(267a) On the Dispersion Dynamics of Liquid-Liquid Surfactant-Laden Flows in Static Mixers
AIChE Annual Meeting
Tuesday, November 15, 2022 - 8:00am to 8:30am
The effects of surfactants are a critical area of interest when dealing with liquid-liquid systems since the properties and stability of most structured goods (i.e., emulsion-based products) are heavily correlated with the manipulation of the interfacial tension between phases [Wong et al., 2015, Leal-Calderon et al., 2007, Valdes et al., 2022]. Very few studies dealing with static mixers have considered the influence of adding surfactants on the mix- ing performance, measured from the droplet size distribution (DSD) generated, and none of them have done so from a fundamental stance. Experimental studies [Lobry et al.,2011, Das et al., 2013, Barega et al., 2013, Farzi et al., 2016] have demonstrated that higher surfactant concentrations (hence lower interfacial tension) results in smaller DSDs. This is often attributed to higher breakage and lower coalescence events, which stems from decreased internal restoring forces and increased repulsion between drops [Barega et al., 2013, Valdes et al., 2022]. However, a deep dive into the physical mechanisms affecting fundamental processes such as droplet deformation, breakage and coalescence under the influence of surface-active agents has not been considered thus far. Further- more, a thorough evaluation of different relevant surfactant properties (e.g., solubility, elasticity, etc) on the dispersion dynamics has not been conducted either. Although some ground has already been covered in regard to the general trends expected, continuation on similar empirical lines of research will not be sufficient to further advance this field [Hakansson, 2019, Valdes et al., 2022]. Considering this, the present work seeks to provide a deeper understanding of the underlying governing physical mechanisms dictating immiscible liquid-liquid mixing when handling surfactant-laden flows.
In this study we implement high-fidelity, three-dimensional direct numerical simulations coupled with a state-of-the-art code based on a hybrid front-tracking level-set interface capturing algorithm, mounted on a massively parallelized computer architecture [Shin et al., 2017, 2018]. This hybrid formulation solves explicitly the unsteady dynamics of the free-interface, providing a wealth of information and detail on interfacial dynamics and physical phenomena which are inaccessible experimentally or via volume-averaged numerical approaches. Based on our previous and on-going studies, we consider a SMX-type mixer with two different initial configurations for the dispersed phase: 1) isolated cases: individual droplets (1 and 3 drops), mimicking a controlled syringe injection; and 2) pre-mixed cases: multiple droplets with different sizes simulating a pre-dispersed inlet. With these configurations we explore two main surfactant flows in order to isolate the effects of different properties on the static mixerâs performance: insoluble and soluble surfactants. For the insoluble case, we vary the elasticity parameter Î², which relates with the strength of the surfactant in terms of its influence on the interfacial tension. In the soluble cases, different levels of desorption (measured from the Bi number) and adsorption (ka) capabilities are explored and contrasted against the clean and fully insoluble case.
The surfactant-free simulations elucidate a two-step dispersion process taking place in the static mixer, consisting of an initial elongational deformation with no breakup, mostly driven by uniform extensional stresses, followed by a myriad of interfacial instabilities which results in breakup events via Rayleigh-Plateau or end-pinching mechanisms. These mechanics can be closely related with different metrics such as the maximum stretching efficiency [Liu et al., 2005] or the flow topology parameter [Soligo et al., 2020]. A similar two-step dispersion process is observed for the surfactant-laden cases. Nonetheless, a significant growth of the interfacial area and number of daughter droplets is noted for the insoluble cases. Furthermore, a saturation point was detected at increasing surfactant strength in the insoluble case, but with different outcomes when comparing a single droplet (lower interfacial growth at higher Î²) vs. a low coalescing three drop set-up (higher growth at higher Î²). Simulations involving soluble surfactants are still on-going but it is expected to observe the formation of surfactant-covered immobile regions and nearly surfactant free mobile regions [Batchvarov et al., 2020]. The implications of these gradients on the restoring and disruptive stresses acting on the droplets will be explored.
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