A method for precise control of movement of a motive phase on a lubricant-impregnated surface includes providing a lubricant-impregnated surface, introducing the motive phase onto the lubricant-impregnated surface, and exposing the droplets to an electric and/or magnetic field to induce controlled movement of the droplets on the surface. The lubricant-impregnated surface includes a matrix of solid features spaced sufficiently close to stably contain the impregnating lubricant therebetween or therewithin. The motive phase is immiscible or scarcely miscible with the impregnating lubricant.