Disjoining pressure isotherm

Comparison of the proposed dynamic stability theory for the critical capillary pressure shows acceptable agreement to experimental data on 100-/im permeability sandpacks at reservoir rates and with a commercial a-olefin sulfonate surfactant. The importance of the conjoining/disjoining pressure isotherm and its implications on surfactant formulation (i.e., chemical structure, concentration, and physical properties) is discussed in terms of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of classic colloid science. 

Figure 4. A conjoining/disjoining pressure isotherm for the constant- potential and weak overlap electrostatic model.

We can conclude that the stability of static foam in porous media depends on the medium permeability and wetting-phase saturation (i.e., through the capillary pressure) in addition to the surfactant formulation. More importantly, these effects can be quantified once the conjoining/disjoining pressure isotherm is known either experimentally (8) or theoretically (9). Our focus... 

Figure 6. Evolution of the lamella thickness as it transports down the periodic pore for the conjoining/disjoining pressure isotherm of Figure 4. Three capillary pressures are considered in curves 1 through 3. These capillary-pressure values are also labelled in Figure 4. Curve 2 defines the critical or marginally...

ENORDET AOS 1618) in an 81- fjtm permeability sandpack. Using the parameters listed and the constant- charge electrostatic model for the conjoining/disjoining pressure isotherm, the data are rescaled A ... 

Figure 5.8 Hypothetical disjoining pressure isotherm for a foam film illustrating the primary and secondary minima. From Nguyen and Schulze [53]. Copyright 2004, Dekker.

Figure 5.15 shows an example of a disjoining pressure isotherm in which the steric force contributions have been superimposed on the classical DLVO force contributions. It can be seen that this creates two regions for meta-stable foam films. One region is the thick, common black film region, with film thicknesses of approximately 50 nm or so. The other region is the thin, Newton black film region, with film thicknesses of approximately 4 nm. While the common black films are mostly stabilized by electrostatic forces, the Newton black films are at least partly stabilized by the steric forces. 

Figure 5.15 Illustration of a disjoining pressure isotherm (17T) that includes contributions from electrostatic (17E), dispersion (77d), and steric (77s) forces.

The direct measurement of the various important parameters of foam films (thickness, capillary pressure, contact angles, etc.) makes it possible to derive information about the thermodynamic and kinetic properties of films (disjoining pressure isotherms, potential of the diffuse electric layer, molecular characteristics of foam bilayer, such as binding energy of molecules, linear tension, etc.). Along with it certain techniques employed to reveal foam film structure, being of particular importance for black foam films, are also considered here. These are FT-IR Spectroscopy, Fluorescence Recovery after Photobleaching (FRAP), X-ray reflectivity, measurement of the lateral electrical conductivity, measurement of foam film permeability, etc. 

The determination of the ( -potential from the directly measured disjoining pressure isotherms will be treated in Section 3.4. Thus, the (po(h) dependence can be followed along with understanding the charge-potential relationship of interacting diffuse electric layers in foam films. 

From a practical point of view the dynamic method is fast and relatively simple. It has the intrinsic advantage over any equilibrium technique that disjoining pressure isotherms with dYl/dh > 0 can be monitored. It has been successfully applied to measure van der Waals attraction and retardation effects in foam films [80,235], The dynamic method has been applied to foam films of liposomal suspensions [234] and quite recently surface forces of oscillating nature were monitored in foam [235] and pseudoemulsion [236] films. 

However, the flow through the brush layer may be ignored in a first approximation [240], whereby the thickness h, appearing in Eq. (3.85), should be identified with the aqueous core thickness, /i2 (rather than hw) [241], The aqueous core thickness is plotted in Fig. 3.36, ( ). The dramatic influence on the interpretation is better seen in Fig. 3.37, ( ). The dependence is linear down to about /itot 90 nm. Thinner films drain faster initially and later on slower than predicted by the linear dependence, i.e. by Reynolds equation. The disjoining pressure isotherm (Fig. 3.38) is no more monotonous. 

The most detailed information about the interaction of two interfaces can be obtained from the disjoining pressure vs. thickness isotherm. Disjoining pressure isotherms were obtained for foam films from 0.7-1.410 5 mol dm 3 F108 aqueous solutions. A disjoining pressure range encompassing 4 orders of magnitude (1 -104 Pa) has been monitored by two complementary techniques the dynamic method and the Thin Liquid Film-Pressure Balance Technique [128,129] (see Section 2.1.8). 

It is well documented that in many respects PEO-PPO-PEO triblock copolymers behave like non-ionic surfactants [e.g. 225], This is also true for the interactions in foam films. The disjoining pressure isotherm in Fig. 3.39 is very much like that obtained earlier with foam films from nonylphenol eicosaoxyethylene ether (NP(EO)2o) [172], In both cases the isotherm is reversible, monotonously increasing (the barrier mechanism typical for low molecular weight surfactants is not observed) and its slope increases with decreasing film thickness. These features seem to be characteristic of surfactants having long PEO chains as already suggested in [172],... 

Formation and stability studies of black foam films can be summarised as follows 1) surface forces in black foam films direct measurement of disjoining pressure isotherm DLVO- and non-DLVO-forces 2) thin foam film/black foam film transition establishing the conditions for the stability of both types of black films and CBF/NBF transition 3) formation of black foam films in relation to the state of the adsorption layers at the solution/air interface 4) stability of bilayer films (NBF) theory and experimental data. 

In Section 3.3.1 it was shown that the state of thin foam films is described by the Fl(/ ) isotherm of disjoining pressure. For relatively thick films, stabilised by surfactants, this isotherm is consistent with the DLVO-theory. However, black foam films exhibit a diversion from the DLVO-theory which is expressed in the specific course of the disjoining pressure isotherm. 

Fig. 3.42. General schematic presentation of disjoining pressure isotherm of a thin foam film 1 - region...

Fig. 3.51 shows the disjoining pressure isotherms at 21 O 3 mol dm 3 CaCl2. Comparatively thick films were formed at low pressures and their thickness decreased with increase in n. The transition CBF/NBF occurred in the pressure interval 510 3 to 610 3 Pa. The black film thickness did not change with further increase in pressure up to 4-10 4 Pa (not shown in Fig. 3.51). 

Bergeron and Radke [235] have performed precise measurement of TT(/x) isotherms of NaDoS foam films at high surfactant concentrations employing both the Pressure Balance Technique and the dynamic method of Scheludko-Exerowa [73]. The disjoining pressure isotherms were established down to pressures of 10 Pa with specially constructed film holders and careful pressure isolation and control. 

In Fig. 3.101,a the transition region for this case is presented schematically line is the real surface, the dashed line is the model (idealised) surface. A conclusion has been drawn by de Feijter and Vrij [22] that k should be negative. However, in later comments these authors point out that this conclusion is not necessarily valid for the NBF, especially at large contact angles. In this case the shape of the real surface in the transition region can be presented like in Fig. 3.101, b due to the different disjoining pressure isotherm the k value should be positive. 

The effect of foam film type on foam stability can be studied from the tp(Apo) dependences in a wide range of pressure drops, as mentioned above, as well as from the Yl(h) dependences (disjoining pressure isotherms) for single foam films having radii close to those of films in the foam [45,46]. Fig. 7.6 depicts the Tp(Ap0) dependence of foams obtained from NaDoS aqueous solutions with different electrolyte (NaCl) concentrations, i.e. the foams are built up of different types of foam films. The surfactant concentration used in all experiments ensured maximum saturation of absorption layer. All three curves have different courses, corresponding to different film types thin films (curve 1), CBF (curve 2) and NBF (curve 3). On increasing Ap0, the foam lifetime strongly decreases compared with the time for decay in... 

Figure 5.15. Disjoining pressure isotherm for a Van der Waals liquid.

A quantitative measure of the sum of the interactions between the two film interfaces is the disjoining pressure II. It is the excess pressure between the pressure in the film and the pressure of the corresponding liquid. This difference is due to interactions between the film interfaces which are mainly determined by electrostatic repulsion between (charged) interfaces, van der Waals attraction, steric repulsion between the adsorbed surfactant molecules, and structural forces. Disjoining pressure isotherms (disjoining pressure as a function of film thickness) have been measured in a so-called thin film pressure balance (TFPB). 

Fig. 3 Disjoining pressure isotherms of PSSH-PEE at two different concentrations— 1.8 g L 1 and 3 g L 1. The solid line corresponds to an exponential fit of the experimental data. For details see text (from Ref. [24])...

Fig. 5 Disjoining pressure isotherm of a Q2G2/PDADMAC film. The solid line represents an exponentially damped cosine function. The mechanically stable and unstable parts are marked (from Ref. [33])...

Fig. 7 Disjoining pressure isotherms of films formed from aqueous solutions containing 3.4X10-1 monomol L I PEI and 10 4 mol L-1 C16TAB at two different pH values...

Fig. 8 Disjoining pressure isotherms of free-standing C16TAB/PDADMAC films at different molecular weight of PDADMAC. The PDADMAC concentration is fixed at a corresponding monomer concentration of 5xl(T3 monomol IT1. Therefore the concentration of the polyelectrolyte molecules changes with the molecular weight. The C16TAB concentration is 1(T4 mol IT1 (from Ref. [33])...

A similar electrostatic disjoining pressure isotherm has been used to interpret the experimental data for aqueous films on mercury. it is worthwhile noting that n (max) depends only on i.e., the maximum repulsion is determined by the potential of the surface of lower charge. 

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