Deformation of Fluid Particles in the Contact Zone

The hydrostatic pressnre in thin liquid films intervening between two drops or bubbles differs from the pressure inside the drops or bnbbles. This difference is 

We now take into account both the finite thickness of a liquid interlayer between droplets or bubbles and the variation in thickness in the transition zone between the interlayer and the equilibrium bulk liquid phase. It was already mentioned that there is a problem in using the approach of thickness-dependent interfacial tension if we try to use the Navier-Stokes equation for description of flow or equilibrium in thin liquid films, a thickness-dependent surface tension results in an unbalanced tangential stress on the surface of thin films. This is the reason why this particular approach is not used in this book. 

In the following text, we use the same approach as in the previous sections of this chapter, which takes into account the interlayer thickness and the effect of the transition zone between the thin interlayer and the bulk liquid. This effect is equivalent to the line tension that is considered in Section 2.10. A low slope and constant surface tension approximations are used. Then, as was shown earlier in Section 2.1 through Section 2.3, it is possible to use the equation taking into account both the disjoining pressure and the capillary pressure in the interlayer. 

FIGURE 2.32 Two identical drops or bubbles (1) at equilibrium in a surrounding liquid, (2) h(,x) is a half thickness of the liquid film between two drops or bubbles. 

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