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180           CHAPTER 6.  STEADY-STATE MACROSCOPIC BALANCES


               e Two steady-state solutions exist when  < 0.25 and y = ymin < ymax or,
                 Ymin  < Y = Ymax,
               e Three steady-state solutions exist when /3  < 0.25 and Y,,,~,,  < y < ymax,
            where ymin and rmax are defined by









            The existence of  more than one steady-state solution is referred to as multiple
            steady-states.  For  more detailed information on this problem see Kauschus et  al.
            (1978).
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