Disjoining pressure effects

A. Disjoining Pressure Effects on the Contact Angle of Small Droplets... 

For "thick films" where disjoining pressure effects are negligible, the constant B in Equation 6 ranges from 1.337 for the perfectly mobile interface case to 2.123 for the immobile interface case. 

Chapter 5 (Section 6) described the conditions when a thin liquid film could become unstable and rupture and thereby cause coalescence of bubbles or drops. Instability was possible when the film became thin enough (less than 100 nm) for the disjoining pressure effects to be significant. However, considraable time may be required for the film to drain to this thickness, so that the rate of drainage has an important influence on the coalescence rate. The literatnre on expmmental and theoretical aspects of thin film drainage is extensive (Exerowa and Kruglykov, 1998 Ivanov and Dmitrov, 1988). 

The final group of equations focuses on the latter stages of adsorption, where the mesopores (ca. 2 nm to 50 nm in width according the lUPAC definition [9,10]) are filled. This is the region where capillary condensation occurs and the Kelvin equation is the simplest of these interpretations. There are numerous variations on the Kelvin equation that account for effects like multilayer adsorption prior to crqrillary condensation (i.e., BJH method [18]), disjoining pressure effects in die condensed liquid (i.e., DBdB method [19]), etc. 

From the dispersion relation (272), it follows that the increase of the surface tension, cr, and/or the magnitude of the density difference, Ap, decreases w (the increment of instability growth) and thus stabilizes the film. The disjoining pressure effect stabilizes the film when dlildh < 0, but it destabilizes the film when dCiIdh > 0. 

Fig. 2. Effective interface potential (left) and corresponding disjoining pressure (right) vs film thickness as predicted by DLVO theory for an aqueous soap film containing 1 mM of 1 1 electrolyte. The local minimum in H(f), marked by °, gives the equiHbrium film thickness in the absence of appHed pressure as 130 nm the disjoining pressure 11 = —(dV/di vanishes at this minimum. The minimum is extremely shallow compared with the stabilizing energy barrier.

Disjoining Pressure. A static pressure difference can be imposed between the interior and exterior of a soap film by several means including, for example, gravity. In such cases the equiHbrium film thickness depends on the imposed pressure difference as weU as on the effective interface potential. When the film thickness does not minimize lV(f), there arises a disjoining pressure II = —dV/(U which drives the system towards mechanical equiHbrium. 

Theoretically, the diffusion coefficient can be described as a function of the disjoining pressure 77, the effective viscosity of lubricant, 77, and the friction between lubricant and solid surfaces. In relatively thick films, an expression derived from hydrodynamics applies to the diffusion coefficients. 

From Eq. (9), the following relation between the effective contact angle and the disjoining pressure under constant volume can be obtained ... 

Capillary phenomena are due to the curvature of liquid surfaces. To maintain a curved surface, a force is needed. In Eq. (8), this force is related to the second term in the integral. The so-called Laplace pressure due to the force to maintain the curved surface can be expressed as, Pl = 2-yIr, where r is the curvature radius. The combination of the capillary effects and disjoining pressure can make a liquid film climb a wall. 

FIG. 7 Effective contact angle of the aqueous KOH droplets on HOPG and mica as a function of droplet height. Solid lines correspond to fits obtained using the disjoining pressure given by Eq. (18). 

Disjoining pressure was attributed in Ref 54 to the combined effect of van der Waals attraction and long-range electrostatic repulsion between similarly charged membrane surfaces. 

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... 

The effect of the nanoparticle volume fraction on the displacement of the contact line becomes pronounced only at higher volume fractions. For example, the displacement of the contact line is 10 times the nanoparticle diameter or approximately 0.2 im for a nanoparticle volume fraction of 0.25, while there is no appreciable change in the contact line position when the volume fraction is 0.2. This non-linear dependence of contact line position on nanoparticle volume fraction is consistent with the form of Eq. 10, where the film energy contribution due to structural disjoining pressure is subtracted from the surface energy contribution. The extent of displacement of the con-... 

As pointed out earlier, the disjoining pressure is the sum of interdroplet forces due to van der Waals, electrostatic and steric interactions. Detailed discussion of the nature of these interactions and their effect on the disjoining pressure can be found elsewhere (3,8). Only the final expressions for the contributions of different interactions to the disjoining pressure are given below. 

From the above equation, the variation of equilibrium disjoining pressure and the radius of curvature of plateau border with position for a concentrated emulsion can be obtained. If the polarizabilities of the oil, water and the adsorbed protein layer (the effective Hamaker constants), the net charge of protein molecule, ionic strength, protein-solvent interaction and the thickness of the adsorbed protein layer are known, the disjoining pressure II(x/7) can be related to the film thickness using equations 9 -20. The variation of equilitnium film thickness with position in the emulsion can then be calculated. From the knowledge of r and Xp, the variation of cross sectional area of plateau border Qp and the continuous phase liquid holdup e with position can then be calculated using equations 7 and 21 respectively. The results of such calculations for different parameters are presented in the next session. 

In a previous paper 8), was inferred for com oil-in-water as well as toluene-in-water emulsions stabilize by bovine serum albumin (BSA). The effects of pH, ionic strength and BSA concentration on Hmax were investigated. Comparison of experimental maximum disjoining pressure witii predicted Ilmax indicated that steric interaction is the predominant mechanism of stabilization in such systems. 

Since monodisperse creams of a range of droplet sizes can readily be prepared, it is possible to study the effect of droplet size on the critical osmotic pressure required for film rupture, n. This was found to increase with increasing droplet size. The critical osmotic pressure is, in effect, the disjoining pressure as smaller droplets have higher disjoining pressures (due to a smaller radius of curvature),... 

To obtain the disjoining pressure we have to realise that the solution in the infinitely extended gap is in contact with an infinitely large reservoir (Fig. 6.6) As the force per unit area is II only the difference of the pressure inside the gap and the pressure in the reservoir is effective. Therefore the osmotic pressure in the reservoir 2kBTc0 must be subtracted from P in order to get the disjoining pressure n = P - 2kBTc0. Finally, for the force per unit area we obtain... 

The stability of foams in constraining media, such as porous media, is much more complicated. Some combination of surface elasticity, surface viscosity and disjoining pressure is still needed, but the specific requirements for an effective foam in porous media remain elusive, partly because little relevant information is available and partly because what information there is appears to be somewhat conflicting. For example, both direct [304] and inverse [305] correlations have been found between surface elasticity and foam stability and performance in porous media. Overall, it is generally found that the effectiveness of foams in porous media is not reliably predicted based on bulk physical properties or on bulk foam measurements. Instead, it tends to be more useful to study the foaming properties in porous media at various laboratory scales micro-, meso-, and macro-scale. 

The principles of colloid stability, including DLVO theory, disjoining pressure, the Marangoni effect, surface viscosity, and steric stabilization, can be usefully applied to many food systems [291,293], Walstra [291] provides some examples of DLVO calculations, steric stabilization and bridging flocculation for food colloid systems. 

In the aqueous washing liquor the fabric surface and the pigment soil are charged negatively due to the adsorption of OH- ions and anionic surfactants and this leads to an electrostatic repulsion. In addition to this effect, a disjoining pressure occurs in the adsorbed... 

---