Forces surface tension

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)] ... 

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 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,... 

Liquid Metal Sources. The source feed is a metal of low melting point - Ga and In are commonly employed. It is introduced as a liquid film flowing over a needle towards the tip whose radius is relatively blunt (10 pm). The electrostatic and surface tension forces form the liquid into a sharp point known as the Taylor cone. Here the high electric field is sufficient to allow an electron to tunnel from the atom to the surface, leaving the atom ionized. 

The vapor pressure in the bubble is related to the liquid pressure at the bubble interface and the surface tension force by Eq. (2-3). Introducing this result into Eq. (2-28), the Rayleigh equation (Rayleigh, 1917) for isothermal bubble dynamics is obtained as... 

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