Drops surface tension forces

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. 

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,... 

Bond number number Nbo N -APd29 /vBo — surface tension (Gravity/surface tension) forces Rise or fall of drops or bubbles... 

Atomization generally refers to a process in which a bulk liquid is disintegrated into small drops or droplets by internal and/or external forces as a result of the interaction between the liquid (dispersed phase) and surrounding medium (continuous phase). The term dispersed phase represents the liquid to be atomized and the atomized drops/droplets, whereas the term continuous phase refers to the medium in which the atomization occurs or by which a liquid is atomized. The disintegration or breakup occurs when the disruptive forces exceed the liquid surface tension force. The consolidating... 

Maximum weight method The detachment method is based upon the following to detach a body from the surface of a liquid that wets the body, it is necessary to overcome the same surface tension forces that operate when a drop is broken away. The liquid attached to the solid surface on detachment creates the following surfaces ... 

As noted in Chapter 2, bubbles and drops remain nearly spherical at moderate Reynolds numbers (e.g., at Re = 500) if surface tension forces are sufficiently strong. For drops and bubbles rising or falling freely in systems of practical importance, significant deformations from the spherical occur for all Re > 600 (see Fig. 2.5). Hence the range of Re covered in this section, roughly 1 < Re < 600, is more restricted than that considered in Section II for solid spheres. Steady motion of deformed drops and bubbles at all Re is treated in Chapters 7 and 8. 

As long as the drop is still hanging at the end of the capillary, its weight is more than balanced by the surface tension. A drop falls off when the gravitational force mg, determined by the mass m of the drop, is no longer balanced by the surface tension. The surface tensional force is equal to the surface tension multiplied by the circumference. This leads to... 

Sitting or pendent drop. Both methods involve the determination of the shape of the drop in mechanical equilibrium. The shape is determined by the balance between gravitation and surface tensional forces. If gravitation is negligible the shape is always spherical irrespective of the surface tension. 

Isolated Droplet Breakup—in a Velocity Field Much effort has focused on defining the conditions under which an isolated drop will break in a velocity field. The criterion for the largest stable drop size is the ratio of aerodynamic forces to surface-tension forces defined by the Weber number, N (dimensionless). 

The correction factor < > is required because on detachment (a) the drop does not completely leave the tip, (b) the surface tension forces are seldom exactly vertical and (c) there is a pressure difference across the curved liquid surface147. (f> depends on the ratio r/Vm. Values of have been determined empirically by Harkins and Brown148,149. It can be seen that values of r/Vm between about 0.6 and 1.2 are preferable (Figure 4.8). 

Here (f> is a correction factor to account for the facts that the drops do not completely leave the tip, and that the surface tension forces are not truely vertical. Values of (f> are reported in the literature. For this method the tip must be completely wetted and the drops must form and detach slowly > 1 min/drop). 

It should be noted diat the detachment of a pendant drop causes a disturbance at die bottom of die tube, which generates waves on die film above and to die side. At die moment die bridge breaks, the liquid remaining attached to the tube is typically shaped like a stretched triangle. The surface tension forces at the tip of diis shape furthest from the tube are very high and cause fast recoil of die liquid, which in turn leads to ripples diat propagate up the tube. These waves can disturb die formation of neighboring droplets and cause some side-to-side motion of droplet formation sites. 

Since surface forces depend on the magnimde of the area, the drops tend to be as spherical as possible. Distortions due to gravitational forces depend on the volume of the drop. In principle, it is however possible to determine the surface tension by measurement of the shape of the drop, when gravitational and surface tension forces are comparable. Two principally different methods must be taken into account. There are methods based on the shape of a static drop lying on a solid surface or a bubble adhering underneath a solid plate, and dynamic methods, based on continuously forming and falling drops. It should be noted that all the principles described here for drops are valid also for bubbles. 

The pressure drop of the vapor across the orifice expressed in inches of vapor-free liquid is computed by use of Eq. (12-10). The head required to overcome the surface tension force at the perforation may be estimated by use of an... 

A rather complex theory of the drop weight method, which makes it possible to tabulate the data required in order to determine the surface tension, has been worked out in some detail [27]. In the first (roughest) approximation, it can be assumed that, at the moment of detachment the gravity force acting on a drop, P, is balanced by the surface tension forces,... 

A liquid interface is the first requirement for all the many forms of capillarity. At least one phase must be sufficiently fluid. The shape of a liquid with an interface to air or another liquid is determined by the surface or interface tension. The shape of a liquid surface or interface at rest changes only when the surface tension, forces of gravity, and in some cases the electric field forces (Lorentz forces) are altered, provided the solid boundaries have constant dimensions and certain angles. The shape of pendant drops, sessile drops on a solid substrate, a meniscus against a solid wall and the length of so-called surface waves are well-known examples of capillarity. These phenomena need separate examination of liquid interfaces, as the surface state between two phases cannot be deduced from their bulk properties. 

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