Dimple drops

For systems in which skirt formation can occur and is slightly less than required for skirt formation, large bubbles or drops tend to be indented at the rear. Skirt formation occurs when viscous forces acting at the rim or corner of the dimpled bubble or drop are strong enough to overcome interfacial tension forces and pull the rim out into a thin sheet (B3, H5, Wl, W5). The onset of skirts is dependent both on the ratio We/Re = fiUj/a, sometimes called a capillary or skirt number, and on Re. Figure 8.4 shows data for the transition from unskirted to skirted bubbles or drops. For bubbles, skirts exist for Re > 9 and... 

When two emulsion drops or foam bubbles approach each other, they hydrodynamically interact which generally results in the formation of a dimple [10,11]. After the dimple moves out, a thick lamella with parallel interfaces forms. If the continuous phase (i.e., the film phase) contains only surface active components at relatively low concentrations (not more than a few times their critical micellar concentration), the thick lamella thins on continually (see Fig. 6, left side). During continuous thinning, the film generally reaches a critical thickness where it either ruptures or black spots appear in it and then, by the expansion of these black spots, it transforms into a very thin film, which is either a common black (10-30 nm) or a Newton black film (5-10 nm). The thickness of the common black film depends on the capillary pressure and salt concentration [8]. This film drainage mechanism has been studied by several researchers [8,10-12] and it has been found that the classical DLVO theory of dispersion stability [13,14] can be qualitatively applied to it by taking into account the electrostatic, van der Waals and steric interactions between the film interfaces [8]. 

Chapter 7, Reactor Design, discusses continuous and batch stirred-tank reactors and die packed-bed catalytic reactor, which are frequently used. Heat exchangers for stirred-tank reactors described are the simple jacket, simple jacket with a spiral baffle, simple jacket with agitation nozzles, partial pipe-coil jacket, dimple jacket, and the internal pipe coil. The amount of heat removed or added determines what jacket is selected. Other topics discussed are jacket pressure drop and mechanical considerations. Chapter 7 also describes methods for removing or adding heat in packed-bed catalytic reactors. Also considered are flow distribution methods to approach plug flow in packed beds. 

The coalescence process can be described by two steps. At first, there is a mutual approach of the drops which is controlled by the rheological properties of the continuous (organic) phase (see Figure 4a). Secondly, a flattening of the droplets appears by the formation of a so called "dimple" (see Figure 4b). The decrease in distance d is determined by the rate of flow out of the continuous phase between the droplets (14,15). A thin film is formed which decreases to a certain critical film thickness, dcrit at which point approach stops (16). 

FIGURE 5.36 Main stages of formation and evolution of a thin liquid film between two bubbles or drops (a) mutual approach of slightly deformed surfaces (b) at a given separation, the curvature at the center inverts its sign and a dimple arises (c) the dimple disappears, and eventually an almost plane-parallel film forms (d) due to thermal fluctuations or other disturbances the film either ruptures or transforms into a thinner Newton black film (e), which expands until reaching the final equilibrium state (f). 

When a certain small separation, h, the inversion thickness, is reached, the sign of the curvature in the contact of the fluid particles (drops, bubbles) changes. A concave lens-shaped formation called a dimple is formed (see Frankel and Mysels" ). This stage is also observed for asymmetric fllms." A number of theoretical studies have described the development of a dimple at the initial stage of film thinning The inversion thickness can be calculated from a simple equation in which the van der Waals interaction is explicitly taken into account (see Section 5.4.2)i 4,43i,465... 

PS/PE ties behave differently fi om wood. When new wood ties are installed in a rail bed of crushed rock, trains passing over the ties press the ties into the rock, creating dents that lock the ties in place. Plastic ties, however, do not dent so readily. Plywood embosses the sides and bottom of its ties with dimples to give the rocks a grip. Oddly, the mechanical properties of Poly wood s ties have been shown to improve over time. Compressive modulus for a Polywood tie is 2600 psi when new and 3100 psi after 20 years simulated aging. New wood ties start at 3200 psi and drop to 1000 psi after aging. 

The physical importance of these results is related to the fact that the coalescence of drops at the early highly dynamic stages of emulsion production is expected to be sensitive to the degree of saturation of the newly created interfaces with surfactant, and correspondingly, to the relaxation time of surfactant adsorption. The surfactant transport is especially important when the emulsion is prepared from nonpre-equilibrated liquid phases. In such cases one can observe dynamic phenomena like the cyclic dimpling (59, 60) and osmotic swelling (61), which bring about additional stabilization of the emulsions (see also Refs 1 and 62). 

Let US consider two spherical emulsion drops approaching each other, which interact through the van der Waals attractive surface force. Sooner or later interfacial deformation will occur in the zone of drop-drop contact. The calculations (138) show that, if the drop radius a is greater than 80 jm, the drop interfaces bend inwards (under the action of the hydrodynamic pressure) and a dimple is formed in the contact zone soon the dimple transforms into an almost plane-parallel film (Fig. 2D). In contrast, if the drop radius... 

Pressure drop in conventional jackets without spiral baffles and dimple jackets are deliberately excluded from this procedure. Other sources should be consulted for these applications. 

For either a dimple jacket design or a half pipe jacket, the pressure drop will be higher flian that of an equivalent conventional jacket, due to flie increased turbulence. 

FIGURE 9.25. Deposition of drops at a glass/elastomer interface by (a) injection (water) or (b) dewetting (PFAS). A film (1) squeezed between a rubber marble and glass thins down (2) and dewets (3). Note the dimple formed during drainage (2) ... 

Brake forming Dimpling Beading Drop hammer Rubber press Sheet stretching... 

---