Long range, continuous flow of liquid metals occurs upon application of an electric current. Here, we report experimental results elucidating the mechanism of current-induced liquid metal flow, and its dependence on substrate surface condition. It is shown that the observed flow is diffusion-controlled, with the flow-rate depending linearly on applied current density, indicating that it is driven by electromigration. The effective charge number for liquid electromigration, Z*, of several pure metals, such as Al, Bi, Ga, Sn, and Pb, were deduced from the experimental results and were found to be close to the elemental valency. With the exception of liquid Pb, Z* for all liquid metals tested in this study were positive, indicating that: (i) electron wind contributes much less to Z* in liquid metals than in solids, and (ii) with a few exceptions, liquid metals generally flow in the direction of the electric current. On smooth substrates which are wetted well by the liquid metal, flow occurs in a thin, continuous stream. On rough surfaces which are poorly wetted, on the other hand, discrete beads of liquid form, with mass transport between adjacent beads occurring by surface diffusion on the substrate. A rationale for the role of substrate roughness in fostering this observed transition in flow mechanism is presented.
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The Wenzel and Cassie states describe two extremes of wetting behavior of a liquid on a rough surface (i.e., surface with asperities). When wetting is poor, the liquid droplet rests on the top of surface asperities only (Cassie), whereas when wetting is good, the liquid penetrates into the troughs between asperities (Wenzel). The apparent contact angles under Wenzel (θapp,W) and Cassie (θapp,C) states may be expressed in terms of the wetting angle (θo) on a flat surface as:36–41 and , where rW and rC are the ratios of the actual solid-liquid contact area to the projected contact area for the Wenzel and Cassie states, respectively.
The contact angle under Cassie condition depends only on p (i.e., the area fraction of asperities), independent of the h/λ value. At p→0 (pinpoint asperities), the wetting is the poorest (largest θapp/θo), and improves with increasing asperity area fraction.
The apparent work of adhesion at the solid-liquid interface, WSL, is given by the Young-Duprée equation: , where γLV is the specific energy of the liquid-vapor interface.
