Use of homotopy-continuation method in stability analysis of multiphase, reacting systems

In nonideal chemical systems, in which chemical reactions occur in more than one phase, more than one equilibrium condition can exist, but not all may be stable. To find stable solutions to chemical and phase equilibria (CPE) problems, a homotopy-continuation is applied and stability criteria are investigated to determine how many stable phases are present at equilibrium. The method is illustrated by two problems.