Tension force

Here again, the older concept of surface tension appears since Eq. 11-22 is best understood in terms of the argument that the maximum force available to support the weight of the drop is given by the surface tension force per centimeter times the circumference of the tip. 

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. 

A. Methods Depending on the Direct Manifestation of Surface Tensional Forces... 

The Weber number. We, is defined as foUows and represents the ratio of the dismptive aerodynamic forces to the restoring surface tension forces. 

Static holdup depends upon the balance between surface-tension forces tending to hold hquiciin the bed and gravity or other forces that tend to displace the liquid out of the bed. Estimates of static holdup (for gravity drainage) may be made from the following relationship of Shulman et al. [Am. Jn.st. Chem. Eng. J., 1, 259 (1955)] ... 

In supported liquid membranes, a chiral liquid is immobilized in the pores of a membrane by capillary and interfacial tension forces. The immobilized film can keep apart two miscible liquids that do not wet the porous membrane. Vaidya et al. [10] reported the effects of membrane type (structure and wettability) on the stability of solvents in the pores of the membrane. Examples of chiral separation by a supported liquid membrane are extraction of chiral ammonium cations by a supported (micro-porous polypropylene film) membrane [11] and the enantiomeric separation of propranolol (2) and bupranolol (3) by a nitrate membrane with a A/ -hexadecyl-L-hydroxy proline carrier [12]. 

A V-belt greatly increases the deliverable torque, since the wedging of the belt in the sheave groove increases the force of contact between the surfaces (N) far above the tension force (P). The driving... 

Figure 3-23 shows the constant speed forces in the V belts with drive sheave transferring power via the V belt to the large driven sheave [11]. If centrifugal forces and slippage are neglected, then taut side tension force Fj (lb) is... 

Note A positive sign indicates a compressive-type force, a negative sign indicates a tensional force. 

The magnitudes of the forces on a belt have significant impact on belt life. When a V-belt bends around a pulley, compressive forces develop in the bottom of the belt and tension forces develop in the top of the belt. The magnitude of each force is a function of the diameter of the pulley and the cross-section of the belt. 

From the experimental observation it is quite clear that the occurrence of the slug flow is rather an entrance phenomenon than one induced from the tube. Slug flow occurs if the speed of long gas bubbles is not high enough to overcome the strong surface tension force of the liquid bridge between them (Fig. 5.6b). 

However, on rigid substrates, the growth of dry zones is accompanied by a rim of excess liquid with width X (Fig. 10). As the dewetting proceeds, X increases. For short times and < K, the growth of dry patches is controlled only by surface tension forces and the dewetting speed is constant. A constant dewetting speed of 8 mm-s has been measured when a liquid film of tricresyl phosphate (TCP) dewets on Teflon PFA, a hard fluoropoly-mer of low surface free energy (p. = 250 MPa, 7 = 20 mJ-m ). 

Weber number Pe L We = -s a inertial force surface-tension force 8 10-2 2 10-2 Relevant for bubble (droplet) flows. Length scale bubble diameter... 

In that case the relevant length scale is 1 m rather than 500 pm, with the result that gravitational and inertial forces dominate over surface-tension forces. 

An important quantity determining the nature of the bubble flow considered by Yang et al. is surface tension, which often plays a dominant role in free-surface micro flows. However, viscous forces are also important in many cases. Hence the ratio of the viscous force and the surface tension force ... 

In flotation it is clear by now that there are three phases air, mineral, and water. The three are shown in Figure 2.23 (A) to meet at a common boundary. In this condition there will be a balance of interfacial tension forces. These can be resolved so that, for equilibrium at the point of intersection ... 

The ratio of deforming viscous forces to resisting interfacial tension forces in the case of droplets is the capillary number, Ca. Similarly, the ratio of viscous to cohesive forces in agglomerates is the fragmentation number, Fa. 

In the context of the preceding model, a drop is said to break when it undergoes infinite extension and surface tension forces are unable to balance the viscous stresses. Consider breakup in flows with D mm constant in time (for example, an axisymmetric extensional flow with the drop axis initially coincident with the maximum direction of stretching). Rearranging Eq. (26) and defining a characteristic length Rip113, we obtain the condition, for a drop in equilibrium,... 

---