A size-structured model describing flocculation of unicellular algae

Abstract

Flocculation is a chemically-based microorganisms separation technology, which is widely used in the field of environmental engineering. The size of algae cell has a significant effect on photosynthesis and flocculation. In view of this, a size-structured model describing flocculation of unicellular algae is constructed for the first time in this paper. In Section 2, the model is introduced and then transformed into a dimensionless form. In Section 3, the well-posedness of the solutions of the model is demonstrated through the use of the theory of integral semigroups. In Section 4, the existence of the steady states of the model is analysed. It is proved that, when the threshold parameter R0>1, there is at least one positive steady state; when the threshold parameter V0<1, there is no positive steady state. Furthermore, the sufficient conditions are obtained for local and global stability of the boundary steady state. In Sections 5 and 6, some numerical examples are given, which show the existence of the interesting phenomenon of backward bifurcation when R0<1<V0.