The ascent of gas bubbles through layers of liquid metal and slag is an essential feature in most metal refining processes.[1,2] However, the ease of escape of a gas bubble depends on draining of the liquid film on its periphery once the bubble reaches the top surface of the liquid. Several workers have investigated the mechanism of foaming in a single liquid phase as well as drainage of liquid film from the surface of a gas bubble when it leaves a liquid surface.[3,4,5,6,7,8,9,10] However, the cases involving coexistence of two liquid layers, one above the other, have been studied much less frequently.[11,12]

In metallurgical operations, rising gas bubbles often encounter two different liquid layers, viz. molten metal and slag. In such cases, a bubble has to first cross a liquid-liquid interface before it can reach the free surface of the upper liquid layer. Entrainment of metal droplets in the molten slag is influenced by the ease of drainage of the liquid metal film around the bubble before, as well as after, it enters the slag layer. Several authors have worked extensively on formation of plume and opening of eye due to gas purging through layers of liquid metal and slag.[13,14,15,16,17,18,19,20,21,22,23] However, these investigations were focused mainly on the mechanics of the gas plume on a macroscopic scale rather than the phenomena around individual gas bubbles during their passage from one liquid into another. Based on the observations of Poggi et al.,[24] Kobayashi proposed a model to estimate the disintegration of the metal film around a bubble and dispersion of fine metal droplets in the slag.[25] The criterion proposed was dependent primarily on the interfacial tensions between slag, metal, and gas, as well as the buoyancy factor. However, the role of viscosity was apparently kept out of consideration. Krishnapisharody and Irons employed particle image velocimetry on water–oil systems to simulate the entrainment of slag droplets into metal.[26,27,28] However, these investigations too were focused more on the bulk circulation currents at the metal-slag interface rather than on individual bubbles and the surrounding liquid film. In view of this, a need was felt to take a fresh look at film drainage at the interface between two liquid layers and to ascertain its influence on the dispersion of one liquid in another.

Liquid metal and slag were simulated in a room-temperature physical model using water and three different oils, designated “A”, “B,” and “C” in the present work. Figure 1 illustrates the experimental setup used for observing the rise of gas bubbles through two liquid layers. The bottom portion of the glass cylinder was fitted with a ceramic filter having a specified pore size, in order to generate bubbles of uniform initial size. Nitrogen gas was supplied through a flow control valve at the bottom. The flow rate of gas, as well as the type of ceramic filter (single pore or multi pore), was chosen to achieve the intended bubble generation rate(s). The water was colored with an organic dye that dissolved easily in water but was insoluble in the oils used. Images captured with a high definition digital camera were analyzed with the help of ImageJ software as well as a noncommercial software for image analysis developed by Taniguchi and Seetharaman at the Royal Institute of Technology (KTH, Stockholm).[9] All measurements were carried out at 300 K (27 °C). The viscosity of the oils was measured using a BROOKFIELDFootnote 1 LVDV series viscometer. The results were found to vary within ± 2 pct of the values reported by the respective suppliers. The bulk of this work was carried out as part of a Master’s thesis.[29] Though a few of the initial observations were presented elsewhere,[30] further experiments as well as more detailed analysis have been carried out subsequently.

Fig. 1
figure 1

(adapted from Ref. [29])

Schematic view of the experimental setup

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The coalescence of bubbles and droplets depends significantly on the interfacial tension between the bubble/droplet and the surrounding phase. The water–oil contact angle, with respect to the glass substrate, was estimated from photographs of sessile drops of water in the oils (Figure 2). The interfacial tension estimated from these images, as well as the viscosities measured, is presented in Table I.

Fig. 2
figure 2

Photographs of sessile water drops in oils A, B, and C

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Table I Density, Viscosity, and Surface Tension of the Three Oils
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Videography of the ascent of bubbles revealed that once a bubble reached the water–oil interface, it tried to push a large amount of water into the oil, causing the interface to become convex in shape. The water started to drain downward due to higher density relative to the oil and the bubble seemed to remain “quasi-stationary” at the interface until most of the water had drained away. After this, the bubble started to rise into the oil layer and the thin film of water on its periphery continued to drain downward and accumulate as a drop at the bottom of the rising bubble. Finally, the water droplet detached from the bubble and descended to the water–oil interface, while the bubble continued to rise through the oil layer. Figure 3 shows individual bubbles rising above the water–oil interface in the three different oils, leaving behind a trail of water carried into the oil layer. Figure 4 presents three sequential images, indicated as (I), (II), and (III), showing the water draining from around a single bubble and eventually forming a droplet in one of the oils used for the experiments. Similar behavior was observed with the other two oils.

Fig. 3
figure 3

Individual bubbles crossing the water–oil interface

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Fig. 4
figure 4

Sequence of drainage of water film around a rising bubble

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If the height of the oil layer was inadequate, the bubble could reach the top surface of oil before the water film was completely drained. Rupture of the bubble at the free surface of the oil layer could then generate fine droplets of water, which would remain dispersed in the oil layer for a long time. The smaller droplet size would naturally imply lower settling velocity and, as result, more time required for separation of the water droplets from oil. A similar phenomenon, together with macroscopic shear at the metal-slag interface, may be responsible for the dispersion of fine metal droplets in molten slag during gas purging. Table II summarizes the observations related to drainage of the water film and upward movement of the bubble.

Table II Kinetics of Bubble Movement Across the Water–Oil Interface
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The authors believe that the buoyancy factor was the main driving force behind this phenomenon, with the rate of water drainage increasing with the difference in density between oil and water. This is illustrated by the higher apparent residence time of the bubble at the water–oil interface in the case of oil B, in comparison with oils A and C. On the other hand, complete drainage of the water film, after the bubble started to rise through the oil layer, took the longest time in the case of oil C and was almost equally fast for oils A and B. Thus, the rate of liquid film drainage from the bubble’s surface is not a function of density alone but clearly involves an interplay between viscosity, interfacial tension, and buoyancy forces.

Figure 5 shows the rate of drainage of water from around the bubble at the oil-water interface, expressed in terms of the apparent residence time of the bubble (τ1), as a function of the relative buoyancy between water and oil. The buoyancy term has been nondimensionalized with respect to the density of water. The variation of τ1 was analyzed as a function of the major forces acting in the system—viscous force, surface tension force, buoyancy force, and inertial force. As seen in Figure 6(a), τ1 was found to have a positive correlation with the ratio between buoyancy and viscous forces, while maintaining an inverse correlation with the ratio between surface tension and inertial forces (Figure 6(b)). It should be mentioned here that the inertial force was rather low in magnitude in all cases owing to the low velocity of bubble movement across the liquid layers.

Fig. 5
figure 5

Influence of buoyancy on the “hold” time of the gas bubble at the oil–water interface

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Fig. 6
figure 6

Combined influence of (a) the buoyancy and viscous forces and (b) the surface tension and inertial forces on the drainage of water around a quasi-stationary bubble at the oil–water interface

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The terminal velocity (Vf) of a bubble rising through the oil layer, after complete drainage of the water film, bears a negative correlation with the viscosity of the oil, as shown in Figure 7. Upon further analysis with respect to the ratios between the forces, Vf can be seen to vary inversely with the ratio between viscous and surface tension forces as well as that between viscous and inertial forces (Figure 8). The parameter ηoil/Δ(ρ) was also found to exert a similar influence on Vf, as visible in Figure 9. These variations, illustrated in Figures 7 through 9, seem to confirm that the flow of liquid(s) around the bubble is largely Newtonian in nature and influenced most significantly by the viscous forces.

Fig. 7
figure 7

Influence of the viscosity of oil on the terminal velocity of the bubble in the oil layer

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Fig. 8
figure 8

Relative influence of (a) viscous and surface tension forces and (b) viscous and inertial forces on the terminal velocity of a gas bubble rising through the oil layer

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Fig. 9
figure 9

Variation of the terminal velocity of a bubble rising through the oil layer with oil viscosity and the buoyancy factor

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It was frequently observed that adjacent gas bubbles, in spite of being in “contact” with each other, would delay their coalescence into a single larger bubble due to the delay in drainage of the liquid film between the bubbles. The magnitude of this delay was dependent on the viscosity of the liquid film as well as interfacial tension. Figure 10(a) further illustrates the combined influence of buoyancy and viscous forces on the drainage of the remnant water film, after the bubble starts to rise through the oil layer (τ2). Variation of τ2 with respect to the nondimensional product of the relative buoyancy effect and viscosity ratio between oil and water (Figure 10(b)) shows a similar trend and implies that the rate of drainage of the water film around the rising gas bubble is primarily dependent on the buoyancy factor, i.e., Δ(ρ), between oil and water.

Fig. 10
figure 10

Variation of τ2 with (a) the product of the buoyancy factor and oil viscosity and (b) the product of the nondimensional buoyancy factor and viscosity ratio between oil and water

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It was also observed that the water droplets detached from the rising gas bubbles may not settle unhindered to the bulk water layer below. A descending droplet of water occasionally encounters a rising gas bubble and the water spreads around the rising bubble as a film. In such a case, this water film needs to drain from around the bubble and then only can the water resume its droplet configuration. It was difficult to simulate this situation by plan in the physical model since the intersection of downward trajectory of the water droplets and upward trajectory of the gas bubbles was stochastic in nature. Figure 4 demonstrates one such instance where the downward motion of a water droplet is interrupted by ascent of a gas bubble. Since the bubbles in the oil layer are continuously moving upward, the volume of water corresponding to a single droplet may even have a small upward translation during the period of spreading and recoalescence. This indicates a possibility that in real-life metal-slag-gas systems, some of the metal droplets may remain dispersed in the slag for a considerably long time due to repeated interaction with rising gas bubbles, whereas some might sink to the bulk metal layer much faster.

The following conclusions could be drawn on the basis of these observations.

  1. 1.

    A gas bubble rising through two liquid layers carries a film of the lower (heavier) liquid as it rises through the upper (lighter) liquid layer.

  2. 2.

    The rate of drainage of the liquid film around a bubble depends on the viscosity, interfacial tension, and buoyancy effect between the liquids.

  3. 3.

    In addition to other factors, the height of the upper liquid layer also influences the complete drainage of the heavier liquid film as well as the chances of its entrapment in the lighter liquid.