One of these distilling apparatus (10) comprises two columns, an evaporation column (14) and a condensation column (16), separated by a partition (18) equipped with rows of slits dividing them into 4 distillation stages. The evaporation column (14) comprises plates with hydrophilic or wettable faces, and the condensation column comprises rectangular hollow-plate (21) heat exchangers (221-6). Cold water ascends in these exchangers and saturated humid hot air descends in the condensation column (16). A perforated sheet (251-4) increases the uniformity of the partial airflows descending between the plates. The water is heated in a boiler (34); the hot water is scattered at the top of the evaporation column and the air cooled in the condensation column is sucked downwards by a fan (34). The air flows in a closed circuit. Performance is maximised, after the top temperature TE2 (45 to 90° C.) and the mass flow rate QE0 of the scattered water have been set, by adjusting the mass flow rate QA1 of the sucked dry air in order to give the temperature TA of this air a preset value at the top of the lowest evaporation chamber. Next, the effective cross sections of the partition apertures are adjusted in order to bring the air exiting from the evaporation chambers of higher rank to other preset temperatures TA2 to TAN, the enthalpy curves of the air deviating from flat by <1.5° C. Next, the effective cross sections are corrected in order to make the temperature of the air at the entrance of an evaporation chamber equal to the temperature at the exit of the condensation chamber of the same rank. The performance coefficient (PCo) of the apparatus may be >6, with a satisfactory flow rate of distilled water. Applications: production of fresh or very high purity water; production of concentrated industrial wastewater; production of high-concentration ethanol, acids or bases.