(480b) From Fundamental Single Drop Analysis to the Description of Liquid/Liquid Dispersions-Part II: Breakage

There are numerous applications in industry, where reactions and mass or energy transfer between two immiscible liquids are the major concerns. When trying to influence or predict the contact area one has to focus on the underlying principles that lead to the formation of the drops. The resulting drop size distributions (DSD) are thereby determined by drop breakage and coalescence. In order to predict the size distributions, both phenomena have to be understood and described properly. Although comprehensive scientific research identified a multitude of theoretical models describing both processes, the prediction of the DSD is only possible with restrictions when varying for example the power input, material and process parameters. Consequently, excessive and expensive experimental investigations are still necessary at different scales of process development. For example the design of extraction columns still requires pilot plants using high amounts of process liquids.

To reduce the amount of influencing factors of the whole process, it is necessary to reduce the problem to the fundamental behavior of single droplets. Therefore, the impact of influencing parameters for drop coalescence and breakup needs to be identified and quantified for each phenomenon separately. The gained knowledge of this microscopic behavior can be used to prove existing models and develop new ones. These models can either be semi-empirical or mechanistic. The obtained detailed models can be implemented into the framework of population balance equations (PBE), which includes separate kernels for drop breakage and coalescence. The PBE can be applied to describe the time dependent DSD in technical applications and therefore connects the microscopic to the macroscopic behavior of droplet swarms. The microscopically based modeling allows a determination of the model parameters using single drop experiments with only a small amount of liquid components in order to adapt the submodels to the present process.

This part focuses on the drop breakage phenomenon in turbulent flows. It is described in literature, that drop breakage occurs when the external forces exerted on particles by the continuous phase exceed the internal forces which hold the particle together. The Weber number describes the relation between both stresses. Thereby only the interfacial tension is considered for the stabilization of the drops. The stabilizing influence of the viscosity is described by the Ohnesorge number which sets the effect of the viscosity in relation to the effect of the interfacial tension. Applying Kolmogorovs theory of isotropic turbulence, correlations between the mean diameter of a turbulent liquid/liquid droplet swarm and the above mentioned dimensionless numbers can be derived.

In the present studies single drop breakage events, where coalescence can be neglected, are analyzed in a turbulent flow field comparable to the field of a stirred tank.  A single stirrer blade, mimicking a part of a Rushton turbine is therefore mounted in a rectangular channel and induces drop breakage. Drop deformation and breakage is analyzed by high-speed imaging. Image data is evaluated by fully automated image analysis. For statistically relevant results, at least 1000 drops entering the vicinity of the stirrer blade are analyzed. The breakage probability and the breakage and oscillation times are determined. Additionally the resulting Sauter mean diameter and the number and the size distribution of the daughter drops are evaluated. 

A variety of different droplet substances were investigated at constant droplet diameter of 1 mm. Thus, the physical properties (density, viscosity) of the dispersed phase and the interfacial tension between the two phases were varied over a wide range. Additionally, surfactants were added to increase the range of the investigated interfacial tensions. Consequently, the role of the stabilizing forces, which determine the Ohnesorge numbers of the investigated systems, can be quantified. 

Furthermore the fluid flow velocity of the continuous water phase was varied (v=1.0 - 2.0 m/s) to also determine the influence of the deforming external forces and therefore the Weber numbers. These experiments allow proving if the drop breakage phenomenon can be described with the above depicted concept using two dimensionless numbers.

The influence of the dispersed phase properties on drop deformation and breakage can be described well with the Weber and the Ohnesorge number. For systems with low Ohnesorge numbers, the breakage probability and the Sauter mean diameter are only a function of the Weber number. The stabilizing influence of the viscosity has to be considered to describe these factors.

The breakage time is set to be the time between the beginning deformation of a droplet and the final splitting in two or more parts. To characterize the deformation, the two major axis of the particle were set into relation. In accordance with literature, droplets with deformation factors smaller than 0.9 were set to be deformed, while the droplets with greater values were defined to be spherical. For very low Ohnesorge numbers, the breakage time only depends on the interfacial tension. For higher Ohnesorge numbers, the breakage time is determined by the ratio of viscosity to interfacial tension which results in a proportional dependency thereof.

When combining both dimensionless numbers, the breakage times, probabilities and Sauter mean diameters of all the investigated systems with different dispersed phases can be described. The PBE breakage kernel includes the breakage time, probability and size distributions of the resulting daughter drops. Therefore, the gained detailed results from the single drop breakage investigations can be used to validate and improve existing mechanistic models from literature.

Partially founded by DFG project “Coalescence efficiency in binary systems” and DECHEMA “Max-Buchner-Forschungsstiftung”