(635e) Insights on Drop Formation Dynamics in Presence of Interfacial Mass Transfer

Summary: Drop formation at fixed, submerged position in stagnant liquid (continuous) phase is experimentally studied. During drop formation of binary mixture, one of the components diffuses (solute) in continuous phase. We found transitions in drop formation regime with a change in solute concentration in drop phase , from axisymmetric drop – deformed drop –oscillating drop – dripping – jetting. Results were confirmed by conducting multiple side, top-view experiments. Shadowgraphy was used to visualize solute diffusion, helping us to better understand its implications on drop formation time and volume. We quantitatively measure real time variations in drop size by image analysis. Present work provides fundamental insights on controlling drop formation in systems away from equilibrium.

INTRODUCTION TO PROBLEM STATEMENT

We observe drop formation in nature, science and technology. It is an obvious phenomenon for ordinary person, and a classic problem of free-surface flow for researchers, mainly due to its rich dynamics and implications in broad range of applications. Specific to drop formation through capillary, what makes the dynamics rich is attempted to summarize in following points: (i) shape and position of interface-boundary separating drop with other phase in its vicinity- is not fixed and need to be analysed in addition to flow field during drop formation, (ii) several factors (inflow velocity, fluid properties, orifice size and shape) or dimensionless parameters governing the underlying physics, (iii) significant topological change during drop pinch-off in short time, also contributing to difficulties in resolving infinite time singularity in theoretical analysis. Thus, we find abundant studies exploring fundamental insights into drop formation, through theory, controlled experiments and numerical simulations. On application side, very often multicomponent drops and that too, in multiphase systems are being used from a long time. But major progress in their fundamental analysis is seen in only recent past, though many intricacies need further exploration.

Here, we focus on drop formation of binary mixture – solute and solvent – at submerged location in stagnant liquid phase. Our system is n-hexane (solvent) – acetone (solute) – water (continuous phase), a standard liquid-liquid extraction system in chemical industries. The objective is to explore (i) how solute transfer – from drop to continuous phase – under different concentration gradient alter drop formation dynamics in real time, and (ii) strategies to control drop formation time and volume in such systems away from equilibrium. Overview of literature survey is presented in following section.

OVERVIEW OF LITERATURE SURVEY

Classic theories such as two-film, penetration and surface renewal theory provide basis to predict interfacial mass transfer in many unit operations under practice in chemical industries. Specific to drop formation, various authors proposed extensions to Higbie’s penetration theory – assuming different mechanism of solute exposure to interface – to better predict rate of mass transfer, mainly in terms of change in interfacial area with real time. Few examples are model by – W. Licht and W F Pansing [1], P.M. Heertjes and L.H. De Nie [2], Walia and Vir [3]. On other note, early experimental approaches were based on mass transfer measurements at end of drop formation lifetime. It include: (i) drop withdrawal through the same nozzle after drop formation i.e. formation-collapse technique [4], (ii) extrapolation of measurements to zero formation time [1], (iii) experimentation in short columns [2], (iv) collection of drops using funnel at the top [5], and so on. Here, as measuring local concentration field in the vicinity of interface is inherently difficult, many papers – published before past two decades – concluded large deviations between experiments and model predictions.

In past two decades, advancement in visualization tools (for e.g., high speed imaging, laser induced fluorescence, rainbow Schlieren deflectometry, confocal Raman spectroscopy) and simulation techniques (for e.g. VOF coupled with level set method, DNS, diffused interface methods), enabled a better understanding of interfacial mass transfer non-invasively [6]. The general consensus – based on these studies – has been that the higher concentration gradient induces solutal Marangoni convection due to interfacial tension inhomogeneity along the evolving interface. It is found to be contributing to significantly higher mass transfer rates than that predicted by early diffusion-based mass transfer models [7]. Presently, the following aspects need further exploration: (i) universal criteria for onset of Marangoni instability, (ii) its implication on governing drop size, shape and formation time with a change in liquid-liquid extraction system, and (iii) techniques for accurate measurement of spatiotemporal gradient in interfacial tension and concentration in the interfacial film between growing drop and continuous phase. Here, we present accurate experimental analysis of drop formation dynamics with interfacial solute transfer. Methodogy is concisely presented in following section.

EXPERIMENTAL METHODOLOGY AND KEY RESULTS

Controlled experiments using high speed imaging and subsequently, image analysis using in-house developed routines are carried out (shown in Figure 1). In experiments, volume fraction of acetone in n-hexane is varied over a range of . Drop is formed at the same submerged position inside stagnant liquid phase (de-ionized water), inflow rate of drop phase and using the same orifice (I.D.:O.D = 0.5 mm:1.5 mm). Sudan-I dye is added as a tracer while preparing drop phase solution, in the same quantity (1.6 mg/20 mL) in each experiment. During experiments, as soon as drop phase liquid arrives at orifice tip, very close images were captured using high speed camera (Photron, FASTCAM Mini UX100) and a zoom lens (NAVITA 6000) connected to an extender set, at a frame rate over a range of 500 – 2000 fps. Sufficient care was taken to ensure (i) non-contamination by using air-filled capillary system and thorough cleaning, drying of setup components for separate experiments, (ii) vibration-free setup using optical bench. Each experiment was repeated 3-4 times to ensure reproducibility.

Our experimental results suggest the transformation in drop formation regimes with a change in solute concentration in drop phase liquid. At , the drops are axisymmetric with minimal influence of interfacial transfer. For 0.2 < < 0.5, prominent Marangoni effects resulted in interface deformations and the growth of the drop shape at relatively slower speed. At = 0.5, the strong tangential movement occurs along the interface alongside the oscillations of drop. Consequently, the drop remains away from equilibrium until detachment. Interestingly, for 0.5 < ≤ 0.6, we find spontaneous ejection of the solute component out of the drop, resulting in the dripping; where multiple smaller droplets were generated very rapidly . Beyond , jetting is observed.

KEY CONCLUSIONS

Experimental results show that interface deformations and drop oscillations occurs under large solute concentration gradient, governed not only by solutal Marangoni flow but also bulk density gradients. Also, we show how solute extraction can be intensified by controlling drop formation time in systems away from equilibrium.

References

[1] W. Licht and W. F. Pansing, Solute Transfer from Single Drops in Liquid-Liquid Extraction, Ind. Eng. Chem. 45, 1885 (1953).

[2] P. M. Heertjes and L. H. de Nie, The Mechanism of Mass Transfer during Formation, Release and Coalescence of Drops. Part I-Mass Transfer to Drops Formed at a Moderate Speed, Chem. Eng. Sci. 21, 755 (1966).

[3] D. S. Walia and D. Vir, Interphase Mass Transfer during Drop or Bubble Formation, Chem. Eng. Sci. 31, 525 (1976).

[4] J. M. C. and S. J. Skinner, The Mechanism of Liquid-Liquid Extraction across Stationary and Moving Interfaces.

[5] Z. Wang, P. Lu, G. Zhang, Y. Yong, C. Yang, and Z. S. Mao, Experimental Investigation of Marangoni Effect in 1-Hexanol/Water System, Chem. Eng. Sci. 66, 2883 (2011).

[6] D. Lohse and X. Zhang, Physicochemical Hydrodynamics of Droplets out of Equilibrium, Nat. Rev. Phys. 2, 426 (2020).

[7] Q. Mao, Q. J. Yang, Y. Liu, and W. Cao, Experimental and Numerical Study of Droplet Formation with Marangoni Instability, Chem. Eng. Sci. 268, (2023).

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* Corresponding author. Email: aa.kulkarni@ncl.res.in