Surface tension force, definition

A solid, by definition, is a portion of matter that is rigid and resists stress. Although the surface of a solid must, in principle, be characterized by surface free energy, it is evident that the usual methods of capillarity are not very useful since they depend on measurements of equilibrium surface properties given by Laplace s equation (Eq. II-7). Since a solid deforms in an elastic manner, its shape will be determined more by its past history than by surface tension forces. 

When the density of a liquid is increased, the buoyancy force corresponding to a specific size of the bubble increases, whereas the surface-tension force may remain constant. Thus, for a definite amount of surface-tension force, the bubble volume obtained is smaller. 

Performing macro-scale experiments it has been observed that the normal surface tension force induces higher normal stresses in the fluid on the concave side of the interface than on the other fluid on the convex side of the interface. In a micro-scale view we may say that this interfacial tension force is exerted by the interfacial material lying on the convex side of the surface upon the material lying on the concave side. The normal component of the surface force is thus frequently (not always ) defined positive into the mean curvature of the surface, in line with the physical observations. The direction of the normal component of the interface force given by (3.9) is determined by two factors, the interface normal unit vector n/ which we have defined positive into the curvature, and the mean curvature variable which we have chosen to define as an absolute value. That is, the variable used here determining the mean curvature of the surface Hi = ( i + K2)/ 2) is consistent with the definition... 

FIGURE 9.4 Definition of the principal radii R and R2 associated with the surface tension force during melt spinning. 

In Chapter III, surface free energy and surface stress were treated as equivalent, and both were discussed in terms of the energy to form unit additional surface. It is now desirable to consider an independent, more mechanical definition of surface stress. If a surface is cut by a plane normal to it, then, in order that the atoms on either side of the cut remain in equilibrium, it will be necessary to apply some external force to them. The total such force per unit length is the surface stress, and half the sum of the two surface stresses along mutually perpendicular cuts is equal to the surface tension. (Similarly, one-third of the sum of the three principal stresses in the body of a liquid is equal to its hydrostatic pressure.) In the case of a liquid or isotropic solid the two surface stresses are equal, but for a nonisotropic solid or crystal, this will not be true. In such a case the partial surface stresses or stretching tensions may be denoted as Ti and T2-... 

This is the definition of the surface tension according to the Gibbs surface model [1], According to this definition, the surface tension is related to an interface, which behaves mechanically as a membrane stretched uniformly and isotropically by a force which is the same at all points and in all directions. The surface tension is given in J m-2. It should be noted that the volumes of both phases involved are defined by the Gibbs dividing surface X that is located at the position which makes the contribution from the curvatures negligible. 

Since the fiber is heavier than the liquid, it would sink when placed on the liquid if it were not sustained by an upward force caused by the surface tension of the liquid. This force is exerted at the three-phase air-liquid-fiber boundary lines. If the contact angle 0 and the surface tension y are high enough, this upward force can become sufficient to balance the sinking force, and the fiber will come to rest when the two forces become equal, at an equilibrium depth corresponding to a definite value of < . In this situation, as shown in Figure 1, the force exerted vertically upward on a unit length (1 cm.) of fiber, measured in dynes, will be ... 

The balance of forces between surface tensions at the contact line results either in the Neumann triangle for a liquid/liquid/liquid or liquid/liquid/gas system or in the Young-Dupre equation on a liquid/liquid/solid or a liquid/gas/solid system (Fig. 1). While the Neumann triangle represents a true balance of forces, the Young-Dupre equation is little more than a definition of the (o As ctbs) term, a difference between the respective solid/fluid surface free energies and not truly solid/fluid interfacial tensions. 

Two somewhat different definitions of the surface tension exist in the literature [Ij. First, as discussed above, the surface tension can be viewed as a force per unit length intending to reduce the area of the interface. We can thus define it in accordance with the following interface force ... 

Second, in thermodynamics it is more common to define surface tension in terms of work or the amount of energy needed to increase the surface with one unit area (i.e., the energy needed to bring a certain amount of molecules from the bulk to the surface). In this context the surface tension has a character of a surface free energy per unit area. The latter definition is in fact equivalent to the unit force per unit length (i.e. Nmjvr = NIm). The energy interpretation is by many researchers in thermodynamics considered the more fundamental one, and thus this interpretation is usually adopted for theoretical derivations. The surface tension is then defined as [1] [166] ... 

In this introduction it may be useful to give a brief definition of surface tension and surface free energy. The dimension of the surface tension is related to unit length. Lenard s classical experiment (1924) is one of the best demonstrations of the surface force of a liquid acting on an extended wire in contact with a liquid surface. By carefully lifting the wire from the level of the surface, a force can be measured for as long as the pendent lamella remains in contact with the liquid bulk. The force measured in this way, divided by the length of the wire, leads to a well-... 

In contrast to the definition of the surface tension of a liquid by the acting force along a unit length, the surface free energy is defined by the reversible work necessary to extend the surface area by a square unit, e.g. 1 cm. The basic form of this definition is given by... 

An important property of the surfaces of droplets is the surface tension that expresses the cohesion of water molecules (Chapter 2.5.1.1). On molecules existing close to the droplet surface, forces are directed to the inner of the droplet. Therefore, each liquid has the tendency to form spherical particles (if they are not counteracting forces such as gravitation and other outer forces). The reason is simple a sphere of a given volume has the smallest surface of all bodies. Thus, a growing droplet needs to overcome the molecular cohesion. There are two equivalent definitions of surface tension ... 

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