This article deals with the development of a non-equilibrium model for solv
ing problems with three liquid phases. The model consists of the material b
alance equations, the interface material balance equations, the transfer-ra
te equations and the interface equilibrium equations. First the two liquid
phase non-equilibrium solution is obtained. Then rigorous stability analysi
s in the form of the tangent plane criterion is used on two liquid phase so
lutions to detect the presence of the third liquid phase. The model equatio
ns are then solved to obtain the three liquid phase non-equilibrium solutio
n.