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Article
Stability properties of surfactant free thin films at different ionic strengths: Measurements and modelling Frederik Jürgen Lech, Peter A. Wierenga, Harry Gruppen, and Marcel B.J. Meinders Langmuir, Just Accepted Manuscript • DOI: 10.1021/la504933e • Publication Date (Web): 17 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
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Langmuir
1
Stability properties of surfactant free thin films at different ionic strengths:
2
Measurements and modelling
3 4
Frederik J. Lecha,b, Peter A. Wierengaa,b, Harry Gruppenb, Marcel B.J. Meindersa,c*
5
a
Top Institute Food and Nutrition, Wageningen, the Netherlands
6
b
Wageningen University, Laboratory of Food Chemistry, Wageningen, the Netherlands
7
c
Wageningen UR, Food and Biobased Research, Wageningen, the Netherlands
8 9
*Corresponding author
10
[email protected]
11
P.O. Box 17, 6700 AA, Wageningen, The Netherlands
12
Telephone: +31 317 480165
13
14
Abstract
15
Foam lamellae are the smallest structural elements in foam. Such lamellae can experimentally be
16
studied by analysis of thin liquid films in glass cells. These thin liquid films usually have to be
17
stabilized against rupture by surface active substances, like proteins or low molecular weight
18
surfactants. However, horizontal thin liquid films of pure water with a radius of 100 µm also show
19
remarkable stability when created in closed Sheludko cells. To understand thin film stability of
20
surfactant free films, the drainage behaviour and rupture times of films of water and NaCl solutions
21
were determined. The drainage was modelled with an extended DLVO model, which combines DLVO
22
and hydrophobic contributions. Good correspondence between experiment and theory is observed,
23
when hydrophobic interactions are included, with fitted values for surface potential (ψ0, water) of −60 ±5
24
mV, hydrophobic strength (Bhb,water) of 0.22 ±0.02 mJ/m2 and a range of the hydrophobic interaction
25
(λhb, water) of 15 ±1 nm in thin liquid films.
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Page 2 of 16
26
In addition, Vrij’s rupture criterion was successfully applied to model the stability regions and rupture
27
times of the films. The films of pure water are stable over long time scales (hours) and drain to final
28
thickness > 40 nm if the concentration of electrolytes is low (resistivity 18.2 MQ). With increasing
29
amounts of ions (NaCl) the thin films drain to < 40nm thickness and the rupture stability of the films is
30
reduced from hours to seconds.
31
Keywords
32
Surfactant free air water interface, surface potential, extended DLVO theory, foam stability
33
Introduction
34
An important aspect in the stability of foams is the life time of the thin liquid films that separate the
35
gas bubbles in the foam.1 Usually, surface active materials, like proteins and low-molecular weight
36
surfactants (LMW), are used to stabilize the films. The stability of LMW surfactant stabilized films
37
has been studied extensively and was recently reviewed.2 Thin films of LMW can quantitatively be
38
described by the DLVO.3 In addition, Vrij developed a criterion to describe how the growth of small
39
surface perturbations leads to spontaneous rupture of the film.4 This criterion was used by others to
40
determine the critical thickness in foam films.5
41
Because it is impossible to make foam of pure water, it is expected that thin liquid water films are
42
unstable. Still, horizontal thin liquid films of pure water and dilute NaCl solutions in closed Sheludko
43
cells have been described by several authors.6-8 The films described are usually very unstable since
44
90% of the films ruptured immediately after creation.6 However, stable, free standing (vertical) thin
45
water films in small glass capillaries are also observed. The stability of the films is ascribed to ionizing
46
x-ray photons, thereby inducing some charge between the two interfaces.8 Wang and Yoon showed the
47
possibility to create horizontal thin films of dilute NaCl solutions that were stable for minutes.7 They
48
argue that the stability of the films originates from equilibrium between hydrophobic and electrostatic
49
forces that is mediated by the electrolytes in solution.
2 ACS Paragon Plus Environment
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Langmuir
50
The electrostatic forces in the thin films are considered the result of a surface wall potential of the air-
51
water interface. This surface wall potential was for instance shown using experiments where the
52
electrophoretic mobility of air bubbles in an electric field was measured.9 The origin, polarity and
53
magnitude of the charge, however, is still under heavy debate. Several studies proposed the structuring
54
of water layers close the hydrophobic interface as a source of the charge.10,
55
however, would only be possible on short length scales up to 20 nm.12 The ordering of water over 40
56
nm is far shorter than the equilibrium thickness (120 nm) of the films reported.
57
explain the stability of the films by itself. For the stabilization of the films by structured water, the
58
ordered layers should overlap to create repulsion. Other studies suggest that the surface charge of
59
water could be due to the preferred adsorption of hydroxide ions to the interface.13-15 Typical values
60
for this surface potential, obtained by different experimental techniques (i.e. Volta potential difference
61
measurements or calomel electrodes) and simulations, were recently summarized, and showed values
62
ranging from -1.1 V to +0.5 V.16
63
Next to the surface charge of the water interfaces, the repulsive hydration interaction has been
64
suggested to attribute to the stabilization of a thin film of clean water.17, 18 Whether or not hydrophobic
65
forces play a role in the stability of thin liquid films is still under debate. 19, 20
66
The aim of this study is to gain a generic understanding of the drainage and stability of surfactant free
67
thin liquid films. To achieve this, drainage behaviour and rupture times of surfactant free thin films,
68
created in Sheludko cells, were described with a model using extended DLVO (including hydrophobic
69
interactions) and the stability criterion of thin films. 4
70
Experimental Section
71
Materials
72
Ultra-pure water (Millipore, EMD Millipore Corp., Billerica, MA, USA) with a surface tension of 72.6
73
± 0.3 mN/m at 20 °C stable over 1 h, a resistivity of 18.6 MΩ*cm and residual total organic carbon of
74
3 ppb was used as is to make the films and the NaCl solutions. NaCl was purchased from Sigma
75
Aldrich (Zwijndrecht, The Netherlands) and roasted at 700 °C for three days to eliminate possible
11
7
This structuring,
Hence, it cannot
3 ACS Paragon Plus Environment
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76
organic contaminants. A stock solution of 0.1 M NaCl was prepared and diluted to make solutions for
77
the thin film experiments. The solutions were prepared on the day of the experiment and kept at the
78
same temperature (20°C) as the experimental set up before making the thin film. All glassware was
79
soaked in dilute (0.1 M) NaOH solution, thoroughly rinsed with ultra-pure water and dried in an oven
80
at 60°C before use.
81
The total ionic strength of water and NaCl solutions is given by (equation 1)
82
= ∑
83
with the sum of all ions i in the solution, ρi∞ is the molar concentration of the ion in bulk at infinite
84
distance from the interface and z is the valence of the ions. Note that this includes the OH- and H+ ions
85
determining the pH of the water films, which was measured to be pH 5.6, for all experiments. The
86
total ionic strength (INaCl + IpH 5.6) of a 0.700 mM NaCl solution is 0.703 mM.
87
Methods
88
Thin liquid films (radius = 100 µm) were made in a modified Scheludko cell as described elsewhere.1
89
A schematic drawing, including relevant dimensions of the setup is depicted in figure 1. The Sheludko
90
cell is encased in glass, closed with a glass cover. The casing has a reservoir of water at the bottom to
91
ensure a relative humidity of 100 % in the cell during the experiments.
92
The thickness of the thin films was determined by image analysis obtained by micro-interferometry
93
using a microscope (Axio plan 01, Zeiss, Jena, Germany), in reflected light mode, equipped with a
94
five mega pixel CCD camera (Mightex Systems, Pleasanton, CA, USA). Images of the thin films,
95
recorded with the CCD camera, were processed by a software script (developed at the Laboratory of
96
Food Chemistry) for Matlab (Software version 2013b, MathWorks. Natick, MA, USA). It calculated
97
the average intensity of light in a defined area (at the centre) of the thin film. The area is typically
98
1963 µm², which is ~6 % of total area of the thin film. The thickness was calculated according to
99
equation (2):
100
(1)
ℎ = ± √Δ
(2)
4 ACS Paragon Plus Environment
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Langmuir
101
with λ as the wavelength of the light (546 nm), n the refractive index of water, l the order of
102
interference and ∆ as (I-Imin)/(Imax-Imin) where is I is the average of the light intensity at each time
103
point, Imin, the minimum intensity (which is measured in the Sheludko cell without a water film
104
present) and Imax as the maximum intensity.
105
The film thickness was measured from the moment it reaches a radius of 100 µm up to 1 hour of
106
lifetime. If a film did not break within one hour, it was considered stable. In this case, the life time will
107
be given as one hour.
108
If the thin films ruptured during this time, at least 20 repetitions were used to calculate the average and
109
standard deviation of the rupture time and thickness at which rupture occurred. The rupture time is the
110
time from reaching a 200 µm wide film until the film breaks. In case of stable films, solutions were
111
measured 4 times, in case of rupturing films; the experiment was repeated at least 20 times.
112
The whole setup, thin film cell, pure water and salt solution were equilibrated to room temperature (20
113
°C) on the microscope table for at least 1 hour prior to the measurement. Liquid was drawn into the
114
capillary by a syringe (500 µL, Hamilton, Reno, NV, USA) and left to equilibrate for 10 minutes
115
before a thin film was made by drawing more solution into the capillary.
116
Modelling and theoretical background
117
Surface forces
118
When two bubbles come into contact, the thin liquid film between the bubbles will drain due to the
119
capillary pressure, caused by the difference in curvature of the thin film and the adjacent meniscus (or
120
Plateau border in foam). When the film thickness becomes smaller than about 100 nm, attractive and
121
repulsive interactions between the interfaces of the film become important and determine the stability
122
of the thin liquid film. Attractive interactions, enhancing film thinning and destabilizing the film,
123
include long range dispersion forces summarized as van der Waals (vdW) forces. Repulsive
124
interactions, acting against film thinning and thereby stabilizing the film, include electrostatic
125
interactions (ES) between two similarly charged surfaces and steric interactions. The vdW and ES
126
interactions are described quantitatively by the DLVO theory. Besides these DLVO forces, other
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127
interactions are recognized that might play a role in film stability. The interactions include steric
128
repulsion (excluded volume), hydration, repulsive and attractive hydrophobic forces as well as
129
oscillatory solvation forces.2, 11, 18 The sum of these surface forces determine the disjoining pressure
130
Π(h), which depends on the film thickness h.
131
The van der Waals contribution is calculated from (equation 3)
132
Πvw = − " #! $
133
with AH as the compound Hamaker constant of a water film in air AH = 4*10-20 J. 18, 21
134
The contribution of the electrostatic interaction to the disjoining pressure is approximated by equation
135
(4)18
136
Πel = 64)* + , e-.#
137
with
138
, = tanh 378 6:;
139
and
140
? @AB 4
(6)
9
C6 CD 89:
*
hb
#
(7)
hb
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Langmuir
152
The theoretical individual attractive and repulsive contributions for an air water interface as well as the
153
resulting disjoining pressure as function of film thickness are calculated (figure 2).
154
Film drainage
155
The drainage of the film is modelled by considering the flow between two circular plane-parallel
156
plates. 23, 24 The change of the film thickness h with time t was described by (equation 8)
157
d# dL
158
where cf is a factor that accounts for the interaction of the fluid with the interface. For an immobile
159
interface, as we will consider here, cf = 1. Furthermore, µ = 10-3 kg/m/s is the viscosity of the water
160
phase, Rf is the radius of the film (in our experimental set-up Rf = 100 µm), and
161
ΔS = Q − Π
162
is the driving capillary pressure, with γ is the surface tension of the water-air interface (in the
163
calculation we used γ= 72 mN/m), 1/Rm is the (mean) curvature of the meniscus and Π is the total
164
disjoining pressure (Π= ΠVW+Πel+Πhb). Rm~1.25 mm, assuming complete wetting of the inner wall of
165
the Sheludko cell. (see figure 1).
166
Starting from an initial thick film with thickness h0, the film will drain. Depending on the precise
167
shape of Π(h), the film can drain to a stable equilibrium thickness where the disjoining pressure equals
168
the capillary pressure (figure 2 B). If the disjoining pressure is smaller than the capillary pressure the
169
thin film can rupture spontaneously.
170
Film rupture
171
Film rupture of surfactant stabilized films has successfully been described by the theory developed by
172
Sheludko and Vrij.4,
173
curve. In these regions of instability, small spontaneous surface perturbations grow in time until both
174
interfaces touch each other and the film ruptures. The unstable regions are given by the Vrij criterion
175
(10)
176
VW V#
M # $
= − OPN QR ΔS
(8)
N
T
(9)
U
Article
Stability properties of surfactant free thin films at different ionic strengths: Measurements and modelling Frederik Jürgen Lech, Peter A. Wierenga, Harry Gruppen, and Marcel B.J. Meinders Langmuir, Just Accepted Manuscript • DOI: 10.1021/la504933e • Publication Date (Web): 17 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
1
Stability properties of surfactant free thin films at different ionic strengths:
2
Measurements and modelling
3 4
Frederik J. Lecha,b, Peter A. Wierengaa,b, Harry Gruppenb, Marcel B.J. Meindersa,c*
5
a
Top Institute Food and Nutrition, Wageningen, the Netherlands
6
b
Wageningen University, Laboratory of Food Chemistry, Wageningen, the Netherlands
7
c
Wageningen UR, Food and Biobased Research, Wageningen, the Netherlands
8 9
*Corresponding author
10
[email protected]
11
P.O. Box 17, 6700 AA, Wageningen, The Netherlands
12
Telephone: +31 317 480165
13
14
Abstract
15
Foam lamellae are the smallest structural elements in foam. Such lamellae can experimentally be
16
studied by analysis of thin liquid films in glass cells. These thin liquid films usually have to be
17
stabilized against rupture by surface active substances, like proteins or low molecular weight
18
surfactants. However, horizontal thin liquid films of pure water with a radius of 100 µm also show
19
remarkable stability when created in closed Sheludko cells. To understand thin film stability of
20
surfactant free films, the drainage behaviour and rupture times of films of water and NaCl solutions
21
were determined. The drainage was modelled with an extended DLVO model, which combines DLVO
22
and hydrophobic contributions. Good correspondence between experiment and theory is observed,
23
when hydrophobic interactions are included, with fitted values for surface potential (ψ0, water) of −60 ±5
24
mV, hydrophobic strength (Bhb,water) of 0.22 ±0.02 mJ/m2 and a range of the hydrophobic interaction
25
(λhb, water) of 15 ±1 nm in thin liquid films.
1 ACS Paragon Plus Environment
Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 16
26
In addition, Vrij’s rupture criterion was successfully applied to model the stability regions and rupture
27
times of the films. The films of pure water are stable over long time scales (hours) and drain to final
28
thickness > 40 nm if the concentration of electrolytes is low (resistivity 18.2 MQ). With increasing
29
amounts of ions (NaCl) the thin films drain to < 40nm thickness and the rupture stability of the films is
30
reduced from hours to seconds.
31
Keywords
32
Surfactant free air water interface, surface potential, extended DLVO theory, foam stability
33
Introduction
34
An important aspect in the stability of foams is the life time of the thin liquid films that separate the
35
gas bubbles in the foam.1 Usually, surface active materials, like proteins and low-molecular weight
36
surfactants (LMW), are used to stabilize the films. The stability of LMW surfactant stabilized films
37
has been studied extensively and was recently reviewed.2 Thin films of LMW can quantitatively be
38
described by the DLVO.3 In addition, Vrij developed a criterion to describe how the growth of small
39
surface perturbations leads to spontaneous rupture of the film.4 This criterion was used by others to
40
determine the critical thickness in foam films.5
41
Because it is impossible to make foam of pure water, it is expected that thin liquid water films are
42
unstable. Still, horizontal thin liquid films of pure water and dilute NaCl solutions in closed Sheludko
43
cells have been described by several authors.6-8 The films described are usually very unstable since
44
90% of the films ruptured immediately after creation.6 However, stable, free standing (vertical) thin
45
water films in small glass capillaries are also observed. The stability of the films is ascribed to ionizing
46
x-ray photons, thereby inducing some charge between the two interfaces.8 Wang and Yoon showed the
47
possibility to create horizontal thin films of dilute NaCl solutions that were stable for minutes.7 They
48
argue that the stability of the films originates from equilibrium between hydrophobic and electrostatic
49
forces that is mediated by the electrolytes in solution.
2 ACS Paragon Plus Environment
Page 3 of 16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
50
The electrostatic forces in the thin films are considered the result of a surface wall potential of the air-
51
water interface. This surface wall potential was for instance shown using experiments where the
52
electrophoretic mobility of air bubbles in an electric field was measured.9 The origin, polarity and
53
magnitude of the charge, however, is still under heavy debate. Several studies proposed the structuring
54
of water layers close the hydrophobic interface as a source of the charge.10,
55
however, would only be possible on short length scales up to 20 nm.12 The ordering of water over 40
56
nm is far shorter than the equilibrium thickness (120 nm) of the films reported.
57
explain the stability of the films by itself. For the stabilization of the films by structured water, the
58
ordered layers should overlap to create repulsion. Other studies suggest that the surface charge of
59
water could be due to the preferred adsorption of hydroxide ions to the interface.13-15 Typical values
60
for this surface potential, obtained by different experimental techniques (i.e. Volta potential difference
61
measurements or calomel electrodes) and simulations, were recently summarized, and showed values
62
ranging from -1.1 V to +0.5 V.16
63
Next to the surface charge of the water interfaces, the repulsive hydration interaction has been
64
suggested to attribute to the stabilization of a thin film of clean water.17, 18 Whether or not hydrophobic
65
forces play a role in the stability of thin liquid films is still under debate. 19, 20
66
The aim of this study is to gain a generic understanding of the drainage and stability of surfactant free
67
thin liquid films. To achieve this, drainage behaviour and rupture times of surfactant free thin films,
68
created in Sheludko cells, were described with a model using extended DLVO (including hydrophobic
69
interactions) and the stability criterion of thin films. 4
70
Experimental Section
71
Materials
72
Ultra-pure water (Millipore, EMD Millipore Corp., Billerica, MA, USA) with a surface tension of 72.6
73
± 0.3 mN/m at 20 °C stable over 1 h, a resistivity of 18.6 MΩ*cm and residual total organic carbon of
74
3 ppb was used as is to make the films and the NaCl solutions. NaCl was purchased from Sigma
75
Aldrich (Zwijndrecht, The Netherlands) and roasted at 700 °C for three days to eliminate possible
11
7
This structuring,
Hence, it cannot
3 ACS Paragon Plus Environment
Langmuir
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Page 4 of 16
76
organic contaminants. A stock solution of 0.1 M NaCl was prepared and diluted to make solutions for
77
the thin film experiments. The solutions were prepared on the day of the experiment and kept at the
78
same temperature (20°C) as the experimental set up before making the thin film. All glassware was
79
soaked in dilute (0.1 M) NaOH solution, thoroughly rinsed with ultra-pure water and dried in an oven
80
at 60°C before use.
81
The total ionic strength of water and NaCl solutions is given by (equation 1)
82
= ∑
83
with the sum of all ions i in the solution, ρi∞ is the molar concentration of the ion in bulk at infinite
84
distance from the interface and z is the valence of the ions. Note that this includes the OH- and H+ ions
85
determining the pH of the water films, which was measured to be pH 5.6, for all experiments. The
86
total ionic strength (INaCl + IpH 5.6) of a 0.700 mM NaCl solution is 0.703 mM.
87
Methods
88
Thin liquid films (radius = 100 µm) were made in a modified Scheludko cell as described elsewhere.1
89
A schematic drawing, including relevant dimensions of the setup is depicted in figure 1. The Sheludko
90
cell is encased in glass, closed with a glass cover. The casing has a reservoir of water at the bottom to
91
ensure a relative humidity of 100 % in the cell during the experiments.
92
The thickness of the thin films was determined by image analysis obtained by micro-interferometry
93
using a microscope (Axio plan 01, Zeiss, Jena, Germany), in reflected light mode, equipped with a
94
five mega pixel CCD camera (Mightex Systems, Pleasanton, CA, USA). Images of the thin films,
95
recorded with the CCD camera, were processed by a software script (developed at the Laboratory of
96
Food Chemistry) for Matlab (Software version 2013b, MathWorks. Natick, MA, USA). It calculated
97
the average intensity of light in a defined area (at the centre) of the thin film. The area is typically
98
1963 µm², which is ~6 % of total area of the thin film. The thickness was calculated according to
99
equation (2):
100
(1)
ℎ = ± √Δ
(2)
4 ACS Paragon Plus Environment
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Langmuir
101
with λ as the wavelength of the light (546 nm), n the refractive index of water, l the order of
102
interference and ∆ as (I-Imin)/(Imax-Imin) where is I is the average of the light intensity at each time
103
point, Imin, the minimum intensity (which is measured in the Sheludko cell without a water film
104
present) and Imax as the maximum intensity.
105
The film thickness was measured from the moment it reaches a radius of 100 µm up to 1 hour of
106
lifetime. If a film did not break within one hour, it was considered stable. In this case, the life time will
107
be given as one hour.
108
If the thin films ruptured during this time, at least 20 repetitions were used to calculate the average and
109
standard deviation of the rupture time and thickness at which rupture occurred. The rupture time is the
110
time from reaching a 200 µm wide film until the film breaks. In case of stable films, solutions were
111
measured 4 times, in case of rupturing films; the experiment was repeated at least 20 times.
112
The whole setup, thin film cell, pure water and salt solution were equilibrated to room temperature (20
113
°C) on the microscope table for at least 1 hour prior to the measurement. Liquid was drawn into the
114
capillary by a syringe (500 µL, Hamilton, Reno, NV, USA) and left to equilibrate for 10 minutes
115
before a thin film was made by drawing more solution into the capillary.
116
Modelling and theoretical background
117
Surface forces
118
When two bubbles come into contact, the thin liquid film between the bubbles will drain due to the
119
capillary pressure, caused by the difference in curvature of the thin film and the adjacent meniscus (or
120
Plateau border in foam). When the film thickness becomes smaller than about 100 nm, attractive and
121
repulsive interactions between the interfaces of the film become important and determine the stability
122
of the thin liquid film. Attractive interactions, enhancing film thinning and destabilizing the film,
123
include long range dispersion forces summarized as van der Waals (vdW) forces. Repulsive
124
interactions, acting against film thinning and thereby stabilizing the film, include electrostatic
125
interactions (ES) between two similarly charged surfaces and steric interactions. The vdW and ES
126
interactions are described quantitatively by the DLVO theory. Besides these DLVO forces, other
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Langmuir
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127
interactions are recognized that might play a role in film stability. The interactions include steric
128
repulsion (excluded volume), hydration, repulsive and attractive hydrophobic forces as well as
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oscillatory solvation forces.2, 11, 18 The sum of these surface forces determine the disjoining pressure
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Π(h), which depends on the film thickness h.
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The van der Waals contribution is calculated from (equation 3)
132
Πvw = − " #! $
133
with AH as the compound Hamaker constant of a water film in air AH = 4*10-20 J. 18, 21
134
The contribution of the electrostatic interaction to the disjoining pressure is approximated by equation
135
(4)18
136
Πel = 64)* + , e-.#
137
with
138
, = tanh 378 6:;
139
and
140
? @AB 4
(6)
9
C6 CD 89:
*
hb
#
(7)
hb
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Langmuir
152
The theoretical individual attractive and repulsive contributions for an air water interface as well as the
153
resulting disjoining pressure as function of film thickness are calculated (figure 2).
154
Film drainage
155
The drainage of the film is modelled by considering the flow between two circular plane-parallel
156
plates. 23, 24 The change of the film thickness h with time t was described by (equation 8)
157
d# dL
158
where cf is a factor that accounts for the interaction of the fluid with the interface. For an immobile
159
interface, as we will consider here, cf = 1. Furthermore, µ = 10-3 kg/m/s is the viscosity of the water
160
phase, Rf is the radius of the film (in our experimental set-up Rf = 100 µm), and
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ΔS = Q − Π
162
is the driving capillary pressure, with γ is the surface tension of the water-air interface (in the
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calculation we used γ= 72 mN/m), 1/Rm is the (mean) curvature of the meniscus and Π is the total
164
disjoining pressure (Π= ΠVW+Πel+Πhb). Rm~1.25 mm, assuming complete wetting of the inner wall of
165
the Sheludko cell. (see figure 1).
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Starting from an initial thick film with thickness h0, the film will drain. Depending on the precise
167
shape of Π(h), the film can drain to a stable equilibrium thickness where the disjoining pressure equals
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the capillary pressure (figure 2 B). If the disjoining pressure is smaller than the capillary pressure the
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thin film can rupture spontaneously.
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Film rupture
171
Film rupture of surfactant stabilized films has successfully been described by the theory developed by
172
Sheludko and Vrij.4,
173
curve. In these regions of instability, small spontaneous surface perturbations grow in time until both
174
interfaces touch each other and the film ruptures. The unstable regions are given by the Vrij criterion
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(10)
176
VW V#
M # $
= − OPN QR ΔS
(8)
N
T
(9)
U
