Two-dimensional bubbles

Lin TJ, Reese J, Hong T, Fan LS. Quantitative analysis and computation of two-dimensional bubble columns. AIChE J 1996 42 301-318. 

Figure 9.8. (a) An NO2 bubble rising in a two-dimensional ballotini bed showing the cloud region of the bubble (b) A two-dimensional bubble rising through a layer of black particles showing the bubble wake in a gas-solid fluidized bed (from Rowe, 1971 reproduced with permission). 

In this section a criterion will be developed for the case of a two-dimensional bubble column. A schematic diagram of the column with the coordinate system is shown in Fig. 31. The criterion will be developed for the continuous mode of operation. The criterion for batch operation will be a special case of the criterion for the continuous mode of operation, in the limiting case of superficial liquid velocity becoming zero. 

Thus, Eqs. (94)-(99) describe the dynamics of gas-liquid dispersion in a two-dimensional bubble column. 

Following a procedure analogous to that used in derivation of the stabihty criterion for two-dimensional bubble columns, the stability criterion for cyhndrical bubble columns is given as... 

If the adsorption equilibrium is not attained instantaneously, a different analysis is needed. Toei et al. (T18) studied the mechanism of heat and mass transfer between bubbles and emulsion phase under such circumstances. The dependence of diffusion rate on bulk flow across the bubble interface also becomes important when coarse particles are fluidized (H16). For two-dimensional bubbles Chavarie and Grace (C7a) compared various interphase mass-transfer models. 

To illustrate application of the Eulerian-Eulerian approach, some results of two-dimensional bubble columns are discussed here. Three-dimensional bubble columns and other reactor engineering applications are discussed in Section 11.3. 

There is no solids in a gas bubble. A three-dimensional bubble is spherical, whereas a two-dimensional bubble is cylindrical. 

Abstract. Propagation of capillary waves along the surface of water covered by a homogeneous insoluble film has been a subject of numerous experimental and theoretical studies. However, it has been shown only recently that real surface films contain two-dimensional aggregates, which influence the characteristics of surface waves. The problem of multiple scattering of surface waves by two dimensional viscoelastic particles is considered briefly below. The results can be compared with the experimental data for condensed films with two-dimensional bubbles of gaseous phase. 

Diaz, M.E., Montes, F.J., and Galan, M.A. (2008), Experimental study of the transition between unsteady flow regimes in a partially aerated two-dimensional bubble column, Chemical Engineering and Processing Process Intensification, 47(9-10) 1867-1876. 

Agostino, L. Brennen, C.E. Acosta A.J. Linearised dynamics of two dimensional bubble and cavitating flows over slender surfaces. 

Walters, J.K. and J.F. Davidson, 1962, The initial motion of a gas bubble formed in an inviscid liquid. Part 1. The two-dimensional bubble. J. Fluid Mech. 12,408-417. 

In a follow-up attempt. Sit and Grace (1978) derived the following equations to include the diffusive mechanism in the expression. For a circular two-dimensional bubble, the equation has the form... 

Shnip AI, Kolhatkar RV, Swamy D, Joshi JB. Criteria for the transition from the homogeneous to the heterogeneous regime in two-dimensional bubble column reactors. Int J Multiphase Flow 18 705-726, 1992. 

Figure 4.7. (a) The two-dimensional bubble raft mode of the indentation process. (b)The amorphous layer disrupted and sticking to the indenter face. Taken from reference (7). 

All of these two dimensional bubble raft demonstrations simulate the arrangement of atoms in crystalline materials. Dislocations, lattice defects, grain boundaries and recrystallization are all phenomena that occur in three dimensional crystalline materials. 

Hysing, S., Turek, S., Kuzmin, D., Parolini, N., Burman, E., Ganesan, S., et al. (2009). Quantitative benchmark computations of two-dimensional bubble dynamics. International Journal for Numerical Methods inFluids, 60, 1259-1288. doi 10.1002/fld.l934. 

---