Pancake equilibrium thickness

For large drops whose radius exceeds, gravitational effects dominate. A drop is flattened by gravity. At equilibrium, it takes on the shape of a liquid pancake of thickness e. The value of e can be calculated by expressing the equilibrium of the horizontal forces acting on a portion of the liquid. 

For dry liquid (nonvolatile), the film spreads at equilibrium like a pancake with an equilibrium thickness, e (Fig.6). This is one of the major findings by Joanny and de Gennes. They have calculated this thickness by taking into account the counter effects of the spreading term in thinning of the film and the disjoining pressure in thickening of the film. Thus, for non-retarded VDW interactions. 

In contrast to our instuitive feeling, the final equilibrium situation is not necessarily a monomolecular layer of liquid. It is rather a pancake"whose thickness results from the balance between spreading parameter S and long range interactions (A). 

We now consider the case of complete wetting (spreading power 5 > 0) for the case where there are van der Waals interactions, which tend to thicken the film. For a finite amount of fluid spreading on an infinite solid substrate, the equilibrium film profile will therefore not be a monolayer, but a pancake with a maximum thickness that is determined by the balance of the surface tensions and the van der Waals energies (see Fig. 4.3). 

Now place a much larger droplet on the surface (see Fig. 1.12b) it forms a pancake-shape, flattened by gravity. The thickness of the pancake can be calculated by writing down the equilibrium condition for the forces acting on a part of the droplet, shaded in Fig. 1.12b there are the capillary forces and the gravitational force due to the hydrostatic pressure exerted by the liquid on the shaded region. At depth z, the pressure is p = Pq + pgz. The gravitational force is thus... 

Answer There is a terminal zone where suddenly drops to zero. In this zone, the film is no longer flat. Indeed, the curvature of the interface modifies the chemical potential. As a matter of fact, we already know the answer in light of our discussion on the equilibrium of a system composed of a film and a dry solid. We have seen that the film thickness must be the pancake thickness Cc Inserting e = Cc into equation (4.23) allows us to find the maximum height 2m,ax-... 

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