Deformed bubble

In system 1, the 3-D dynamic bubbling phenomena in a gas liquid bubble column and a gas liquid solid fluidized bed are simulated using the level-set method coupled with an SGS model for liquid turbulence. The computational scheme in this study captures the complex topological changes related to the bubble deformation, coalescence, and breakup in bubbling flows. In system 2, the hydrodynamics and heat-transfer phenomena of liquid droplets impacting upon a hot flat surface and particle are analyzed based on 3-D level-set method and IBM with consideration of the film-boiling behavior. The heat transfers in... 

Figure 18 Schematic of experimental setup for measurement of 3D bubble deformation and flow structure in the wake using the combination of PIV/LIF and double-SIT (a) schematic of the measurement system and (b) top view of the experimental facility (Fujiwara et al., 2004a).

In devolatilizing systems, however, Ca 1 and the bubbles deform into slender S-shaped bodies, as shown in Fig. 8.12. Hinch and Acrivos (35) solved the problem of large droplet deformation in Newtonian fluids. They assumed that the cross section of the drop is circular, of radius a, and showed that the dimensionless bubble surface area, A, defined as the ratio of the surface area of the deformed bubble A to the surface area of a spherical bubble of the same volume, is approximated by (36) ... 

Favelukis et al. (37,38) dealt with the problem of droplet deformation in exten-sional flow with both Newtonian and non-Newtonian Power Law model fluids, as wellas bubble breakup. For the Newtonian case, they find that as an inviscid droplet (or bubble) deforms, the dimensionless surface area is proportional to the capillary number... 

Bubble deformation in shear flow increases mass transfer because of the increase in surface area and because of convection. The latter brings volatile-rich liquid to the bubble surface. Favelukis et al. (39) studied the (identical but experimentally easier) reverse problem of dissolution of a gas bubble in a sheared liquid, both theoretically and experimentally, and they confirmed the increase of mass transfer with increasing shear rate. They also showed that the rate of dissolution, da/dt, where a is the equivalent radius of the bubble, is given by... 

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). 

Bubble Deformation A 5-mm radius bubble is placed in a viscous liquid of 0.2 lbf s/in2 and surface tension of 22 dyne/cm. Calculate the shape of the bubble, the half-length, and slenderness ratio of the bubble at shear rates 1, 10, and... 

To quantify the increase of a due to pressure, a mean bubble diameter has been estimated using Taylor s stability theory [7] on bubble deformation and break-up in sheared emulsions. According to this theory, bubble size in a sheared emulsion results from a balance between viscosity and surface tension forces. The dimensionless number that describes the ratio of these forces is called the capillary number Q. For large bubble deformations, the maximum stable bubble diameter in a shear flow is expressed as [8] ... 

Ryskin, G., and Leal, L. G., Numerical solution of free-boundaty problems in fluid mechanics. Part III, Bubble deformation in an axisymmetric straining flow. J. Fluid Mech. 148,37 (1984c). 

Figure 7.5. Marks produced in laser recording (a) shallow pit, (b) deep pit, (c) bubble deformation, and (d) optical property change.

For bubble (b) the Eotvos number is 6.24 and the Morton number is 6.31 X 10 . The bubbles have totally different motion depending on whether the bubble deforms or not. Bubble (a) does not deform significantly, and rotates with the flow as it rises, and eventually experiences a lift to the right. Bubble (b) deforms due to the shear and the upward motion. The bubble thus takes the form of an airfoil, and experiences lift to the left. The circulation of bubble (b) changes as the bubble deforms, and settles in the opposite direction of the circulation of bubble (a). 

For usual liquids like water, we have Mo 10 10, and one must take account of the bubble deformation starting from Re 102. (For oil, Mo 10-2, and the bubble deformation is essential even for low Reynolds numbers.)... 

For common fluids such as water, one must take into account the bubble deformation starting from Re 102, where Re = atU /u is the Reynolds number and v is the kinematic viscosity. 

These relationships are important in examining and interpreting the rate of mass transfer in solid/liquid, gas/liquid, and liquid/liquid systems and in examining droplet and bubble deformation and break-up in liquid/liquid and gas/liquid systems respectively. More details on these concepts can be found in subsequent chapters. 

The first parameter, the Strouhal s number, is a measure of non-stationarity of the process. At St 1 or t L/U the first term in the left part of (5.107)-(5.109) can be neglected. At that, the flow can he considered as stationary. In this connection it is necessary to notice, that there are problems in which the time-dependence can exist at the boundary, for example in problems with time-varying interface (drops or bubbles deformation, surface waves in liquid etc.). In this case the bulk flow can be assumed stationary everywhere except for a thin layer near a surface. This kind of a problem is called sometimes the quasi-stationary problem. 

Surface tension is a liquid property that tends to counter bubble deformation and encourages bubble breakup (Akita and Yoshida, 1974 Mehmia et al 2005 Walter and Blanch, 1986). The result is a more stable bubble interface that leads to smaller bubble diameters, a more stable flow regime (Lau et al., 2004 Schafer et al., 2002), and higher gas holdups and interfacial areas (Kluytmans et al., 2001). It is also thought that a lower surface tension leads to a higher contact time because the liquid flow over the bubble surface is slowed (Lau et al., 2004). 

Le6n-Becerril, E., Cockx, A., and Lind, A. (2002), Effect of bubble deformation on stability and mixing in bubble columns, Chemical Engineering Science, 57(16) 3283-3297. 

The lattice Boltzmann method (LBM) has been a very active mesoscopic numerical tool for fluid flow simulations since the late 1980s [4]. Recently, it has been developed to complex flows, including acoustic-fluid interaction, elec-trokinetic flows in complex geometries, red blood cells or bubble deformations in shear flows, and... 

The finite difference numerical simulation was carried out by solving the Euler equations by the Lagrangian approach. The DANE code was used for computation. The air bubble radius was 1.0 mm and the shock overpressure was 1 kbar. Computational grids were, in the axlsymmetric Cartesian coordinates, 150 x 300 and one grid size was 0.025 mm. Figure 5 shows the sequential isobars. It is clearly seen that the peak pressure appear on the side where the shock first impinged the bubble, and the bubble deformation starts which indicates the microjet initiation. However, the rebound shock is so weak that, if compared with the incident shock, the wave front could not be resolved in this numerical scheme. 

It is found that through the complicated wave interaction, the incident shock energy was in part absorbed by reflected expansion wave, rebound shock wave and then the bubble deformation, and the incident shock wave is significantly attenuated. The present study has been done under an idealized condition. Therefore, more works have to be done in the future with combining various parameters such as shock overpressures and the size and number of bubbles. 

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. 

In many situations, bubbles move through nonuniform flows. The flows may be either laminar or turbulent. For bubbles in sufficiently strong flows, the buoyancy of the bubble may be negligible or have a small effect on the motion of the bubble. In general, such problems are extremely difficult because one must account for bubble deformation and the disturbance created by the bubble and one must make use of empiricism to develop an approximate equation governing the motion of a bubble. However, for sufficiently small bubbles, approximate equations of motion have been developed that account for the deviation of the bubble trajectory from the path of a fluid particle due to buoyancy, fluid inertia, finite size effects, and related phenomena. We will first consider this regime. 

Rheological properties of foams (elasticity, plasticity, and viscosity) play an important role in foam production, transportation, and applications. In the absence of external stress, the bubbles in foams are symmetrical and the tensions of the formed foam films are balanced inside the foam and close to the walls of the vessel [929], At low external shear stresses, the bubbles deform and the deformations of the thin liquid films between them create elastic shear stresses. At a sufficiently large applied shear stress, the foam begins to flow. This stress is called the yield stress, Tq- Then, Equation 4.326 has to be replaced with the Bingham plastic model [930] ... 

Figure 8. Bubble deformation in gel specimen in the central part of the cuvette Nl(at the scale ofltoO. 75)...

Figure 6.2 illustrates the force balance acting on a bubble on an inclined surface. When the solid substrate is tilted (with a tilt angle of a), the bubble deforms due to the net vertical force (Figure 6.2a). In this case, the A in Equations (6.3) and (6.4) represents the horizontally projected surface area of the bubble base, i.e., A=(nw /4)cosa. If the net vertical force in the tangential direction sina) is as large as the adhesion (or static...

Fig. 9 Bubble coalescence. 1 Simultaneous injection of two air bubbles Ki = 3,5ml and 2 = 9.3 ml in the 1.0 mass % polyacrylamide solution described in Fig. 1. The initial separation between the bubbles is 24 mm. 2 A 1.0-ml bubble moves into the wake of a 4.7-ml bubble. The initial separation between the bubbles was 9 mm. The fluid is again the 1.0 mass % polyacrylamide solution. 3 Bubble contact for the system in frame 2. 4 Bubble deformation and capture following a three-bubble injection in a 1.0 mass % aqueous carboxymethyl cellulose solution. The bubbles all had a volume of 7.5 ml and their initial separation was 30 mm. (From Dajan, 1985.)...

A modification of this scenario would be a nanobubble-coated surface, that is, a heterogeneous two-phase depletion layer. " However, as it has been discussed yet in, nanobubbles will reduce the viscosity of the surface layer only if surface tension is small enough (which means that the bubbles deform). If the shape of the nanobubbles will remain a spherical lens, rjg should exceed the bulk viscosity. There remains still an open question connected with the exact expression for the effective viscosity of the layer of surface nanobubbles. 

Figure 8.5 Illustration of the forces connected to bubble deformation. Arrows indicate deformation-induced pressure. Upon shearing a hemispherical bubble, a Laplace pressure of magnitude y x A[l/r] develops at the deformed surfaces. Here 1/r is the curvature and A[l/r] is the shear-induced change in curvature. For a given shear deformation, the change in curvature is proportionai to the curvature in the undeformed state. The Lapiace stress wiii significantiy deviate the flow whenever y/r is comparabie the shear stiffness of the liquid, which is o r]. With r] 10 Pa.s, (o 2jt S MHz, and y 72 x 10 N/m, one finds that shear-induced Lapiace pressure matters when the radius is less than about a micron.

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