Bubbles shape deformation

The comparison of the two figures shows that the characteristic bubble frequency for ground conditions is two times smaller than that for microgravity conditions. The most probable reason for the decrease of the characteristic bubble frequency under ground conditions is the bubble shape deformation due to gravity on which the characteristic frequency strongly depends. 

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... 

The history of these large bubbles after release is interesting. A stretched vapor filament is the last part of a bubble to break from the hot solid. The filament contracts rapidly, because of surface tension, and rams into the main body of the bubble. The bubble shape is distorted by the impact, becoming umbrellalike. The deformed surface then snaps back down, and the bubble vibrates as it rises. The true shape of rising, large bubbles is evident in Fig. 10. 

One complication is that the boundary conditions (4-264)-(4-266) must be applied at the bubble surface, which is both unknown [that is, specified in terms of functions R(t) and fn(9,tangent unit vectors n and t, that appear in the boundary conditions are also functions of the bubble shape. In this analysis, we use the small-deformation limit s 1 to simplify the problem by using the method of domain perturbations that was introduced earlier in this chapter. First, we note that the unit normal and tangent vectors can be approximated for small e in the forms... 

Thus, for each deformation mode k, there are a discreet set of frequencies for which the bubble shape is unstable. This is consistent with the stability diagram in Fig. 4-17 for the limit eb -> 0. 

One other aspect of the present problem to reconsider is the bubble shape. So far in this section we have assumed that the bubble is exactly spherical. However, in general we would expect a bubble to deform in a flow, and we have shown earlier that the shape can be determined from the normal-stress condition,... 

Closer examination of (10-291) shows that the bubble is deformed into an oblate ellipsoid of revolution. A sketch of the bubble shape for several small values of We is given in Figure 10-12. 

The dynamic interaction between flow and drops and bubbles floating in the flow may deform or even destroy them. This phenomenon is important for chemical technological processes since it may change the interfacial area and the relative velocity of phases and cause transient effects. In this case, the viscous and inertial forces are perturbing actions, and the capillary forces are obstructing actions. The bubble shape depends on the Reynolds number Re = aeU,p/p and the Weber number We = aeU2p/cr, where p, and p are the dynamic viscosity and the density of the continuous phase, a is the surface tension coefficient, and ae is the radius of the sphere volume-equivalent to the bubble. 

Let us consider the motion of a gas bubble at high Reynolds numbers. For small We, the bubble shape is nearly spherical. The Weber numbers of the order of 1 constitute an intermediate range of We, very important in practice, when the bubble, though essentially deformed, conserves its symmetry with respect to the midsection. For such We, the bubble shape is well approximated by an ellipsoid with semiaxes a and b = xa oblate in the flow direction the semiaxis b is directed across the flow, and x 1 ... 

Drops and especially bubbles show deformation and shape fluctuations with increasing size of the fluid particles, and these deviations from spheres become stronger with increasing size of the fluid particles and with increasing data of the parameter t]/ rj and - A/ - g)/cr. In Fig. 3.6-4 a qualitative survey of possi-... 

Kelbaliyev, G. and Ceylan, K., Development of new empirical equations for estimation of drag coefficient, shape deformation, and rising velocity of gas bubbles ot liquid drops. Chem. Eng. Commun. 194, 1623-1637, 2007. 

In ellipsoidal shape regime, the bottom of the upper bubble deforms under the influence of the lower bubble, thus, making it possible to preserve a thin liquid film between the bubbles. The upper bubble develops a dimpled-ellipsoidal rather than an ellipsoidal shape. When the bottom of the upper bubble cannot deform any more, the liquid film between the bubbles starts getting thinner, and, finally, the lower bubble merges with the upper one. 

It was found that finite Marangoni number effects, representing the convection of energy, at small Reynolds number had a negligible effect on the bubble shape. However, finite Reynolds number effects caused sufficient deformation to significantly retard the bubble. 

Relatively large bubbles with low excess pressure are likely to behave as if they were closed, whereas the reverse should hold true for very small bubbles. Thus, upon increasing the bubble size, a transition takes place from instability to practically complete stability. Invoking shape deformations will not necessitate any major modifications of the above discussion as the spherical shape is always associated with minimal free energy for a given bubble volume. 

Consider two bubbles pressed into contact by body forces F. The force F represents the sum of body forces, such as gravity, and the net force imposed by other contacting bubbles. We assume that the deviation from a spherical shape is small and that the bubble s deformed shape is a truncated sphere [16] see Figure 12.7a. Deformed bubbles do not, in fact, assume this shape the sharp corner at the edge of the thin film, in particular, is unrealistic. Nevertheless, the anszatz suffices to give an approximate idea of the elastic interaction between bubbles of similar size. 

Eoj — 0.0204Eod + 0.474. The lift coefficients obtained with this closure yield values between 0.29 and change sign once bubbles start to deform (Bod 6). Usually, a constant virtual mass constant of Cvm = 0-5 is used. However, Tomiyama (2004) also proposed virtual mass coefficients that account for the bubble shape. To our knowledge, only very few researchers have actually appHed these closures for the virtual mass force though. 

The calculation of the strain and stress from the bubble shape data depends on the deformation theory chosen. The plate theory is valid when the deformation is small compared with the film thickness. In this case, the film deforms mainly by bending. This will occur when the pressure applied is small or the film thickness is large compared with the hole diameter or the material is in the glassy state. For a clamped sample, the deflection as a function of radial position is given as [9] ... 

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). 

Two wooden beams are butt-jointed using an epoxy adhesive (Fig. A1.3). The adhesive was stirred before application, entraining air bubbles which, under pressure in forming the joint, deform to flat, penny-shaped discs of diameter 2fl = 2 mm. If the beam has the dimensions shown, and epoxy has a fracture toughness of 0.5 MN mT , calculate the maximum load F that the beam can support. Assume K = cT Tra for the disc-shaped bubbles. 

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. 

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