(267b) Numerical Simulation of Surfactant-Laden Emulsion Formation in a Stirred Vessel

Given the heavy involvement of immiscible liquid mixing both in our daily life (e.g., food and cosmetics) and in high-end industrial applications (e.g., drug development), understanding the interfacial flows under highly dynamic condition (e.g., within a stirred vessel) is of practical significance. The addition of surface-active agents (surfactants), either as additives or as contaminants, can affect both the mixing performance and the final quality of the mixed product. Under dynamic flow conditions, surfactants not only reduce the interfacial tension but also modify the interfacial rheology (although this will not be considered here) in a complex manner that depends on the surfactant mass transfer between bulk-phase and interface, and its transport along the interface. The elevated complexity hampers the understanding and control of interfacial behaviours within a surfactant-laden mixing vessel, which is a prevalent scenario in industry.

Previous studies have shown the deviation of predicted drop size in surfactant-laden mixing vessel by using surfactant-free drop breakup model [1]. Subsequent studies were dedicated to investigating the surfactant effect on the final drop size and their distribution [2] by considering surfactant concentration [3, 4], rheological properties of surfactant-laden interfaces [5], and types of surfactant head group [6]. More related work has been on the modification of the velocity field in stirred vessels due to the presence of surfactant [7, 8]. However, these studies only addressed the problem regarding the drop size distribution inside a surfactant-laden mixer leaving a gap in our understanding of the underlying physical mechanisms governing the interfacial behaviours within such a system. Nevertheless, interfacial dynamics on the surfactant-laden interface has been well studied in the early times by investigating drop deformation subjected to a simple flow field [9], resembling linear shear flow and uniaxial elongational flow. More recently, numerical studies have been carried out on a surfactant-laden drop dispersed in turbulent channel flow [10]. From the short review above, a systematic study of flow structure and interfacial dynamics in a practical mixing unit, i.e., stirred vessel, in the presence of surfactant remains lacking.

The present study aims to establish the transparent interplay among interfacial deformation, surfactant transportation, and the underlying flow structure inside a cylindrical stirred vessel equipped with a pitched blade turbine (PBT). Massively parallel, three-dimensional, interface-tracking, large eddy simulations [11] of O/W emulsification are deployed to provide detailed, realistic visualization of the intricate interfacial dynamics coupled to the turbulent flow fields, from the onset of impeller rotation through to the attainment of a dynamic steady state. In particular, this study investigates the effect of surfactant elasticity (the sensitivity of interfacial tension to the surfactant concentration), the Biot number (the ratio of characteristic desorptive to convective time scale), and Marangoni stresses. Allied to this, the transient drop counts, and their size distribution have been tracked.

The simulations have elucidated that the impeller rotation introduces a primary vortex (generating a centripetal force at the interface) which leads to a high surfactant concentration region near the axis and a low concentration area near the vessel wall. The continuous phase appears to be characterized mainly by pure rotational flow region (flow topology parameter [12], Q = -1) and pure elongational flow region (Q = +1), with small regions of pure shear flow (Q = 0) squeezing in between. Ligaments are produced as the deforming interface reaches the impeller, followed by elongational deformation and pinch-off giving rise to small drops. The ligament stretching is shown to be mostly located in pure shear flow regions, while drop breakup follows the interaction with the rotational flow (turbulent vortices). Moreover, the simulations have demonstrated that the presence of surfactant is associated with interfacial rigidification, suppression of end-pinching [13], and promotion of tip-streaming. The interfacial dynamics in the surfactant-laden system alters the evolution of drops count and their size distribution, where the appearance of the first dispersed drop occurs earlier and a larger number of relatively small drops are observed in comparison to their surfactant-free counterparts carried out in our previous work.

REFERENCES

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[11] Shin, S., Chergui, J., Juric, D., Kahouadji, L., Matar, O. K., and Craster, R. V. “A hybrid interface tracking–level set technique for multiphase flow with soluble surfactant.” Journal of Computational Physics, 359, 409-435 (2018).

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