Particles as surfactants and antifoams N. D. Denkov and S. Tcholakova Department of Chemical...

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

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

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

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

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

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 !

Desorption energy

Desorption is favored into the phase which wets better the particle!

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

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

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

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

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

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

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

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

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

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

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

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

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 !

Destabilization of films

Particles can aggregate on the surface and forming empty regions in the film.

The stability is much lower !

Thank you for your attention !

Thank you for your attention !