Drops break

The degree of deformation and whether or not a drop breaks is completely determined by Ca, p, the flow type, and the initial drop shape and orientation. If Ca is less than a critical value, Cacri the initially spherical drop is deformed into a stable ellipsoid. If Ca is greater than Cacrit, a stable drop shape does not exist, so the drop will be continually stretched until it breaks. For linear, steady flows, the critical capillary number, Cacrit, is a function of the flow type and p. Figure 14 shows the dependence of CaCTi, on p for flows between elongational flow and simple shear flow. Bentley and Leal (1986) have shown that for flows with vorticity between simple shear flow and planar elongational flow, Caen, lies between the two curves in Fig. 14. The important points to be noted from Fig. 14 are these ... 

In the second regime, by considering that one drop breaks into v - -1 droplets per unit time, the increase in the number of drops per unit time can be written as ... 

The previous experiments were all performed on dilute emulsions for which the dispersed phase represents 2.5 wt% of the emulsion. The results obtained for a concentrated emulsion with oil mass fraction equal to 75% sheared at 500 s and 3000 s are reported in Fig. 1.16 [156]. The primary emulsion was polydisperse with d = 57 am. The two previously described regimes still exist. The first regime is particularly efficient in reducing the diameter because one drop breaks into 160 droplets through the Rayleigh instability for an applied shear rate of 500 s (di( = 10.5 am) and into 6200 droplets for an applied shear rate of 3000 s ... 

The slow formation of a drop at a submerged circular orifice or nozzle will result in a drop size, predicted by equations for determining interfacial tension by the drop-weight method. At the instant a slowly forming drop breaks away from a nozzle, the force balance may be written... 

Above the critical value, the viscous shear stresses overrule the interfacial stresses, no stable equilibrium exists, and the drop breaks into fragments. For p > 4, it is not possible to break up the droplet in simple shear flow, due to the rotational character of the flow. Figure 7.23 also indicates that in shear flow, the easiest breakup takes place when the... 

The breakup or bursting of liquid droplets suspended in liquids undergoing shear flow has been studied and observed by many researchers beginning with the classic work of G. I. Taylor in the 1930s. For low viscosity drops, two mechanisms of breakup were identified at critical capillary number values. In the first one, the pointed droplet ends release a stream of smaller droplets termed tip streaming whereas, in the second mechanism the drop breaks into two main fragments and one or more satellite droplets. Strictly inviscid droplets such as gas bubbles were found to be stable at all conditions. It must be recalled, however, that gas bubbles are compressible and soluble, and this may play a role in the relief of hydrodynamic instabilities. The relative stability of gas bubbles in shear flow was confirmed experimentally by Canedo et al. (36). They could stretch a bubble all around the cylinder in a Couette flow apparatus without any signs of breakup. Of course, in a real devolatilizer, the flow is not a steady simple shear flow and bubble breakup is more likely to take place. 

In quasi-static conditions, it has been established both theoretically [7, 12] and experimentally [6, 12] that a drop breaks when the applied stress a overcomes the product of the critical capillary number Cacr and the Laplace pressure... 

Formation of a liquid thread, which eventually disintegrates by the formation of successive beadlike swellings and contractions along the length of the thread (symmetrical drop break-up)... 

Fig. 2. Typical drop break-up dynamics from an inkjet print head.

Polymer conformation within the solvent system in question also has an impact on both the ink viscosity and the cleanliness of drop break up. Some polymer chains have a tendency to fold in upon themselves, thus not entangling as much with other polymer chains in solution. These tend to break off well and not form satellites, whereas other polymers can form very twisted and entangled networks in solution. These very entangled polymer chains more often lead to what is termed "stringy break-up" and usually form the unwanted satellites. 

Provided that the drop is not too big and has therefore broken spontaneously in the beaker, and provided that the glass was free from airlines which would expand and relieve the internal stresses, then all attempts to break the Prince Rupert s drop will fail. If, however, the tail is broken off, the drop breaks, with an appreciable shock, into very small... 

Brown DE and Pitt K. Drop break-up in a stirred liquid-liquid contactor. In Proceedings of CHEMECA 1970, Melbourne and Sydney, 1970 83-97. 

It follows from this simple relationship that the vapor pressure over a convex surface is greater than over a planeJ ° Various interesting consequences arise from this fact. One, for example, is that water vapor will not condense in a totally dust-free environment for lack of nucleating centers. Another is that when mercury is spilled and the drops break down into very small microdroplets, the increased vapor pressure greatly augments the risks of toxic exposure to mercury. 

The final method discussed here is the drop time technique. At the critical size when a mercury drop breaks from the end of a capillary placed in an electrolyte solution, the weight of the drop is balanced by the interfacial tension forces so that... 

It is generally recognized that equation (10.3.5) is an approximate description of the condition for drop break away. However, this method can be used to obtain high-quality interfacial tension data provided one considers the more detailed description of the related physics. More details can be found in the work of Barradas and Kimmerle [6]. 

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