(171g) Utilization of the Euler-Lagrange Approach for Modelling of Gas-Liquid and Liquid-Liquid Systems

Multpihase systems are often encountered in chemical engineering. Gas-liquid (GL) systems are commonly used to carry out biochemical reactions (cell cultivation, etc.). On the other hand, liquid-liquid (LL) systems are involved in processes such as polymerisation or specific crystalization methods (utilising transient LL emulsion). All of these processes have some requirements to be met (hydrodynamic stress, oxygen uptake, k_La, mass and heat transfer, etc.). For example, in the case of living cells/microorganisms, we must ensure sufficient supply of oxygen while there is no damage caused to them. In LL systems, the overall performance is also influenced to a great extent by the droplet size (interfacial area). Of course, other process parameters, such as impeller speed and dispersed phase concentration/gas sparging rate, have to be taken into account.

For the development of such processes, it is advantageous to use computational methods such as computational fluid dynamics (CFD). It can significantly reduce the number of lengthy and expensive experiments and speed up development by helping us to determine the appropriate process parameters necessary to achieve the required conditions inside the system. Thus, the aim of this work is to use CFD for prediction of bubble/droplet breakage and coalescence.

Methods

The simulations were performed in commercial CFD software ANSYS Fluent combined with user defined functions (UDF) written in C/C⁺⁺ language. For multiphase modelling, we employed the Euler-Lagrange (EL) approach together with the Volume of Fluid (VOF) method to account for the liquid level. Continuous phases were modelled using a 3D time-dependent problem using the Reynolds-averaged Navier-Stokes (RANS) method with a realizable k-ε model for the description of turbulence. The dispersed phase is treated as a large number of individual particles (bubbles/droplets), and their motion is tracked by solving the Newton equation of motion. Such approach allows us to predict breakage and coalescence on the level of the individual bubbles and also to access various information about individual bubbles.

Results

In this work, we present recent results obtained from modelling both breakage and coalescence phenomena in GL and LL systems. The GL system was represented by bioreactors of various scales. There, we used multiple impeller speeds and one gas flow rate for each vessel. For bubble coalescence, the model developed by Prince and Blanch [1] and further modified by Sommerfeld [2] and Sungkorn [3] for use in the Lagrangian approach to bubbles was initially used. For breakup, a model developed by Martínez-Bazán [4,5] was initially tested. Then, after various modifications in models describing the above-mentioned phenomena and choosing the propper solver settings, we obtained the final version of the model. [6]

Afterwards, we moved on to the LL system, for which we used an EasyMax vessel (350 mL) equipped with a Rushton impeller. We tested various impeller speeds, viscosities and volume fraction of the dispersed phase (silicon fluids). The original kernels used for the bubbles had to be modified accordingly to be applicable also to the droplets. There, two modifications had to be made – altering the drag force correlation and considering larger influence of dispersed phase viscosity. This meant that both the breakage criterion [7–10] and the efficiency of coalescence now depend on the viscosity of the dispersed phase [7,11,12].

The correct choice of models for bubble/droplet breakage and coalescence was proven by comparing simulation outputs with measured experimental values or to available data from literature. In both GL and LL systems, we compared resulting bubble and droplet size respectively. For GL systems, we also characterized the vessels in terms of volumetric mass transfer coefficient (k_La) and maximal hydrodynamic stress to which the cell could be exposed during cultivation.

Conclusion

The Euler-Lagrange approach was used to predict behaviour in GL and LL systems. The simulation outputs provided relatively good agreement with experimental data supporting the choice of models and their parameters.

References

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