Analyses of conventional microchannel and microgap cooling show that galinstan, a recently developed non-toxic liquid metal that melts at -19°C, may be more effective than water for high flux thermal management applications. This is because its thermal conductivity is nearly 28 times that of water. However, since the specific heat per unit volume of galinstan is about half that of water and its viscosity is 2.5 times that of water, caloric, rather than convective, resistance is dominant. We analytically investigate the effect of using microgaps that incorporate structured surfaces to ascertain their efficacy in reducing overall thermal resistance of galinstan-based thermal management in the laminar flow regime. Significantly, the high surface tension of galinstan (10 times that of water) implies that it can remain in the non-wetting Cassie state at the requisite pressure differences for driving flow through microchannels and microgaps. The flow over the structured surface encounters a limited liquid/solid contact area and a low viscosity gas layer interposed between the channel walls and galinstan. Consequent reductions in friction factor result in decreased caloric resistance and reductions in Nusselt number produce an increase in convective resistance. These are accounted for by recently developed expressions in the literature for hydrodynamic and thermal slip.
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