Norbert Rillieux Multiple-Effect Vacuum Evaporator

Rillieux's multiple-effect system operates through five coordinated thermodynamic principles: (1) Raw clarified cane juice ($14^\circ\text{Bx}$) is pumped into the first closed vessel, where submerged horizontal copper tube bundles are heated by low-pressure steam ($P_1 = 160\text{ kPa}, T_{\text{sat}} = 113^\circ\text{C}$) supplied from the mill's steam-engine exhaust. (2) As the juice boils at near-atmospheric pressure ($100^\circ\text{C}$), the generated water vapor rises into an upper vapor dome. (3) Instead of venting this steam to the sky, Rillieux pipes it into the heating tubes of a second enclosed vessel maintained under partial vacuum ($P_2 = 50\text{ kPa}$) by an air pump. (4) Because water boils at a lower saturation temperature under vacuum ($T_2 = 81^\circ\text{C}$), the $100^\circ\text{C}$ vapor from Effect 1 has a positive temperature driving potential ($\Delta T \approx 19^\circ\text{C}$) to boil the juice in Effect 2 without consuming any additional fuel. (5) The vapor generated in Effect 2 is similarly piped to heat a third vessel operating under deep vacuum ($P_3 = 16\text{ kPa}, T_3 = 55^\circ\text{C}$), evaporating three pounds of water for every single pound of boiler steam ($S = \dot{m}_{\text{evap}} / \dot{m}_{\text{steam}} \approx 2.85$).