Dynamic behavior of a liquid/liquid interface at an oscillating wall
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I.
INTRODUCTION
THE shape o f the interface between coexisting gaseous and liquid phases, or between two liquid phases, is determined by a balance of forces acting on the system which include the forces due to interracial energy, due to gravity,, due to fluid flow, and, possibly, due to an electromagnetic field. In three-phase systems composed of three fluids, or o f two fluids and a solid, three-phase contact lines (TPLs) exist and the static contact angles between the phases are determined by the three interracial energies. In many materials processing operations, interfaces between phases exist, and the precise knowledge of their form is often highly desirable. For instance, many investigations have been carried out recently on the electromagnetic shaping of metal ,,' slag or metal / gas boundaries in casting processesJ ~.'-.3~on the form of the metal melt in levitation melting or cold crucible melting, ~4,~I and on the shapes of solder joints. ~61 These studies deal with the static or quasistatic phase boundaries. Another group of problems is that involving the dynamic shapes. Trapaga and Szekely investigated the impingement of droplets in spraying processes3~q In such problems, the TPL may develop, if the impingement is on a third-phase solid substrate, and the dynamic behavior of the contact angle represents an additional point of interest. The present study focuses also on a dynamic system. We investigated the shape of a liquid / liquid interface at an oscillating wall. A mathematical fluid flow model has been developed and cold experiments involving mercury and oil have been carried out to check the theoretical results. The subject is related to the behavior of the meniscus between liquid melt and liquid slag in an oscillating mold during continuous casting of steel. II.
mm i.d. serves as the "mold". The mercury (and oil) rests on a piston which is stationary with respect to the laboratory floor. So, its bulk stays in a fixed position. A section, indicated by the circle, around the TPL wall / oil / mercury (three-phase point in Figure I) is filmed with a high speed camera. The same relative velocity range as in continuous casting can be realized. That is, the downward movement of the strand in continuous casting with constant velocity is attained by a linear upward movement of the plexiglass wall, and the oscillatory motion is attained by a super'posed sinusoidal motion. The corresponding velocity is v,,. = v, + h~o cos tot. The path of a point A with respect to the stationary piston is indicated in the diagram of Figure 1. The piston is made up from alternating discs of metal and TEFLON.* The latter have a slightly smaller diameter *TEFLON is a trademark of E.I. Du Pont de Nemours & Co.. Inc., Wilmington, DE.
and have O-rings at their periphery. By tightening the screws holding the metal and TEFLON parts together, a tight fit can be achieved at the cylindrical wall to prevent leakage of the mercury. The motion of the plexiglass block was performed with a single electrical motor via a transmission and a
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