An energy-efficient liquid-gap distillation apparatus includes a source of a feed liquid; a distillation module comprising: (a) a feed-liquid chamber n fluid communication with the feed-liquid source to establish a flow of the feed liquid there through, wherein the feed-liquid chamber includes a selectively porous material that allows a component of the feed liquid to pass through the selectively porous material and exit the feed-liquid chamber in vapor form but not in liquid form; (b) a condensing surface maintained at a lower temperature than the feed liquid in the feed-liquid chamber, wherein the condensing surface is sufficiently hydrophobic to produce a contact angle with water of at least 150; and (c) a gap between the selectively porous material and the condensing surface. Vapor passing through the membrane can be condensed as jumping droplets at the condensing surface.