Modeling of Ascending/Descending Velocity of Metal Droplet Emulsified in Pb-Salt System DUK-YONG SONG, NOBUHIRO MARUOKA, GOVIND SHARAN GUPTA, HIROYUKI SHIBATA, SHIN-YA KITAMURA, and SMITA KAMBLE Metal–slag emulsion is an important process to enhance the reaction rate between the two phases; thus, it improves the heat and mass transfer of the process significantly. Various experimental studies have been carried out, and some system specific relations have been pro- posed by various investigators. A unified, theoretical study is lacking to model this complex phenomenon. Therefore, two simple models based on fundamental laws for metal droplet velocity (both ascending and descending) and bubble velocity, as well as its position at any instant of time, have been proposed. Analytical solutions have been obtained for the developed equations. Analytical solutions have been verified for the droplet velocity, traveling time, and size distribution in slag phase by performing high-temperature experiments in a Pb-salt system and comparing the obtained data with theory. The proposed model has also been verified with published experimental data for various liquid systems with a wide range of physical properties. A good agreement has been found between the analytical solution and the experimental and published data in all cases. DOI: 10.1007/s11663-012-9642-6 Ó The Minerals, Metals & Materials Society and ASM International 2012 I. INTRODUCTION THE mixing of two immiscible liquids is required in many processes (biodiesel, metal-slag, nuclear reactor, etc.) to increase the efficiency of the process. The mixing can be achieved either by stirring the liquids mechan- ically or by injecting a gas. [1] In many metallurgical processes (ladle metallurgy, secondary refining, Cu convertor, etc.), the metal-slag reaction is of prime importance to increase the efficiency of the process. Slag and metal are immiscible liquids at high temperature and are in contact only at the interface, which leaves little room for a good rate of reaction between them unless the surface area of one of the phases is increased. The reaction rate, efficiency, and productivity of the process are related to each other. An effective method to increase the area is to emulsify the slag into the metal phase or the metal into the slag phase. The first method is unstable and not desirable. [2] The second is effective. The current work deals with the second method, which is called metal emulsification. [3–7] As shown in Figure 1, the molten metal is placed at the bottom, whereas the slag is placed at the top as it is lighter compared with the metal. A nozzle, placed at the bottom of the metal phase, blows a gas bubble into it. This bubble rises from the metal into the slag phase, and as it does so, it carries with it a metal film into the slag phase. This film then disintegrates in the slag phase to form the metal droplets. The process of metal emulsification can be divided into three stages. The first stage includes the formation and motion of gas bubble in the metal and slag phase. The nozzle blows gas into the metal. The bubble grows until its diameter reaches a critical value, [8,9] at which it starts its upward motion. The bubble rises with its terminal velocity and reaches the interface. From here, the second stage begins (in continuation of the first stage), i.e., the formation of the film and the breakage of the film. As the bubble crosses the interface it drags some lower phase liquid in its wake and forms a film of molten metal around bubble and carries this film into the slag phase. When the bubble crosses the interface completely, a few large metal drops are formed from the dragged phase. [10,11] Bubble with liquid film around it still continues its journey in the slag phase. After some distance from the interface, the liquid film ruptures, [12,13] producing many tiny metal droplets in the slag phase. The gas bubble continues its journey in the second phase until it reaches the top surface of the second phase, which is open to the atmosphere. The final stage is the motion of these microdroplets in the slag phase before settling down into the metal phase. This work deals with the modeling of the first and third stages, i.e., motion of the bubble from the interface to the top of the surface and motion of the droplets in the slag phase. Many researchers have studied the DUK-YONG SONG, Ph.D. Student, is with the Graduate School of Engineering, Tohoku University, 6-6 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan. Contact e-mail: ssongdy@mail.tagen.tohoku. ac.jp NOBUHIRO MARUOKA, Assistant Professor, HIROYUKI SHIBATA, Associate Professor, and SHIN-YA KITAMURA, Professor, are with the Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan. GOVIND SHARAN GUPTA, Professor, and SMITA KAMBLE, Ph.D. Student, are with the Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India. Manuscript submitted January 10, 2012. Article published online March 8, 2012. METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 43B, AUGUST 2012—973