Young’s relation

If one of the phases is solid, the contact line lies in the solid interface and the angle with the liquid interface is called the contact angle 9. If the three phases present are solid/liquid/air, the equation describing the balance of forces projected in the plane of the solid surface, known as Young s relation, is ... 

Combining this with Young s relation 7so = ycos E + 7sl, we find that... 

The first method consists in tallying up the capillary forces acting on the line of contact (also called triple line) and equating the sum to zero. When normalized to a unit length, these forces are the interface tensions between the three phases (S/L/G). By projecting the equilibrium forces onto the solid plane, one obtains Young s relation (which he derived in 1805) ... 

A liquid is normally contained in a solid vessel with vertical walls. The surface of the liquid is horizontal because of gravity, except near the walls where Young s relation [equation (1.23)] induces a distortion. When the... 

Also in accordance with Young s relation, the ordinate at the origin gives the solid/vapor surface tension. From the graph, we read directly 750 = 21 mN/m, in excellent agreement the value determined previously. 

These measurements constitute a direct experimental validation of Young s relation, in which all parameters are determined independently. It is truly amazing that, as famous and widely used as Young s law is, it took nearly two centuries to finally verify it directly. 

It is often desirable to spread a thin film of solution W) on a hydrophobic surface (5). This does not happen spontaneously. If one tries to spread a thin film in a partial wetting regime, the film tends to fragment in droplets, each of which conforms to the contact angle 6e specified by Young s relation. As discussed in chapter 7, only thicker films, with a puddle thickness 6c = s h 6e/2) in the millimeter range, are stable. One must therefore... 

One the first attempts at understanding the influence of roughness on wetting is due to Wenzel (1936). We assume that the local contact angle is given by Young s relation [equation (9.1)], and we seek to determine the... 

If 5 < 0, the drop does not spread. If it were exposed to air, it would form a spherical cap with a contact angle 0 given by Young s relation (chapter 1). A simple measurement of would determine 5. Unfortunately, when the liquid is encapsulated in a soft matrix, this method is unusable. 

Young s relation is valid only in the immediate vicinity of the line since the shape of the drop will be determined by the elastic deformation of the elastomer. Together with the spreading parameter S and Young s modulus E of the rigid substrate, we can introduce a characteristic length ho, which we call the elastic length, defined by... 

While the capillary length (introduced in chapter 1) describes the competition between gravity and capillarity, the length ho describes the competition between, the deformation energy of the soft matrix and the surface energy. Young s relation would be valid only over dimensions srnaller than ho, where other types of forces (such as van der Waals) modify the profile anyway. 

The Young s equation is the well-known relationship used to describe a sessile drop at equilibrium on top of a solid surface. This relationship has been discussed thermodynamically and microscopically for purely flat surfaces in the literature. To characterize the non-flatness of a surface, one may introduce the Wenzel s roughness r defined as the area of the wall surface devided by the area of its projection onto the horizontal plane. Obviously, r is equal to 1 once the surface is flat. For r>l, it is known that Young s equation has to be modified to take into account the increase of surface. The generalization of Young s relation is the so-called Wenzel s law. In this presentation, we will study this relation within microscopic models. We will in particular show that the roughness may enhance the wetting of the substrate even at the microscopic scale. 

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