 34 3 iiRN 323 R
Mean volume surface radius
2
3
32ii
ii
RN
RNR
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Formation of complete adsorption layer
Close packing of particles on interface
2min aA
Number of particles 232min
3
aRA
SNP
Volume of particles
Particles required to cover the specific drop surface area
32
3 4
3
4
R
aaNV pP
Mass of particles32
4
R
aVm pppP
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Particles in continuous phase
Particles in dispersed phase
Concentration of the particles
EMC VV 1 EMD VV
1
4
32R
a
m
mC
C
p
c
PP
32
4
R
a
m
mC
D
p
D
PP
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Dispersed volume fraction,
0.0 0.2 0.4 0.6 0.8 1.0
Par
ticl
e co
nce
ntr
atio
n,
wt
%
0
10
20
30
40
50
60
Particles in continuous phase
P = C = 1 g/ml a = 30 nm R32 = 1 m
Particles
Surfactant
25 times lower C are sufficient to cover the same drop area by surfactant molecules, 1.5 mg/m2
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Problem 4 Pressure for rupturing film
stabilized by particle monolayer
Problem 4 Pressure for rupturing film
stabilized by particle monolayer
22
sin sin2 2
sin
C CC
C
P p a ab
2 cos Ch h a z
2 2
22 2 2sin C
b b rz dr
r p b r
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Capillary pressure vs film thickness
h, nm
0 5 10 15 20
PC, M
Pa
0
1
2
3
4
b/a = 1.5; = 00
b/a = 2; = 00
b/a = 2; = 450b/a = 2; = 850
= 30 mN/m, a = 10 nm
The maximal pressure at h = 0 the critical capillary pressure for film rupturing
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Contact angle, deg
0 20 40 60 80
Cri
tica
l cap
illar
y p
ress
ure
, MP
a
0
1
2
3
4
5
b/a = 1.5
b/a = 2
a = 10 nm= 30 mN/m
Critical capillary pressure vs contact angle
Critical pressure decreases with increasing of contact angle and with increasing the distance
between particles
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Optimal contact angle for film stability
Contact angle, deg
0 20 40 60 80 100 120 140 160 180
ED/ k
T
0
500
1000
1500
2000
2500
Desorption energy
Contact angle, deg
0 20 40 60 80
Cri
tica
l ca
pil
lary
pre
ssu
re,
MP
a
0
1
2
3
4
5
b/a = 1.5
b/a = 2
a = 10 nm= 30 mN/m
Critical pressure
12 = 30 mN/m a = 10 nm
30 80 ED > 40 kT (irreversible adsorbed)
PCMAX > 0.7 MPa (b/a = 1.5)
Very high critical capillary pressure !
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Destabilization of films
Particles can aggregate on the surface and forming empty regions in the film.
The stability is much lower !
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Thank you for your attention !
Thank you for your attention !