(267a) On the Dispersion Dynamics of Liquid-Liquid Surfactant-Laden Flows in Static Mixers | AIChE

(267a) On the Dispersion Dynamics of Liquid-Liquid Surfactant-Laden Flows in Static Mixers


Kahouadji, L., Imperial College London
Matar, O. K., Imperial College London
Shin, S., Hongik University
Chergui, J., LISN CNRS
Juric, D., LISN CNRS
Liang, F., Imperial College London
The characterization of liquid-liquid mixing processes is arguably one of the most chal- lenging problems of modern process engineering, encompassing a broad range of non- idealities such as complex interfacial dynamics, surfactant-laden flows, among several others. These operations are heavily involved in a wide spectrum of applications, ranging from fast-moving consumer goods in the food, personal care and pharmaceutical indus- tries to high-end sectors such as (petro) chemical, polymer processing, and biotechnology [Paul et al., 2004]. In particular, the dispersion dynamics behind static mixers has shown growing interest in the past decades, given their potential as an attractive alternative to conventional stirred vessels [Valdes et al., 2022]. Despite this, design and scale-up procedures for these processes are largely dependant on limited empirical models and heuristics due to the intrinsic complexity of liquid-liquid systems. In turn, this has led to over-design and over-consumption practices aiming to ensure a minimum threshold of product quality, thus compensating for the lack of fundamental knowledge on the mixing itself [Valdes et al., 2022]. Blind application of simplified models and design heuristics on inherently complex flow systems can pose numerous risks to the manufacturing process, resulting in significant disruptions such as major adjustments to the plant, inflated costs due to over-sizing, and lost opportunity of unsuccessful products due to lacking quality or inadequate physico-chemical properties [Valdes et al., 2022, Paul et al., 2004].

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 mixer’s performance: insoluble and soluble surfactants. For the insoluble case, we vary the elasticity parameter β, 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 β) vs. a low coalescing three drop set-up (higher growth at higher β). 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.


Esayas W. Barega, Edwin Zondervan, and Andre B. De Haan. Influence of physical properties and process conditions on entrainment behavior in a static-mixer settler setup. Industrial and Engineering Chemistry Research, 2013. ISSN 08885885. doi: 10.1021/ie301580m.

A. Batchvarov, L. Kahouadji, M. Magnini, C. R. Constante-Amores, S. Shin, J. Chergui, D. Juric, R. V. Craster, and O. K. Matar. Effect of surfactant on elongated bubbles in capillary tubes at high Reynolds number. Physical Review Fluids, 5(9), 9 2020. ISSN 2469-990X. doi: 10.1103/PhysRevFluids.5.093605.

Mainak D. Das, Andrew N. Hrymak, and Malcolm H.I. Baird. Laminar liquid-liquid dis- persion in the SMX static mixer. Chemical Engineering Science, 2013. ISSN 00092509. doi: 10.1016/j.ces.2013.06.047.

G. A. Farzi, N. Rezazadeh, and A. Parsian Nejad. Droplet Formation Study in Emulsification Process by KSM using a Novel In Situ Visualization System. Jour- nal of Dispersion Science and Technology, 37:575–581, 2016. ISSN 15322351. doi: 10.1080/01932691.2015.1052144.

Andreas Hakansson. Emulsion Formation by Homogenization: Current Understanding and Future Perspectives. Annual Review of Food Science and Technology, 10:239–258, 2019. ISSN 19411421. doi: 10.1146/annurev-food-032818-121501.

Fernando Leal-Calderon, Jerome Bibette, and Veronique Schmitt. Emulsion science: Basic principles. Springer, 2nd edition, 2007. ISBN 0387396829. doi: 10.1007/ 978-0-387-39683-5.

Shiping Liu, Andrew N. Hrymak, and Philip E. Wood. Drop breakup in an SMX static mixer in laminar flow. Canadian Journal of Chemical Engineering, 2005. ISSN 00084034. doi: 10.1002/cjce.5450830501.

Emeline Lobry, Felicie Theron, Christophe Gourdon, Nathalie Le Sauze, Catherine Xuereb, and Thierry Lasuye. Turbulent liquid-liquid dispersion in SMV static mixer at high dispersed phase concentration. Chemical Engineering Science, 2011. ISSN 00092509. doi: 10.1016/j.ces.2011.06.073.

Edward L. Paul, Victor A. Atiemo-Obeng, and Suzanne M. Kresta. Introduction. In Handbook of Industrial Mixing - Science and Practice, chapter 1, pages xxxiii–lx. John Wiley & Sons, 2004. ISBN 0-471-26919-0.

Seungwon Shin, Jalel Chergui, and Damir Juric. A solver for massively parallel direct numerical simulation of three-dimensional multiphase flows. Journal of Mechanical Sci- ence and Technology, 31(4), 4 2017. ISSN 1738-494X. doi: 10.1007/s12206-017-0322-y.

Seungwon Shin, Jalel Chergui, Damir Juric, Lyes Kahouadji, Omar K. Matar, and Richard V. Craster. A hybrid interface tracking – level set technique for multiphase flow with soluble surfactant. Journal of Computational Physics, 359:409–435, 4 2018. ISSN 00219991. doi: 10.1016/j.jcp.2018.01.010.

Giovanni Soligo, Alessio Roccon, and Alfredo Soldati. Effect of surfactant-laden droplets on turbulent flow topology. Physical Review Fluids, 5(7):073606, 7 2020. ISSN 2469- 990X. doi: 10.1103/PhysRevFluids.5.073606.

Juan P. Valdes, Lyes Kahouadji, and Omar K. Matar. Current advances in liquid–liquid mixing in static mixers: A review. Chemical Engineering Research and Design, 177, 1 2022. ISSN 02638762. doi: 10.1016/j.cherd.2021.11.016.

S. F. Wong, J. S. Lim, and S. S. Dol. Crude oil emulsion: A review on formation, classification and stability of water-in-oil emulsions. Journal of Petroleum Science and Engineering, 135:498–504, 2015. ISSN 09204105. doi: 10.1016/j.petrol.2015.10.006.