Vapour bubble, spherical

The following considerations hold for the equilibrium of a vapour bubble, assumed to be spherical, Fig. 4.33, with the liquid surrounding it. Between the gaseous bubble (gas = index G) and the surrounding liquid (liquid = index L), thermal equilibrium exists... 

If a surface element of the spherical shell is cut out of the vapour bubble, as depicted in the right hand side of Fig. 4.33, with side lengths r dp, the forces ar dp exerted by the surface tension a (a is force per unit length) act upon the edges. The resultant FR of these forces is given by... 

Fig. 4.33 Mechanical Equilibrium between a spherical vapour bubble and the liquid surrounding it...

Fig. 4.34 Vapour and liquid pressure between a liquid and a spherical vapour bubble...

H. S. Lee and H. Merte, Spherical Vapour Bubble Growth in Uniformly Superheated Liquids, Int. J. Heat Mass Transfer (39) 2427-2447,1996. 

Fet us consider a spherical bubble of vapour inside its coexisting liquid. Again the gas phase is assumed to be ideal, and eq. (6.52) becomes... 

The circulation and bubble tubes are vertical apparatuses with vapour jackets. The reactors are vertical cylindrical apparatuses with spherical welded bottoms and removable lids (with cylindrical baskets" with cationite KU-23 or askanite. The reactors are fashioned with capacitance moisture indicators. To moisturise cationite or ascanite, the apparatus is filled with live steam. The separators are vertical cylindrical apparatuses with conical bottoms and removable spherical lids. The reactors and separators operate under 0.02 MPa. 

In bubble flow, Fig. 4.44 a, the gas or vapour phase is uniformly dispersed in the continuous liquid phase. Only very small bubbles are spherical the larger ones are oblate. This type of flow pattern occurs when the gas fraction is small. In plug flow, Fig. 4.44 b, large bubbles (plugs) almost fill the entire tube cross section. Between the plugs, the liquid is interspersed with small bubbles. 

The nucleation barrier is easy to formulate considering that the created gas-liquid interface related to bubble nucleation increases the system energy by 27ir (r is the radius of the spherical bubble, and y is the liquid-vapour surface tension), while the formation of the most stable phase provides bulk energy (4/37ir AP, with AP = Pliquid - Pvapour) According to the CNT, the competition between these two opposite effects results in an energy barrier... 

The presently most powerful technique for obtaining the liquid-vapour or liquid-liquid interfacial tension is based on the shape of a drop or bubble. In essence, the shape of a drop or bubble is determined by balance of surface tension and gravity effects. Surface forces tend to make drops spherical whereas gravity tends to elongate a pendant drop or buoyant bubble. Fig. 26 shows the schematic of an experimental set-up (for details see Chen et al. 1998, Loglio et al. 2001). 

For polymers interfacial and surface tensions are more practically obtainable from analysing the shapes of pendant or sessile drops or bubbles, all of which are examples of axisymmetrical drops. Bubbles may be used to obtain surface tensions at liquid/vapour interfaces over a range of temperatures and for vapours other than air. Drops can also be used to obtain vapour/liquid surface tensions but they are particularly suited to determination of liquid/liquid interfacial tensions, for example for polymer/polymer interfaces. All the methods are based on the application of equation (2.2.1). The principles are illustrated in figure 2.4, in which a sessile drop is used as the specific example. Just like for the capillary meniscus, the drop has two principal radii of curvature, R in the plane of the axis of symmetry and / 2 normal to the plane of the paper. At the apex, O, the drop is spherically symmetrical and R = Rz = b and equation (2.2.12) becomes... 

Heretofore we have only addressed the properties of planar interfaces. For a curved surface, the radius of curvature affects the interfacial properties, in particular the interfacial profile and the surface tension. Consider a spherical bubble of vapour surrounded by liquid. In this case, the Laplace equation relates the pressure difference between inside the droplet and outside the droplet to the surface tension and the radius of curvature R as Ap = 2a/R. The curvature-dependent surface tension can be expanded in powers of the curvature as... 

The anti-bubbles are intrinsically unstable. The shell of air is contained between two spherical surfaces of fluid, one being convex and the other concave. The saturated vapour pressure of the inner surface is larger than the outer one. This will lead to evaporation from the inner sphere of fluid and condensation on the other concave surface of fluid. Also the film of air is intrinsically unstable against draining . 

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