Deformation of bubbles

Furthermore, Fujiwara et al. (2004a) performed an experimental study using PIV/LIF combining with double-SIT to construct approximated 3D shape deformation of bubbles as well as to investigate quantitatively the 3D wake flow structures behind bubbles in a simple shear flow. The... 

In order to clarify the conditions which determine the mechanical equilibrium of films, the contact of three gas bubbles in a surfactant solution (Fig. 1.6,a) is to be considered. When three bubbles get into contact simultaneously, they shift to assume positions determined by the capillary pressure and surface tension. At the place of contact of two bubbles a circular film is formed and its size increases with further deformation of bubbles. 

Surface active agents (surfactant) are either present as impurities that are difficult to remove from a system or they are deliberately added to fluid mixtures to manipulate interfacial flows. It has been well known that the presence of surfactant in a fluid mixture can critically alter the motion and deformation of bubbles moving through a continuous liquid phase. Probably, the best-known example is the retardation effect of surfactant on the buoyancy-driven motion of small bubbles. Numerous experimental studies have shown that the terminal velocity of a contaminated spherical bubble is significantly smaller than the classical Hadamard-Rybczynski prediction... 

Unlike the original flotation whose elementary act is complicated by an inertia impact and the accompanying deformation of bubble surface, microflotation is completely a colloid chemical process and it can be described in terms of modem colloid chemistry as orthokinetic heterocoagulation (Deijaguin Dukhin, 1960). 

The second method for measuring dilational elasticity and viscosity is based on rotation, translation or deformation of bubbles and droplets [52], Agrawal and Wasan [57] have suggested that the translational velocity of bubbles or droplets in a quiescent liquid might be used to determine the apparent dilational viscosity. Unfortunately, this simple method is not suitable since the settling velocity is not sensitive enough to the magnitude of the apparent surface viscosity. Wei et al. [58]... 

Tsukada, T., H. Mikami, M. Hozawa, and N. Imaishi, Theoretical and experimental studies of the deformation of bubbles moving in quiescent Newtonian and non-Newtonian liquids, J. Chem. Eng. Jpn. 25 192 (1990). 

The elasticity ( ) is related to changes in the surface tension (y), caused by deformation of bubble walls E = 2A.dy/dA, where A = surface area. 

HF Fibre arrangement Deformation of bubbles Deformation of bubbles (non-circular shape) was found due to the flow channel confinement Higher mixture velocities were observed in the flow channels without fibres The deformation of bubbles was affected by module design such as air sparger and the local fibre arrangement Buetehorn (2010)... 

Flow Past Deformable Bodies. The flow of fluids past deformable surfaces is often important, eg, contact of Hquids with gas bubbles or with drops of another Hquid. Proper description of the flow must allow for both the deformation of these bodies from their shapes in the absence of flow and for the internal circulations that may be set up within the drops or bubbles in response to the external flow. DeformabiUty is related to the interfacial tension and density difference between the phases internal circulation is related to the drop viscosity. A proper description of the flow involves not only the Reynolds number, dFp/p., but also other dimensionless groups, eg, the viscosity ratio, 1 /p En tvos number (En ), Api5 /o and the Morton number (Mo),giJ.iAp/plG (6). 

I, have a fairly broad distribution of bubble sizes and can therefore maintain spherical bubbles with significantly less Hquid. Empirically, foams with greater than about 5% Hquid tend to have bubbles that are stiH approximately spherical, and are referred to as wet foams. Such is the case for the bubbles toward the bottom of the foam shown in Figure 1. Nevertheless, it is important to note that even in the case of these wet foams, some of the bubbles are deformed, if only by a small amount. 

The alternative option for counteracting cavitation damage is the use of a resilient material such as rubber. The mechanical forces attendant on collapse of the bubbles are absorbed by elastic deformation of the resilient material. 

Dispersed bubbly flow (DB) is usually characterized by the presence of discrete gas bubbles in the continuous liquid phase. As indicated in Fig. 5.2, for the channel of db = 2.886 mm, dispersed bubbles appeared at a low gas superficial velocity but a very high liquid superficial velocity. It is known that for large circular mbes dispersed bubbles usually take a sphere-like shape. For the triangular channel of dh = 2.886 mm, however, it is observed from Fig. 5.2 that the discrete bubbles in the liquid phase were of irregular shapes. The deformation of the gas bubbles was caused by rather high liquid velocities in the channel. 

Rallison, J. M., The deformation of small viscous drops and bubbles in shear flows. Ann. Revs. Fluid Mech. 16, 45-66 (1984). 

The most common cause of it is the neglect of 3-dimensional effects as compared with those in two dimensions. Thus, all stresses in a loaded wire or ribbon are disregarded in the shrinkage method, Section III. 1. The work of deformation leading to rupture is a bulk effect which does not receive its due consideration in the calculation of fracture energy, Section III.3. Bulk deformations associated with thermal etching, Section III.4, demand more attention than was alloted to them by many scientists. The method of bubbles, Section III.5, is invalid both because of the above neglect (that is, that of the volume stresses around the bubble) and because of another popular error, namely an erroneous treatment of capillary pressure Pc. 

There is considerable evidence (D3, G7, PI, P4, SI) that bubbles in liquid metals show the behavior expected from studies in more conventional liquids. Because of the large surface tension forces for liquid metals, Morton numbers tend to be low (typically of order 10 ) and these systems are prone to contamination by surface-active impurities. Figure 8.10a shows a two-dimensional nitrogen bubble in liquid mercury. For experimental convenience, the bubbles studied have generally been rather large, so that there are few data available for spherical or slightly deformed ellipsoidal bubbles in liquid metals. Data... 

A horizontal interface between two fluids such that the lower fluid is the less dense tends to deform by the process known as Rayleigh-Taylor instability (see Section UFA). Spikes of the denser fluid penetrate downwards, until the interface is broken up and one fluid is dispersed into the other. This is observed, for example, in formation of drops from a wet ceiling, and of bubbles in film boiling. For low-viscosity fluids, the equivalent diameter of the particle formed is of order Ja/gAp. 

In order to understand the basis for the prevention of bubble coalescence and hence the formation of foams, let us examine the mechanical process involved in the initial stage of bubble coalescence. The relatively low Laplace pressure inside bubbles of reasonable size, say over 1 mm for air bubbles in water, means that the force required to drain the water between the approaching bubbles is sufficient to deform the bubbles as illustrated in Figure 8.2. The process which now occurs in the thin draining film is interesting and has been carefully studied. In water, it appears that the film ruptures, joining the two bubbles, when the film is still relatively thick, at about lOOnm thickness. However, van der Waals forces, which are attractive in this system (i.e. of air/water/air), are effectively insignificant at these film thicknesses. 

Kinsella (13, 14) summarized present thinking on foam formation of protein solutions. When an aqueous suspension of protein ingredient (for example, flour, concentrate, or isolate) is agitated by whipping or aeration processes, it will encapsulate air into droplets or bubbles that are surrounded by a liquid film. The film consists of denatured protein that lowers the interfacial tension between air and water, facilitating deformation of the liquid and expansion against its surface tension. 

Finally, another equibiaxial deformation test is carried out by blowing a bubble and measuring the pressure required to blow the bubble and the size of the bubble during the test, as schematically depicted in Fig. 2.52. This test has been successfully used to measure extensional properties of polymer membranes for blow molding and thermoforming applications. Here, a sheet is clamped between two plates with circular holes and a pressure differential is introduced to deform it. The pressure applied and deformation of the sheet are monitored over time and related to extensional properties of the material. 

The formation of assymetric cavities on the metal surface is a direct result of destruction of the low-life bubbles near the surface. As a result of the cavitation, the deformation of surface takes place, together with fragmentation and decrease of size of appearing particles. 

Fig. 8.12 Deformation of a bubble in simple shear flow at Ca 3> 1. R(x) is the bubble radius as a function of coordinate x L is the half-length of the bubble a is the inclination angle and y = r (x) is the position of the bubble centerline.

E. L. Canedo, M. Favelukis, Z. Tadmor, and Y. Talmon, An Experimental Study of Bubble Deformation in Viscous Liquids in Simple Shear Flow, AIChE J., 39, 553 (1993). 

If a sample shows elastic, solid-like deformation below a certain shear stress ay and starts flowing above this value, ay is called a yield stress value. This phenomenon can occur even in solutions with quite low viscosity. A practical indication for the existence of a yield stress value is the trapping of bubbles in the liquid Small air bubbles that are shaken into the sample do not rise for a long time whereas they climb up to the surface sooner or later in a liquid without yield stress even if their viscosity is much higher. A simple model for the description of a liquid with a yield stress is called Bingham s solid ... 

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