AIChE â?? Annual meeting 2014, Atlanta Georgia

Sizing bubbles in turbulent systems â?? facing the challenge to determine accurate distributions in multiphase systems containing nonspherical shaped fluid particles

S. Ulrich1, R. Panckow1,2, M. Kraume2 and S. MaaÃ?1

1SOPAT GmbH, c/o Technische Universität Berlin, Fraunhoferstra�e 33-36, 10587 Berlin, Germany; 2Technische Universität Berlin, Chair in Chemical and Process Engineering, Fraunhoferstra�e 33-36, 10587 Berlin, Germany

KEY WORDS

bubble size distribution, circularity, droplets, irregular shape, measurement technique, process control, shape factor

ABSTRACT

There are many experimental and numerical investigations needed to achieve a desired design of a particular multiphase reactor. For an exact prediction of heat and mass transfer, as well as reac- tion efficiency, e.g. growth rates during fermentation, the precise knowledge of the interfacial area is required. Therefore, the quantification of bubble and drop size distributions during such process- es needs to be established.
Complete models for the particle size distribution (PSD) as a function of power input, material and process parameters are rare and relatively inaccurate. Therefore, it is necessary to experimentally
analyze PSDs for accurate modeling. Furthermore industrial applications, such as suspension

polymerization processes, require a distinct average drop diameter and a small standard deviation of the distribution.
Another step forward is the control of the fluid particle size in
such systems. To accomplish this, rapid online information acquisition is needed. However, this is difficult to obtain. While many users are confronted with all of these require- ments, an adequate measurement technique for all applica- tions is needed but has not yet been developed. Bubbles in particular are often far away from the spherical shape and have a complex curved surface. In this paper we will discuss the possibilities of interpreting such irregular shaped parti- cles recorded with a two-dimensional (2D) photo-optical measurement device [1]. The results used were obtained by means of an automated image analysis software [2] that measures the particle diameters in each of the photographs.
Due to the infinite number of forms possible for a three- dimensional (3D) object it is not possible to get the exact knowledge of the shape of that irregular shaped particle by obtaining a 2D photograph.

Figure 1: Detection of fluid nonspher- ical particles by the automated image analysis

Thanks to the shape factors presented in literature, it is possible to make a classification of the particles. The idea is to consider a 2D projection of the particles and define how far it is related to
the spherical one. Circularity ? gives an understanding of the particles, since it is equal to one for
spherical particles and decreases with upcoming irregularity of the particle shape.

AIChE â?? Annual meeting 2014, Atlanta Georgia

With this parameter it is possible to understand the closeness of the particleâ??s shape to a sphere and to estimate the magnitude of the error under 3D abstraction. A major aspect of this work is to extrapolate 3D information from a 2D picture. When considering the Sauter mean diameter, the volume diameter and the surface diameter are needed. The volume diameter is a function of Vp, which is difficult to calculate,
whereas the surface diameter
can easily be calculated by the software if some assumptions are made.
The first assumption is that the surface area is considered
equal to the projected area
measured by the software, where the project area diame- ter is defined as the diameter of a sphere having the same projected area as the particle viewed in a direction perpen- dicular to the plane. Considering Vp as a function of circularity and ? as equal to one, that particle volume equals the volume of a sphere

1

0,8

0,6

0,4

0,2

0

0 1 2 3 4 5 6

Volume of surfactant Vsurf [ml]

with the same diameter ds. When ? is different from one,
another approach must be taken into account.

Figure 2: Relation of measured circularity and the induced

spherical shape of the fluid particles due to the addition of a surfactant

Wadell [3] suggested approximating the circularity with the operational circularity. He also pro- posed [4] to take the operational circularity as a 2D approximation of the sphericity ?, so with the sphericity the surface area of volume-equivalent sphere is easy to calculate.
With these assumptions, an approach for obtaining the volume of fluid-deformed particles in a 2D
projection is presented. This is used to obtain the distribution function of the dispersed phase, which is a fundamental aspect of inferring the coherences of the transport mechanisms and vari-
ous process parameters.

ACKNOWLEDGMENTS

We would like to thank Alexander Schurreit for the great support in a lot of ways.

REFERENCES AND CITATIONS

[1] S. MaaÃ?, S. Wollny, A. Voigt, M. Kraume, Exp. Fluids 2011, 50 (2), 259-269. DOI:
10.1007/s00348-010-0918-9.
[2] S. Maa�, J. Rojahn, R. Hänsch, M. Kraume, Comput. Chem. Eng. 2012, 45, 27-37. DOI:
10.1016/j.compchemeng.2012.05.014. [3] H. Wadell, J. Geol. 1933, 41, 310-331.
[4] H. Wadell, J. Geol. 1935, 43, 250-280.
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