Multiplicity and stability analysis of continuous pre-fermentation of cheese culture

Abstract

Unlike the usual multiplicity of steady states in continuous stirred- tank bioreactors caused by the non-monotonicity of substrate dependent rate expression(s), this paper described a different multiplicity caused by the effect of [H+]. The multiplicity of the bioreactor for cheese pre- fermentation is also described in this paper. Phase plane analysis shows clearly the separatrix that separates the zone of stable steady state from that of unstable steady state. The steady state becomes unique and elimination of multiplicity by supplying a seed stream, which also guarantees stability. Stability analysis of the multiple steady state shows that unlike the usual necessary condition (δμ/δS > 0), this process stability demands the opposite necessary condition (δμ/δ[H+] < 0).