An analysis for spreading kinetics of liquid metals on solids
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instantaneous contact angle O decreases progressively with contact time (spreading time). The O vs t experimental data for selected systems were fitted (Figure 2) to an empirical relationship of the form O = O0 + O0 exp [B - At]
where the empirical constants A and B were determined from a plot of In [(O/O0) - 1] vs t and are listed in Table I. This relationship appears to adequately describe the time dependence of dynamic angles. A similar exponential relationship between O and t has been observed earlier in some polymeric It3j and metallic 1141 systems. During spreading (Figure 3), the droplet makes a point contact with the solid at t = 0 (O -- 180 deg and the contact radius a = a0 = 0). (In reality, however, the idealized situation is seldom observed due to difficulties in measurements at t = 0; as a result, O < 180 deg and a0 > 0 at t = 0.) Thereafter, the liquid droplet begins to spread onto the solid, and the instantaneous value of O progressively decreases with time, eventually reaching an equilibrium value O0. The mechanism of spreading is generally quite complex, and the progression of wetting perimeter is often spearheaded by a thin precursor film of liquid tjS'161 so that the measured | is, in effect, an apparent rather than a true value. As the shape of the spreading droplet can be approximated to a hemispherical cap to a fair degree of accuracy, the droplet volume can be expressed as (12 + 3a 2)
An Analysis for Spreading Kinetics of Liquid Metals on Solids R. A S T H A N A It is well known that contact angles in metallic systems measured using the sessile drop technique, generally show a very significant time dependence at a constant temperature. Typically, the contact angle O is obtuse at small contact times t but decreases rapidly to a constant (equilibrium or static) value 190 at long times. Many materials processes of technological importance that require consideration of wetting behavior proceed to completion on timescales that are comparable in magnitude to the transient phase of wetting in a given system. It is therefore inappropriate to use equilibrium values of contact angles in modeling dynamic processes that proceed at sufficiently small timescales. Insights into the dynamic character of the process of wetting can be obtained from the time dependence of contact angles. A simple analysis of dynamic contact angle data has been presented in this article to estimate spreading kinetics of liquid metals on different types of solids. Figure 1 shows literature values It-t21 of sessile drop contact angles as functions of time in the following systems: Sn-Mo, Si-C, A1-AI203, AI-SiC, Au-AI203, AI-BN, AI-Cu, AI-4.5Cu-I.45Ce-AI203, and Cu12.6Ti-AI203. In all these systems, the magnitude of the R. ASTHANA, National Research Council Associate, is with NASA Lewis Research Center, Cleveland, OH 44135. Manuscript submitted June 9, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS A
[1]
v = ~rl
[2]
6 where the cap height l and the radius of the base of the droplet a are both functions of time. For small cont
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