Drops turbulent dispersers

A. Maximum and Minimum Drop Size in Turbulent Dispersions... 

There is little work on direct determination of coalescence frequencies in a turbulent dispersion. Kuboi et al. (KI7) and Park and Blair (P4) have used high-speed cinephotography to directly observe and measure the drop coalescence frequencies in pipe flow and in an agitated vessel, respectively. The difficulty with this method is that only a few coalescences are observed at great expense of cine film after tedious/examination. Thus there is doubt regarding the statistical representation of coalescence in the dispersion from a small sample. 

Delichatsios and Probstein (D4-7) have analyzed the processes of drop breakup and coagulation/coalescence in isotropic turbulent dispersions. Models were developed for breakup and coalescence rates based on turbulence theory as discussed in Section III and were formulated in terms of Eq. (107). They applied these results in an attempt to show that the increase of drop sizes with holdup fraction in agitated dispersions cannot be attributed entirely to turbulence dampening caused by the dispersed phase. These conclusions are determined after an approximate analysis of the population balance equation, assuming the size distribution is approximately Gaussian. 

Luo, H. and Svendsen, H.F. (1996), Theoretical model for drop and bubble break-up in turbulent dispersions, AIChE J., 42, 1225-1233. 

The turbulent gas/liquid flow in baffled tanks with turbine stirrer can be predicted. A mathematical model has been developed for turbulent, dispersed G/L flow. The time-averaged two phase momentum equations were solved by using a finite volume algorithm. The turbulent stresses were simulated with a K-fi-model. The distribution of gas around the stirrer blades is predicted for the first time. This model also enables an a priori prediction of the drop in the power dissipated by the stirrer in the presence of gas. Predicted flow characteristics for the gas/liquid dispersion show good agreement with the experimental data. 

Das P.K., Prediction of Maximum Stable Diameter of Viscous Drops in a Turbulent Dispersion, Chem.-Eng. Technol. 19 (1996), p. 39-42... 

Luo H, Svendsen HF (1993) Theoretical Model for Drop and Bubble Breakup in Turbulent Dispersions. AIChE J 42(5) 1225-1233. 

Luo H (1993) Coalescence, break-up and liquid circulation in bubble column reactors. Dr ing Thesis, the Norwegian Institute of Technology, Trondheim Luo H, Svendsen HF (1996) Theoretical Model for Drop and Bubble Breakup in Turbulent Dispersions. AIChE J 42(5) 1225-1233... 

Tsouris C, Tavlarides LL (1994) Breakage and Coalescence Models for Drops in Turbulent Dispersions. AIChE J 40 395-406... 

Current spray models may not have the correct physics, may have unknown limits of applicability, and may contain empirical constants. In a recent test conducted by the author and United Technologies Research Center (UTRC), models of primary atomization, secondary atomization, droplet breakup, droplet collision, and turbulent dispersion were applied to an air blast spray. The predictions were compared to experimental data taken at UTRC. The predicted drop size was as much as 35% different from the measured values [8]. In contrast to the typical conference or journal publication, the models were not adjusted to make the agreement as close as possible. They were taken from the literature as is. The conclusion is that physical models of high-speed spray behavior are still lacking, despite years of research in this area. Primary atomization, the beginning of the spray, is one area that is particularly poorly understood. 

For this example we combine the approaches used in Examples 2-lb and 2-lc, neglecting turbulent dispersion (see Section 2-3). Since the eddies are all assumed to be at their minimum size, all we need to determine is the time needed for the diffusion across an eddy radius (lt/2 = 0.05 mm) for 99% diffusion. If the turbulence in the various test and commercial units does not change, the calculation will be the same for all cases, as it is based on a fixed eddy size, not on the system size. Of course, the total power will increase with the volume of the system. The only real difference from Example 2-lb is that we need to consider a sphere rather than a slab. The value of DabI/L drops from 2.0 to 0.56 (see Brodkey and Hershey, 1988, p. 680), giving a diffusion time of... 

Example 7-3 Liquid-Liquid Contacting—Turbulent Dispersion. A stream from a reactor is be contacted with an immiscible solvent to extract the product. A motionless mixer is planed. After the mixer the two streams will enter a decanter (Table 7-9). The cut size of the decanter is 125 pm, so a goal drop size for the mixer is 500 pm. Choose a Kenics KMS mixer based on past experience. No line size is given. 

Turbulent Dispersion Coalescence. After the dispersed phase leaves the motionless mixer, it will tend to coalesce to an equilibrium drop or bubble size characteristic of the shear field in the downstream piece of pipe. This coalescence is not just a phenomenon of the downstream tailpipe but is a process happening in parallel with dispersion. It is not as well understood. We do know that just like dispersion, coalescence is affected by volume concentration and is promoted by turbulence. Coalescence is strongly affected by surface chemistry effects. The role of many chemicals added to stabilize dispersions is to slow down the coalescence rate. 

Tsouris, C., and L. L. Tavlarides (1994). Breakage and coalescence models for drops in turbulent dispersions, AIChE J., 40, 395-406. 

Baldyga, J., J. R. Bourne, A. W. Pacek, A. Amanullah, and A. W. Nienow (2001). Effects of agitation and scale-up on drop size in turbulent dispersions allowance for intemiit-tency, Chem. Eng. ScL, 56, 3377-3385. 

Levich VG (1962) Physicochemical hydrodynamics. Prentice Hall, Englewood Cliffs Liao Y, Lucas D (2009) A literature review of theoretical models for drop and bubble breakup in turbulent dispersions. Chem Eng Sci 64 3389-3406... 

Atomization. A gas or Hquid may be dispersed into another Hquid by the action of shearing or turbulent impact forces that are present in the flow field. The steady-state drop si2e represents a balance between the fluid forces tending to dismpt the drop and the forces of interfacial tension tending to oppose distortion and breakup. When the flow field is laminar the abiHty to disperse is strongly affected by the ratio of viscosities of the two phases. Dispersion, in the sense of droplet formation, does not occur when the viscosity of the dispersed phase significantly exceeds that of the dispersing medium (13). 

Drop breakage occurs when surrounding fluid stresses exceed the surface resistance of drops. Drops are first elongated as a result of pressure fluctuations and then spHt into small drops with a possibiUty of additional smaller fragments (Fig. 19). Two types of fluid stresses cause dispersions, viscous shear and turbulence. In considering viscous shear effects, it is assumed that the drop size is smaller than the Kohnogoroff microscale, Tj. 

This correlation is valid when turbulent conditions exist in an agitated vessel, drop diameter is significantly bigger than the Kohnogoroff eddy length, and at low dispersed phase holdup. The most commonly reported correlation is based on the Weber number ... 

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