Disjoining pressure positive

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-... 

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. 

Alternatively, experimental measurement of the variation of equilibrium continuous liquid holdup with position for a concentrated oil-in-water emulsion can be employed to infer the variation of disjoining pressure with film thickness. Since the continuous phase liquid holdup e is known as a function of position, xp, Op and r can be calculated using equations 7,21 and 24. Equation 24 will then yield the disjoining pressure II at the film thickness xp. ... 

Figure 10.4 shows the results of some measurements on aqueous sodium oleate films. The sensitivity of the equilibrium film thickness to added electrolyte reflects qualitatively the expected positive contribution of electric double layer repulsion to the disjoining pressure. However, this sensitivity to added electrolyte is much less than that predicted from electric double layer theory and at high electrolyte concentration an equilibrium film thickness of c. 12 nm is attained which is almost independent of the magnitude of the disjoining pressure. To account for this observation, Deryagin and Titijevskaya have postulated the existence of hydration layers... 

Newton black films, which are the only ones that can exist in the absence of double layer interactions, can be obtained only if the disj oining pressure has a positive value (otherwise, the film will collapse). The extrema of the disjoining pressure are obtained through the derivation of eq 19 with respect to d... 

Under certain conditions aqueous electrolyte solutions form foam films of equilibrium thickness. For a microscopic horizontal film this thickness is determined by the positive component of disjoining pressure (FU) which depends on the potential of the diffuse electric layer at the foam film/air(gas) interface. 

The results obtained indicate that at (po]Cr only NBF form. These studies prove that the barrier in the TT(/i) isotherm, impeding the transition of one film type to another, is mainly determined by the electrostatic component of disjoining pressure, Tlf(. It should not be forgotten that if there exist other components of disjoining pressure, this estimation is no more valid. A CBF/NBF transition could not even be realised if there is another positive component, such as steric one in polymer films. 

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. 

Thus, it might be assumed that stabilisation of foam films will depend also on the action of other positive components of disjoining pressure. For example, equilibrium films are obtained from concentrated butyric acid solutions and, therefore, in this concentration range the foam lifetime also increases. On the basis of these concepts it should be expected that a foam consisting of films with equilibrium thicknesses at a constant capillary pressure pa = n, should be infinitely stable. In fact, a real foam decays both in bulk and as a disperse system, due to gas diffusion transfer and certain disturbances (shift of films and borders on structural rearrangement as a result of the collective effects , etc.)... 

It follows from these data that the electrostatic component of disjoining pressure cannot alone provide the formation of a stable (long-living) foam. It is necessary to account for other positive components of n and the different conditions under which the films exist in the foam. 

FIGURE 4.6. The interface profile (relative to the interface position at r = 0) for an alkane drop in water with a silica probe at an axial separation distance Do of 6.5 and 4.5 nm. The dots denote the coiresponding disjoining pressure value at the marked radial distance. The inset is the disjoining pressure (electrostatic and van der Waals) for a water/aUtane/silica system with a univalent (non-surface-active) electrolyte ( " = 30 nm ijfo = 50 mV). Reprinted from Ref. [67], with permission from Elsevier. 

The answer has to be found in the stability of the thin liquid film, formed at the interface between solid and vapour. Colloquially stated, what is stronger, the interned cohesion of the adsorbate or the adhesion between adsorbate and surface In colloidal parlance, is the disjoining pressure /7(h) across a film of thickness h positive or negative, and how does 77 change as a function of h ... 

Hence, for nanoscopic one-dimensional pores, w e are in a position to calculate the so-called disjoining pressure defined as [cf., Eq. (5.57)]... 

In fact, Equation 5.170 is applicable to the dispersion contribution in the van der Waals interaction. When components 1 and 2 are identical, Ag is positive (see Equation 5.169), therefore, the van der Waals interaction between identical bodies, in any medium, is always attractive. Besides, two dense bodies (even if nonidentical) will attract each other when placed in medium 3 of low density (gas, vacuum). When the phase in the middle (component 3) has intermediate Hamaker constant between those of bodies 1 and 2, Ag can be negative and the van der Waals disjoining pressure can be repulsive (positive). Such is the case of an aqueous film between mercury and gas. ... 

The dimensional coefficient A that appears in (6 84) is known as the Hamaker constant. Its value depends on the materials involved, but a typical magnitude is 10 20 to 10 19 J. Generally A is positive, which corresponds to a positive disjoining pressure and attraction between the interface and the solid substrate. However, in some circumstances, A < 0, and the surfaces repel. 

The molecular component of the disjoining pressure, IIm(/i), is negative (repulsive). It is caused by the London-van der Waals dispersion forces. The ion-electrostatic component, IIe(/i), is positive (attractive). It arises from overlapping of double layers at the surface of charge-dipole interaction. At last, the structural component, IIs(/i), is also positive (attractive). It arises from the short-range elastic interaction of closed adsorption layers. 

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