Thermal management is the current bottleneck in advancement of high-power integrated circuits (ICs), and phase change heat sinks are a promising solution. With a unique structural configuration consisting of a membrane positioned above the heater surface, membrane-based heat sinks (MHS) have thus far attained heat fluxes of up to 2 kW/cm2 and HTC of up to 1.8 MW/m2K using water as the working fluid. This work reports the latest progress and performance evaluation of MHS for high flux thermal management. MHS is implemented in conjunction with a low surface tension liquid to rapidly expel bubbles from the heated surface and reach a CHF of 340 W/cm2 and a HTC of 120 kW/m2K. A parametric comparison shows that thermal efficiency, defined as the ratio of cooling capacity and pumping power consumption, of the prototypical devices exceed values reported hitherto in literature by more than two orders of magnitude. Our results indicate that coupled with surfaces of higher thermal conductivity and membranes of higher permeability, MHS devices could be a promising solution to thermal management needs of high-power electronics and lasers.