A distillation apparatus includes at least one evaporation space in which feed water is evaporated into a vapour and at least one condensation space, in which vapour from a preceding evaporation space is condensed into distillate. The evaporation space and the condensation space each include a chamber and a plurality of interdigitated pockets arranged between said chambers, such that a first pocket of the evaporation space is present between a first and a second pocket of the condensation space, and that the first pocket of the condensation space is present between the first and a second pocket of the evaporation space. The spaces are mutually separated by means of a separation barrier that is configured for transmission of heat and for definition of the interdigitated pockets.