Drops forming, shape

The topic of capillarity concerns interfaces that are sufficiently mobile to assume an equilibrium shape. The most common examples are meniscuses, thin films, and drops formed by liquids in air or in another liquid. Since it deals with equilibrium configurations, capillarity occupies a place in the general framework of thermodynamics in the context of the macroscopic and statistical behavior of interfaces rather than the details of their molectdar structure. In this chapter we describe the measurement of surface tension and present some fundamental results. In Chapter III we discuss the thermodynamics of liquid surfaces. 

Shape of the liquid drop (Pendant drop method) The liquid drop forms as it flows through a tubing (Figure 2.11). At a stage just before it breaks off, the shape of the pendant drop has been used to estimate y. The drop shape is photographed and, from the diameter of the shape, y can be accurately determined. 

The shape of a drop forming slowly at a submerged orifice is the basis for the hanging-drop (pendant-drop) method for determining inter-... 

While the measurement protocol is fairly simple, there are a number of important factors that need to be considered when using the drop shape analysis method. First, a sufficient visual contrast between the drop and the surrounding liquid is required to be able to extract the drop profile. If the external phase is slightly turbid, or if the refractive indices of the two phases match each other, it may be difficult or even impossible to extract the drop profile. If possible, the more turbid phase should be chosen as the internal drop-forming... 

A suspended liquid drop forms a sphere, because this shape has minimum surface area (hence minimum interfacial free energy) for a given volume area is related to the cube of droplet radius. Distortion is a flow shear effect, depending on droplet cross-section, related to the square of the radius. At large diameters, shear forces are greater than interfacial tension forces, droplets are distorted into cylinders, and subdivision occurs. Droplet radius decreases, until the interfacial tension forces balance (or exceed) shear forces, and further division stops. In emulsification experiments in which the amount of mixing energy is constant and y... 

One point that has not been emphasized is that all of the preceding analysis and discussion pertains only to the steady-state problem. From this type of analysis, we cannot deduce anything about the stability of the spherical (Hadamard Rybczynski) shape. In particular, if a drop or bubble is initially nonspherical or is perturbed to a nonspherical shape, we cannot ascertain whether the drop will evolve toward a steady, spherical shape. The answer to this question requires additional analysis that is not given here. The result of this analysis26 is that the spherical shape is stable to infinitesimal perturbations of shape for all finite capillary numbers but is unstable in the limit Ca = oo (y = 0). In the latter case, a drop that is initially elongated in the direction of motion is predicted to develop a tail. A drop that is initially flattened in the direction of motion, on the other hand, is predicted to develop an indentation at the rear. Further analysis is required to determine whether the magnitude of the shape perturbation is a factor in the stability of the spherical shape for arbitrary, finite Ca.21 Again, the details are not presented here. The result is that finite deformation can lead to instability even for finite Ca. Once unstable, the drop behavior for finite Ca is qualitatively similar to that predicted for infinitesimal perturbations of shape at Ca = oo that is, oblate drops form an indentation at the rear, and prolate drops form a tail. 

The functioning of the instrument, as described in detail also in the book chapter mentioned above [176], is different from most of the other instruments. Due to the large internal gas volume (about 35 cm ) an easy procedure for determining the effective adsorption time in the moment of maximum pressure was derived (see below). The surface tension y can be calculated from the measured maximum capillary pressure P and the known capillary radius r jp using the Laplace equation in the simplified form for spherical drop/bubble shapes... 

In recent years, several theoretical and experimental attempts have been performed to develop methods based on oscillations of supported drops or bubbles. For example, Tian et al. used quadrupole shape oscillations in order to estimate the equilibrium surface tension, Gibbs elasticity, and surface dilational viscosity [203]. Pratt and Thoraval [204] used a pulsed drop rheometer for measurements of the interfacial tension relaxation process of some oil soluble surfactants. The pulsed drop rheometer is based on an instantaneous expansion of a pendant water drop formed at the tip of a capillary in oil. After perturbation an interfacial relaxation sets in. The interfacial pressure decay is followed as a function of time. The oscillating bubble system uses oscillations of a bubble formed at the tip of a capillary. The amplitudes of the bubble area and pressure oscillations are measured to determine the dilational elasticity while the frequency dependence of the phase shift yields the exchange of matter mechanism at the bubble surface [205,206]. 

Figure 4.32 Schematic structures of spinnerets (a) Laminar flow disturbed by drop of molten pitch formed on spinneret surface. Jet material with good wettability gives larger drop (b) Shape of spinneret hole with narrow and wider parts designed to convert from laminar to turbulent flow (c) Laminar flow disturbed by a plug of stainless steel particles or mesh. Source Reprinted with permission from Otani S, Oya A, In Kawata K, Umekawa S, Kobayashi A eds. Composites 86 Recent Advances in Japan and the United States. Proc Japan-US CCM III Jpn Soc Compos Mater, Tokyo, 1-23,1986. Copyright 1986, Japan Society of Composite Materials.

Once again, small drops adopt spherical cap shapes, and larger drops form fiat lense shapes. These floating lenses are subject to an Archimedean upthrust. Their thickness can be discovered by measuring their radii as a function of volume. The spreading parameter 5 = 7b — (7a + 7ab) can be deduced from the formula pe /2 = —S, where... 

In some cases, the amount of liquid available for surface tension measurement is very small, such as fluid from the eye, etc. Under these conditions, one finds that the following procedure is most suitable for the measurement of y. The liquid drop forms as it flows through a tubing. Figure 1.19. At a stage just before it breaks off, the shape of the pendant drop has been used to estimate y. The drop shape is photographed, and from the diameters of the shape, one can accurately determine y. Actually, if one has only a drop of fluid, then one can measure its y without the loss of sample volume (as in the case of eye fluid, etc.). 

If the Hquid is not exposed to external forces (e.g. in a vacuum), it occupies a spherical shape as it gains the smallest surface at the given volume. On the surface of another liquid, it either forms a drop that has a lenticular shape, or can be spread over its surface. The liquid s behaviour at a given temperature depends on the size of the liquid-air surface tension, and on the interfacial liquid-liquid surface tension. On the sohd surface the liquid also either spreads out evenly or forms a drop. The shape and size of the drop depend on how the Kquid wets the solid surface, which is related to the liquid-air surface tension (Kig), surface energy of a sohd (Ksg) solid-liquid surface tension (y j) and temperature (Figure 7.14). 

Bohr called his idea the liquid droplet theory. He suggested that a mass of atoms behave like a drop of liquid—clustering around one another to form the drop. When bombarded by a neutron, the drop forms the shape of a dumbbell and then splits into two, forming two new drops. During the split into two drops, energy is released. Bohr s theory provided scientists with a visualization of how the actual process of fission would be achieved. 

Polygonal-Like Shape. For higher CTAB concentrations, a polygonal-like shape is observed (Fig. 10). After the induction period small tips form along the edge of the drop, which confers the drop the shape of a polygon. This tips move and when two of them collide they can give rise to the ejection of a smaller... 

In 1676, Boyle (Philos. Transact., vol. XI, pp. 775 and 779) on the basis of the fact that drops of rain and dew have a round shape, and noticing that these drops, surrounded by air, are made of a fluid in another fluid, proposes to test what happens to drops of a liquid immersed in another liquid with which they do not mix. To this end, he introduces into a bottle a layer of potash a concentrated carbonate solution, and, over, a sufficient quantity of also concentrated alcohol then he drops in this last liquid drops of spirits of turpentine, and he sees these drops, which do not dissolve immediately in the ambient liquid, descend through this and to come to rest, with an appreciably spherical shape, on the surface of the alkaline liquid he notes that sphericity starts to appear faded when a drop formed by the meeting of several others reached approximately a third of an inch in diameter. He then pours drqas of water in essence of clove, a liquid whose density is very little higher than that of water, and these drqas, which reach the top of the ambient liquid, show him in the same way a form very spherical when they are smaO, and slightly flattened when they reach about double the size of a pea. 

At all events, Segner, then applying to his deductions a clever method of calculation and experiment, arrives at this other result that, in drops formed of the same liquid, but having different shapes and dimensions, the tension has the same value, which corresponds to saying that it is independent of the curvatures this principle is also recognized true today. 

Deformation is the relative displacement of points of a body. It can be divided into two types flow and elasticity. Flow is irreversible deformation when the stress is removed, the material does not revert to its original form. This means that work is converted to heat. Elasticity is reversible deformation the deformed body recovers its original shape, and the appHed work is largely recoverable. Viscoelastic materials show both flow and elasticity. A good example is SiEy Putty, which bounces like a mbber ball when dropped, but slowly flows when allowed to stand. Viscoelastic materials provide special challenges in terms of modeling behavior and devising measurement techniques. 

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