научная статья по теме EFFECT OF THE ADSORPTION COMPONENT OF THE DISJOINING PRESSURE ON FOAM FILM DRAINAGE Химия

Текст научной статьи на тему «EFFECT OF THE ADSORPTION COMPONENT OF THE DISJOINING PRESSURE ON FOAM FILM DRAINAGE»

КОЛЛОИДНЫЙ ЖУРНАЛ, 2013, том 75, № 2, с. 197-201

УДК 541.183+544.7

EFFECT OF THE ADSORPTION COMPONENT OF THE DISJOINING PRESSURE ON FOAM FILM DRAINAGE © 2013 г. Stoyan I. Karakashev*, Anh V. Nguyen**, Roumen Tsekov*

*Department of Physical Chemistry, University of Sofia 1164 Sofia, Bulgaria **School of Chemical Engineering, The University of Queensland Brisbane, QLD 4072, Australia Поступила в редакцию 03.05.2012 г.

The present work is trying to explain a discrepancy between experimental observations of the drainage of foam films from aqueous solutions of sodium dodecylsulfate and the theoretical DLVO-accomplished Reynolds model. It is shown that, due to overlap of the film adsorption layers, an adsorption component of the disjoining pressure is important for the present system. The pre-exponential factor of this adsorption component was obtained by fitting to the experimental drainage curves. It corresponds to a slight repulsion, which reduces not only the thinning velocity as observed experimentally but corrects also the film equilibrium thickness.

DOI: 10.7868/S0023291213020092

1. INTRODUCTION

Karakashev et al. have investigated the drainage of foam films of dilute aqueous solution of sodium dodecylsulfate within the concentrations range 1—100 ^M [1]. They tried to describe the kinetics of foam film thinning by the Reynolds lubrication approximation accounting for the Marangoni effect, surface shear viscosity and DLVO forces. Significant discrepancy between the theoretical prediction and the experimental results was observed. The detailed analysis showed that the deviation of the theory from the experimental data originates from the interaction between the film surfaces. Therefore it was concluded that the classical DLVO theory only is not sufficient to match the experimental data. It was suggested that the discrepancy between theory and experiment is due to a neglected variation of the adsorption component of the surface tension during the film drainage.

Large number of literature confirms the applicability of the DLVO theory to foam films. However, number of papers [2—6] report deviations of this theory from experimental data. This discrepancy is pronounced mostly in thin films between hydrophobic surfaces. To solve the problem some authors [7—11] introduced in the theory additional non-DLVO force, the so-called "hydrophobic force", which can be attractive or repulsive [12—14]. There is a number of attempts in the literature [15—19] to explain the nature of the hydrophobic interaction but still no full agreement of the opinions is reached. However, the classical DLVO theory does not account also for other interactions in the thin liquid films. For instance, the dispersion interactions between the overlapping diffusive ad-

sorption layers should contribute to the overall interaction between the film surfaces and this contribution should increase with decreasing film thickness.

The idea of the adsorption interaction between the film surfaces originates from the work of Ash, Everett and Radke [20] and is further developed by the Russian school of colloid chemistry. The dispersion interaction between the solutes and the film surfaces is accounted for in [21—23] and it results in a correction in the van der Walls disjoining pressure. This additional adsorption term in the total interaction between the film surfaces could be important but it has been overlooked in a large volume of literature causing diversity of the opinions regarding the hydrophobic interaction. The reason for this is that the researchers cited above have described the surfactant distribution only as a result of interactions with the surfaces but neglected the interactions between solute molecules. Of course, the latter are not important in dilute solutions far away from the surface, but when the adsorption is considered the concentration near a surface is tremendously increased. Tsekov and Schulze [17] suggested first a clear thermodynamic interpretation of the adsorption term in the total disjoining pressure. They called it hy-drophobic force, since the origin of the adsorption is the surface hydrophobicity and the surfactant ability to reduce it. The aim of this paper is to employ this approach for explanation of our experimental data [24]. The good agreement will certainly draw attention on the importance of the adsorption disjoining pressure.

198

STOYAN I. KARAKASHEV u gp.

2. ADSORPTION DISJOINING PRESSURE

According to the thin liquid film thermodynamics any change of the film free energy F at constant temperature is given by

dF = - pdV + y dA + ^ p ¡dnh

(1)

where the extensive film parameters are volume V, film area A and number of moles {n,} of the film components. The relationship between the intensive parameters pressurep, film tension y and electrochemical potentials {p;} is given by the Gibbs—Duhem equation

-Vdp + Ady + ^ njdfij = 0.

(2)

It is known that the thin liquid films are anisotropic structures [25] and their pressure tensor possesses two distinct components, the normal and tangential ones. At equilibrium the normal component of the pressure tensor equals to the gas pressure outside, while the tangential component equals to the pressure in the meniscus adjacent to the film. The pressure p is the normal component of the pressure tensor. The film tension y consists in two additives [26]

Y = 2a + n h,

(3)

-Vdp + Ad(2a + n h) + ^ n,dp t = 0.

(5)

After Gibbs the film can be idealized by filling it with the bulk liquid from the meniscus. Hence, subtracting from

Eq. (5) the Gibbs—Duhem relation dpL = ^ c,dp, for

the liquid in the meniscus, where {c,} are the concentrations of the chemical components there, and keeping in mind that n = p - pL, one yields an important interfacial Gibbs—Duhem relation [27]

da = rdfit - ndh/2,

(6)

where {r, = (nt - cV)/2A} are the components adsorptions. Eq. (6) provides straightforward an important definition of the disjoining pressure as the thickness derivative of the film surface tension

n = - 2

\dh!

(7)

as well as the following Maxwell relation for the disjoining pressure

= 2 (dr

dP,- J h Vdh

(8)

The latter already hints the important effect of adsorption on the disjoining pressure [28, 29].

Since the surfactants could be charged species the film surface tension depends on electrostatics as well. It can be split into superposition of water, electrostatic and adsorption components, a = aW + aEL + aAD, which are independent if the surface potential ^s does not depend on the film thickness. Thus, during the film drainage the adsorptions and surface charge density, respectively, can vary but the electrostatic component aEL will not be affected by. At constant temperature the water component depends only on the film thickness, while the surfactant component depends on the adsorption. Substituting this presentation in Eq. (7) the disjoining pressure splits also into three distinct components

n = n^ + n EL

^ dr i )\dh

d<5AD \(dri

(9)

where h = Vf A is the film thickness. The purely interfacial part is twice the film surface tension a while the "bulk" part is accounted by the disjoining pressure n. Introducing Eq. (3) in Eq. (1) the latter changes to

dF = -pAdh - (p - U)hdA + 2adA + ^ pdn (4)

It is obvious now that the normal and tangential components of the film pressure tensor are not equal and their difference is the disjoining pressure.

Using Eq. (3) one can derive an alternative form of Eq. (2)

where nvw = -2(<9aw/dh)p and n el = -2(daelIdh)p are the well-known van der Waals and electrostatic components. Indeed, at low surface potentials the electrostatic component of the surface tension equals

to a EL = -6 06k^2 tanh (kh/ 2)/2, where k is the reciprocal Debye length, and the corresponding electrostatic

disjoining pressure n EL = s 0sk 2 ^/2cosh2(Kh/ 2) acquires its classical form [30].

Let us consider now the last adsorption component of the disjoining pressure in Eq. (9). To calculate its thickness dependence of the adsorption one can employ the Maxwell relation (8). Introducing the following definition AhX = X(h) - X(<») for a difference between the values of a property X of the equilibrium films with thickness h and infinity, respectively, one can write that n = -A hpL. Note, that changing the film thickness only its tangential pressure component changes, while the normal one pG = pL(h = to) remains constant. Thus, the Maxwell relation (8) can be consecutively modified to

(dh )ü (dp,,- h h (öp;-

= C

(10)

Knowing the adsorption isotherm c;-(T;-) at constant surface potential one is able to integrate this equation to obtain the thickness dependence of adsorption. If the changes of the concentration and adsorption, respectively, are small one can employ the following linear relationship Ahrt- ~ aiAhci, where at = (dri/dci)h=xa is the adsorption length on a single flat liquid/gas interface. The latter, representing the thickness of the

EFFECT OF THE ADSORPTION COMPONENT OF THE DISJOINING PRESSURE

199

adsorption layer, depends on the adsorption equilibrium constants and fa. Solving now the linearized differential equation (10) yields

A,Ti = A0r exp I -

2a,

(11)

n ^ = s

da

AD

dr,

A 0r,

exp

2a,

(12)

dh = 2h\pa - n) dt 3n R2 '

(13)

Capillary pressure pCT, zeta potential adsorption length a and fitting parameter A0ctd for different SDS concentrations

where {A 0r} is the difference between the adsorptions in a surfactant bilayer (h = 0) and on a single flat surface (h = ro). Substituting now this expression into the definition of the adsorption disjoining pressure from Eq. (9) leads to

c, p.M Fa, Pa fa, mV a, nm AqÜad, p.N/m

1 72.6 -63.0 275 7

5 72.5 -56.1 275 7

8 72.5 -52.7 275 7

10 72.4 -49.2 275 7

50 72.4 -48.6 274 7

100 71.8 -48.0 274 10

500 70.0 -52.8 249 13

Note that depending on the sign of {A0rj, the adsorption disjoining pressure can be either positive or negative. It could be also zero if no changes in the

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