Predicting the spreading kinetics of high-temperature liquids on solid surfaces
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Predicting the spreading kinetics of high-temperature liquids on solid surfaces Douglas A. Weirauch, Jr. Alcoa Technical Center, 100 Technical Drive, Alcoa Center, Pennsylvania 15069 (Received 15 September 1997; accepted 12 March 1998)
The rate of movement of liquid drops toward their equilibrium position on smooth, horizontal solid surfaces (spreading kinetics) is considered in this study. A model for nonreactive liquid spreading which was developed for low-temperature liquids is applied to results for a set of high-temperature liquids and room-temperature liquids. These data were generated in a single laboratory following a consistent experimental methodology. The liquid-solid pairs were chosen to result in weak or no interfacial chemical reaction. Furnace atmospheres were chosen to provide data for liquid metals with submonolayer, thin or thick oxide films. Analysis of the high-temperature spreading kinetics for liquids covering a broad range of viscosity, surface tension, and density shows that they can be predicted with a constant shift factor applied to the deGennes expression for nonreactive spreading. The consequences of gravitational and inertial forces, substrate roughness, weak interfacial reactions, and liquid-metal oxide films are discussed.
I. INTRODUCTION
A model for the spreading of low-temperature, nonreactive liquids which is described by deGennes1 has been found useful in describing the earliest stages of flow of liquid metals on solid metal surfaces2 and liquid silicates on ceramic surfaces.3,4 This model allows quantitative predictions of the effect of liquid surface tension, viscosity, and drop geometry on spreading kinetics. A brief discussion of key developments in understanding which led to the deGennes model will aid in the discussion of its limitations and usefulness. Tanner5 described the power law behavior of the spreading radius of silicone oil droplets with the following expression r , t 0.1 .
(1)
This form was demonstrated to apply to small droplets (influenced by viscous and interfacial forces only) with a range of viscosity of 1.1 to 106 Pa ? s. Marmur reviewed the literature for droplet spreading and showed this general form was valid for liquids covering a broad range of viscosity (0.1–500 Pa ? s), surface tension (0.020–0.073 Nym) and droplet volumes (1.6 3 1029 to 1.3 3 1027 m3 ).6 They also concluded that the most likely dependency of spreading radius on droplet volume, V , was V 0.333 . The dependency of spreading on surface tension and viscosity was stated to be unclear. Hoffman7 in earlier work had forced various fluids through a 2 mm diameter glass capillary and developed the following relationship between the apparent contact angle, ua , and contact line velocity, U, Ca Uhyg constant xuam .
(2)
J. Mater. Res., Vol. 13, No. 12, Dec 1998
The exponent, m, equals 3 at the limit of low contact line velocity and low contact angles. As the contact angle approaches 180±, it becomes independent of contact line velocity. deGe
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