Maximum stable drop size

Arai K., Konno M., Matunaca Y., Saito S., Effect of dispersed-phase viscosity on the maximum stable drop size for breakup in turbulent flow, J. Chem. Engng. Japan 10 (1977) 4, p. 325-330... 

Diameter of pipe, m or ft diameter of impeller Dj, diameter of jet and nozzle Dg, orifice diameter D, diameter of particles, drops, or bubbles D tank diameter maximum stable drop size in dispersion... 

A reasonably successful approach to finding the maximum stable drop size ( d)max in turbulence using this approach has been made by Arai et alP. For drop sizes much larger than the Kolmogoroff length scale, i.e. 

From the above the maximum stable drop size can be estimated. There will be smaller drops, but in theory no drops larger than this. No data on distribution as yet exist for laminar breakup. Figure 7-28 compares drop size by laminar mechanisms with those calculated for turbulent flow. Smaller droplets are expected for laminar versus turbulent flow at the same energy dissipation rate. 

It is not our purpose to provide a complete discussion of drop deformation and breakup in idealized laminar flow fields. There have been numerous studies that have been reviewed by Rallison (1984), Stone (1994), and others. Only the most practically relevant studies are discussed below. Of central importance is to predict and/or correlate the size above which a parent drop of known physical properties (that is subjected to an imposed deformation) will become unstable and break up into smaller drops. This size is referred to as the critical or maximum stable drop size, dmax-... 

Mechanistic Modeis and Correiation of Mean Drop Size. Mechanistic models for maximum stable drop size in tmbulent flow are based on arguments put forth by Kolmogoroff (1949) and Hinze (1955). The stress acting to deform a drop of size d is given by... 

An examination of eqs. (12-17) to (12-19) reveals that there exists a maximum stable drop size, d ax. above which the disruptive forces are sufficient to break the drop, and below which the drop is stabilized by surface and internal viscous forces. For d = d ax. the disruptive force exactly balances the cohesive forces, so that... 

Figure 12-40 Relationship between rocking bomb reactor and lab scale stirred autoclave using the maximum stable drop size as a calibration tool.

The work on coalescence and breakage from this school considers the simultaneous effects of surface tension and flow in the drop and predicts the maximum stable drop size in a stirred vessel as a function of various operating parameters." The previous models overpredicted the maximum drop size. 

Sleicher JCA (1962) Maximum stable drop size in turbulent flow. AIChE J 8 471-477... 

Maximum Stable Drop and Bubble Sizes for Systems at Room Temperature... 

In liquid-liquid reacting systems, one of the important parameters is the surface area per unit volume, a, in the dispersion, which can be related to the Sauter mean drop diameter dn- In some processes, the drop size distribution and especially the minimum drop size or the maximum stable drop diameter are also important factors in analysing the process results. 

At this time, it is instructive to note that Eqs. (34) and (42) predict that the large drops will continuously break down to a size flniax> where the breakage function g(fl ) approaches some arbitrary low value close to zero. At this point, the exponential term dominates the behavior of the breakage rate expression and a relation for Oniax is obtained similar to the one given by Eq. (18), which was derived on the basis of maximum stable drop theory. 

Sauter mean diameter for finite ([) (m) mass mean drop diameter (m) maximum stable drop diameter (m) number mean drop diameter (m) average drop diameter in eqs. (12-8) and (12-9) (m) bin width for size class i in DSD (m) impeller diameter (m) mass diffusivity, general use (m /s) diameter of cylinder (m) critical drop deformation mass diffusivity in continuous phase (m /s) diameter of static mixer pipe (m) death rate of drops of size d (s ) energy spectral density function for eddies of wavenumber k... 

Kolmogorov AN. The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl Akad Nauk SSSR 1941 30 301-305. Baldyga J, Podgorska W. Drop breakup in intermittent turbulence. Maximum stable and transient sizes of drops. Can J Chem Eng 1998 76 456-470. 

Eq. (17.117) allows us to estimate the maximum size of a stable drop ... 

Equating the dynamic thrust Qto the surface tension force for the drop, 2E/R, one obtains the formula for the maximum stable size of the drop ... 

Figure 6. Critical positions on an axially S3nnmetric sinusoidal surface of wavelength A and maximum slope A5° for various drop sizes and for 6=60°. The stable regions are shown heavier. The slope angles at the critical positions are indicated, x is the radius of the contact line.

---