Bubbles cylindrical

Fuel-pair mixtures, in soap bubbles ranging from 4 to 40 cm diameter and with no internal obstacles, produced flame speeds very close to laminar flame speeds. Cylindrical bubbles of various aspect ratios produced even lower flame speeds. For example, maximum flame speeds for ethylene of 4.2 m/s and 5.5 m/s were found in cylindrical and hemispherical bubbles, respectively (Table 4.1a). This phenomenon is attributed to reduced driving forces due to the top relief of combustion products. 

Obstacles introduced in unconfined cylindrical bubbles resulted only in local flame acceleration. Pressures measured at some distance from the cylindrical bubble were, in general, two to three times the pressure measured in the absence of obstacles. 

The reversal area is the area of the cylindrical vertical plane between the top of the riser and the underside of the bubble cap through which the incoming vapor must pass. The vapor then moves into the annulus area between the inside diameter of the cap and the outside diameter of the riser before entering the slots in the cap. 

Yoshitome et al. (Y2) examined mass transfer from single samples of benzoic acid suspended in an air-water bubble-column. Spherical, cylindrical, and disk-shaped samples of diameters from 25 to 75 mm were used,... 

Kolbel et al. have published a series of studies of heat transfer from a cylindrical heating element suspended in bubble-columns with and without suspended solids (K14, K15, K19, M10). 

The gas core with a thick liquid film is also shown in Fig. 5.14a, the second channel from the top. It is seen from this figure that a liquid film formed at the side walls of the channel with a continuous gas core in which a certain amount of liquid droplets exist. The flow with elongated cylindrical bubbles may be referred to as slug flow (Fig. 5.14b, the third channel from the top). 

Fig. 6.18 Scheme of explosive boiling J micro-channel, 2 main area of visual observation, 3 ONB point, 4 elongated cylindrical bubble, 5 liquid in front of the bubble, 6 vapor, 7 liquid droplets and clusters. Reprinted from Hetsroni et al. (2005) with permission... 

Influence of Soluble Surfactants on the Flow of Long Bubbles Through a Cylindrical Capillary... 

In 1961 Bretherton solved the problem of a long gas bubble, uncontaminated by surface-active impurities, flowing in a cylindrical tube at low capillary numbers, Ca /xU/a (/x is the... 

Figure 2. Flow of a single gas bubble through a liquid-filled cylindrical capillary. The liquid contains a soluble surfactant whose distribution along the bubble interface is sketched.

In this section we illustrate how the proposed theory for single, surfactant-laden bubbles in a cylindrical tube can be extended to predict the hydrodynamic resistance of bubble trains flowing in porous media. Some of the basic ideas are known (7, 23), so the present discussion is brief. 

The effect of a soluble surfactant on the flow of long bubbles in a cylindrical tube has been quantified when the surfactant... 

The surface tension is of great importance when dealing with bubbles and particulate contaminations in microchannels and determining how strong the capillary forces are in a microchannel. For a cylindrical cross-section, the capillary force, Fcap, can be expressed quantitatively as shown in the following equation,... 

White, E.T. and Beardmore, R.H., The velocity of rise of single cylindrical air bubbles through liquids contained in vertical tubes, Chemical Engineering Science, 17, pp. 351-61 (1962). 

Resistance functions have been evaluated in numerical compu-tations15831 for low Reynolds number flows past spherical particles, droplets and bubbles in cylindrical tubes. The undisturbed fluid may be at rest or subject to a pressure-driven flow. A spectral boundary element method was employed to calculate the resistance force for torque-free bodies in three cases (a) rigid solids, (b) fluid droplets with viscosity ratio of unity, and (c) bubbles with viscosity ratio of zero. A lubrication theory was developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions were derived to accurately represent the numerical data over the entire range of particle positions in a tube for all particle diameters ranging from nearly zero up to almost the tube diameter. The resistance functions formulated are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels. 

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