Because the boiling temperature of water decreases as pressure decreases, the vapor boiled off in one vessel can be used to heat the next, and only the first vessel (at the highest pressure) requires an external source of heat.
The multiple-effect evaporator was invented by the American (Louisiana Creole) engineer Norbert Rillieux.
Although he may have designed the apparatus during the 1820s and constructed a prototype in 1834, he did not build the first industrially practical evaporator until 1845.
In practice the design liquid flow paths can be somewhat complicated in order to extract the most recoverable heat and to obtain the highest evaporation rates from the equipment.
Entrainment of the product in the solvent causes a number of issues including firstly decrease in the amount of product recovered, secondly potential damage or fouling of the evaporation lines and steam chest of the next stage, and thirdly problems dealing or disposing of the solvent.