Surface Forces and Liquid Films (Continued)

1
Surface Forces and Liquid Films (Continued)
Krassimir D. Danov Department of Chemical
Engineering, Faculty of Chemistry Sofia
University, Sofia, Bulgaria Lecture at COST D43
School Fluids and Solid Interfaces Sofia
University, Sofia, Bulgaria 12 15 April, 2011

Oscillatory structural forces measured by colloid
probe AFM.
Sofia University
2
(1) Van der Waals surface force
The Hamaker parameter, AH, depends on the film
thickness, h, because of the electromagnetic
retardation effect 1,4. The expression for AH
reads 4
?e 3.0 x 1015 Hz main electronic absorption
frequencyhP 6.6 x 10 34 J.s Plancks
const c0 3.0 x 108 m/s speed of light in a
vacuum.
3
(2) Electrostatic (Double Layer) Surface Force
(General Approach)
Poisson equation in the film phase relates the
electrostatic potential, y, to the bulk charge
density, rb 2,5,7
All ionic species in the bulk with
concentrations, nj, follow the Boltzmann
distribution (constant electro-chemical
potentials)
where q is the elementary charge, zj is the
charge number, nj0 is the input concentration.
The bulk charge density, rb is 2,5
The first integral of the Poisson-Boltzmann
equation reads
where p is the local osmotic pressure
Eq. (2.1)
In the case of symmetric films the electrostatic
disjoining pressure (repulsion), Pel, is defined
as a difference between the pressure in the film
midplane, pm, and that at large film thicknesses,
p0 5
Eq. (2.2)
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(2) Electrostatic (Double Layer) Surface Force
(General Approach)
For constant surface potential, ys, ys and h are
known and ym is calculated from
Eq. (2.3)
The surface charge density, rs, is calculated
from the charge balance at the film surface
Eq. (2.4)
where ps is the osmotic pressure in the
subsurface phase (at y ys).
For constant surface charge the system of
equations, Eqs. (2.1), (2.3), and (2.4), is
solved numerically to obtain ys and ym.
Charge regulation. In this case the surface
charge density, rs, relates the surface potential
through the condition of constant
electro-chemical potentials 6 and
Counterion binding Stern isotherm (KSt Stern
constant) leads to the equation
For example For (11) surface active ion 1 and
counterion 2 with adsorptions G1 and G2
5
(3) Equilibrium Film Thicknesses, h0 Theory vs.
Experiment 8
Sodium dodecyl sulfate (SDS) - NaC12H25SO4, CMC 8
mM
Cetyl-trimethylammonium bromide (CTAB) -
(C16H33)N(CH3)3Br, CMC 0.9 mM
Cetyl-pyridinium chloride (CPC) - (C21H38NCl),
CMC 1.0 mM
6
(3) Disjoining Pressure Isotherms Theory vs.
Experiment 21
Setup for measurement of disjoining pressure,
?(h), isotherms (Mysels-Jones porous plate cell
9).
Sodium dodecyl sulfate (SDS)
Hexa-trimethylammonium bromide (HTAB)
7
(3) Disjoining Pressure Isotherms Experiments
no Theory
For small concentration of ionic surfactants the
DLVO theory cannot explain experimental data.
8
(3) Colloidal Probe AFM Measurements of
Disjoining Pressure 10
Force, F, in nN for 80 mM Brij 35. Micelle volume
fraction 0.257.
Force/Radius, F/R, in mN.m-1 for 133 mM Brij 35.
Micelle volume fraction 0.401.
The aggregation number of micelles is 70.
The solid lines are drawn without adjustable
parameters (formulas by Trokhimchuk et al. 11).
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(4) Hydrodynamic Interaction in Thin Liquid Films
2,3
Two immobile surfaces of a symmetric film with
thickness h(t,r) approach each others with
velocity U(t). Rf is the characteristic film
radius.
where t is time r and z are the radial and
vertical coordinates.
Simplest version of the lubrication approximation
(hltltRf)
Continuity equation
Momentum balance equation is simplified to
Simple solution
Hydrodynamic force, F
P(h) is the disjoining pressure, which accounts
for the molecular interactions in the film.
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(4) Taylor vs. Reynolds regimes 2,3
In the case of two spheres (Taylor) 12
where hin is the initial thickness and hcr is the
final critical film thickness.
The life time can be defined as
where g is the gravity constant and Dr us the
density difference.
In the case of buoyancy force
The life time decreases with the increase of drop
radii.
For two disks (Reynolds) 13
In the case of buoyancy force
The life time increases with the increase of drop
radii.
11
(4) Taylor vs. Reynolds regimes
Taylor regime
Dickinson experiments for the life time of small
drops (ß-casein, ?-casein or lysozyme, 104 wt
protein 100 mM NaCl, pH7) 14.
Our experiments for the life time of small and
large drops 15 (4x10-4 wt BSA 150 mM NaCl,
pH6.4).
Strong dependence of the drops life time on the
drop and film radii for tangentially immobile
film surfaces.
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(4) Lubrication Approximation and Film Profile
2,16
Two immobile surfaces of a symmetric film with
thickness h(t,r) approach each others. The film
profile changes with time and pm is the pressure
in the meniscus.
Simple solution
Continuity equation
Normal stress boundary condition
Film-profile-evolution equation (stiff nonlinear
problem)
The applied force is given by the expression
13
(4) Study of Drainage and Stability of Small Foam
Films Using AFM
Microscopy photographs of bubbles in the AFM with
schematics of the two interacting bubbles and the
water film between them 17 (A) Side view of
the bubble anchored on the tip of the cantilever.
(B) Plan view of the custom-made cantilever with
the hydrophobized circular anchor. (C) Side
perspective of the bubble on the substrate. (D)
Bottom view of the bubble showing the dark
circular contact zone of radius, a (in focus)
on the substrate and the bubble of radius, Rs.
(E) Schematic of the bubble geometry.
Evolution of film profiles and rim rupture effect.
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(5) Interfacial Dynamics and Rheology Complex
Boundary Conditions
The velocities of both phases are equal at
liquid/liquid interface S
The jump of bulk forces at S are compensated by
the total surface forces
where Ts is the surfaceviscous stress tensor.
Marangonieffect
Capillarypressure
Surface viscosityeffect
For Newtonian interfaces (Boussinesq Scriven
law) 16
where Is is the surface idem factor
hdil surface dilatational viscosity
hsh surface shear viscosity.
Rate of relative displacement of surface points
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(5) Lubrication Approximation for Complex Fluids
in the Films 18
The film phase contains one surfactant with bulk
concentration, c, adsorption, G, and interfacial
tension, s.
Integrated-surfactant-mass-balance equation
cs the subsurface concentration, u the
surface velocity, the mean velocity is defined as
For slow processes the deviations of
concentrations and adsorptions are small and
Adsorption length (known from the adsorption
isotherm)
The larger bulk and surface diffusivities lead to
larger surface velocity (mobility)!
Continuity equation for mobile surfaces
16
(5) Lubrication Approximation for Complex Fluids
in the Film 19
Tangential stress boundary condition (ms
mdilmsh total interfacial viscosity)
viscous friction(film phase)
viscous friction(drop phase)
Marangonieffect
Boussinesqeffect
For slow processes the Marangoni term has an
explicit form and
The Gibbs elasticity, EG, is known from the
surface equation of state or from independent
rheological experiments.
The larger Gibbs elasticity and surface viscosity
suppress the surface mobility!
Normal stress boundary condition closes the
problem for film evolution in time
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(5) Role of Surfactant on the Drainage Rate of
Thin Films 19
In the case of two spheres(Taylor velocity)
In the case of two plates(Reynolds velocity)
Two truncated spheres
In the case of surfactants for this geometry we
have
characteristic surfacediffusion length
bulk diffusivitynumber
dimensionless film radius
In the case of emulsion plane parallel films
In the case of two spherical drops
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(5) Inverse Systems Surfactants in the Disperse
Phase
In this case the diffusion fluxes from the
disperse phase are large enough to suppress the
Marangoni effect and 3,20
where rc the density of liquid in the film
phase Fs force arising from the
disjoining pressure d
characteristic thickness of the boundary layer
in the drop phase.
Surface active componentsin the disperse phase
Surfactant in the continuous phase0.1M lauryl
alcohol (1) 2 mM C8H18O3S (2).
Surfactantin the dispersephase (benzene films)
C8H18O3S 0 mM (1) 0.1 mM (2) 2 mM (3).
Film life time diagram
Film life timediagram
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Basic References 1. J.N. Israelachvili,
Intermolecular and Surface Forces, Academic
Press, London, 1992. 2. K.D. Danov, Effect of
surfactants on drop stability and thin film
drainage, in V. Starov, I.B. Ivanov (Eds.),
Fluid Mechanics of Surfactant and Polymer
Solutions, Springer, New York, 2004, pp. 138.
3. P.A. Kralchevsky, K.D. Danov, N.D. Denkov.
Chemical physics of colloid systems and
Interfaces, Chapter 7 in Handbook of Surface and
Colloid Chemistry", (Third Edition K. S.
Birdi, Ed.). CRC Press, Boca Raton, 2008 pp.
197-377. Additional References 4. W.B.
Russel, D.A. Saville, W.R. Schowalter, Colloidal
Dispersions, Cambridge Univ. Press,
Cambridge, 1989. 5. B.V. Derjaguin, N.V.
Churaev, V.M. Muller, Surface Forces, Plenum
Press Consultants Bureau, New York, 1987. 6.
P.A. Kralchevsky, K.D. Danov, G. Broze, A.
Mehreteab, Thermodynamics of ionic surfactant
adsorption with account for the counterion
binding effect of salts of various valency,
Langmuir 15(7) (1999) 23512365.
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7. L.D. Landau, E.M. Lifshitz, Electrodynamics of
Continuous Media, Butterworth-Heinemann, Oxford,
2004. 8. K.D. Danov, E.S. Basheva, P.A.
Kralchevsky, K.P. Ananthapadmanabhan, A. Lips,
The metastable states of foam films containing
electrically charged micelles or particles
Experiment and quantitative interpretation, Adv.
Colloid Interface Sci. (2011) in press. 9.
Mysels, K. J. Jones, M. N. Direct Measurement of
the Variation of Double-Layer Repulsion with
Distance. Discuss. Faraday Soc. 42 (1966)
42-50. 10. N.C. Christov, K.D. Danov, Y. Zeng,
P.A. Kralchevsky, R. von Klitzing, Oscillatory
structural forces due to nonionic surfactant
micelles data by colloidal-probe AFM vs. theory,
Langmuir 26(2) (2010) 915923 . 11. A.
Trokhymchuk, D. Henderson, A. Nikolov, D.T.
Wasan, A Simple Calculation of Structural and
Depletion Forces for Fluids/Suspensions Confined
in a Film, Langmuir 17 (2001) 4940-4947. 12.
In fact, this solution does not appear in any
G.I. Taylors publications but in the article by
W. Hardy, I. Bircumshaw, Proc. R. Soc. London A
108 (1925) 1 it was published.
21
13. O. Reynolds, On the theory of lubrication,
Phil. Trans. Roy. Soc. (Lond.) A177 (1886)
157?234. 14. E. Dickinson, B.S. Murray, G.
Stainsby, Coalescence stability of emulsion-sized
droplets at a planar oil-water interface and the
relationship to protein film surface rheology, J.
Chem. Soc. Faraday Trans. 84 (1988) 871?883. 15.
T. D. Gurkov, E. S. Basheva, Hydrodynamic
behavior and stability of approaching deformable
drops, in A. T. Hubbard (Ed.), Encyclopedia of
Surface Colloid Science, Marcel Dekker, New
York, 2002. 16. D.A. Edwards, H. Brenner, D.T.
Wasan, Interfacial Transport Processes and
Rheology, Butterworth-Heinemann, Boston, 1991.
17. I.U. Vakarelski, R. Manica, X. Tang, S.Y.
OShea, G.W. Stevens, F. Grieser, R.R. Dagastine,
D.Y.C. Chan, Dynamic interactions between
microbubbles in water, PNAS 107 (2010) 11177.
18. I.B. Ivanov, D.S. Dimitrov, Thin film
drainage, Chapter 7, in I.B Ivanov (ed.), Thin
Liquid Films, M. Dekker, New York, 1988.
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19. K.D. Danov, D.S. Valkovska, I.B.
Ivanov, Effect of surfactants on the film
drainage, J. Colloid Interface Sci. 211 (1999)
291303. 20. I.B. Ivanov, Effect of surface
mobility on the dynamic behavior of thin liquid
film, Pure Appl. Chem. 52 (1980) 1241?1262. 21.
K.D. Danov, E.S. Basheva, P.A. Kralchevsky, The
Hydration Surface Force an Effect Due to
the Discreteness and Finite Size of Surface Ions
and Bound Counterions. Curr. Opin. Colloid
Interface Sci. (2011) a manuscript in
preparation.