  Flocculation is the process whereby particles (i.e., flocs) in suspension
reversibly combine and separate. The process is widespread in soft matter and
aerosol physics as well as environmental science and engineering. We consider a
general size-structured flocculation model, which describes the evolution of
flocs in an aqueous environment. Our work provides a unified treatment for many
size-structured models in the environmental, industrial, medical, and marine
engineering literature. In particular, our model accounts for basic biological
phenomena in a population of microorganisms including growth, death,
sedimentation, predation, renewal, fragmentation and aggregation. Our central
goal in this paper is to rigorously investigate the long-term behavior of this
generalized flocculation model. Using results from fixed point theory we derive
conditions for the existence of continuous, non-trivial stationary solutions.
We further apply the principle of linearized stability and semigroup
compactness arguments to provide sufficient conditions for local exponential
stability of stationary solutions as well as sufficient conditions for
instability.
  Abstract. The end results of this analytical development are relatively
simple inequality-criteria which thus allows for the rapid evaluation of the
existence and stability of a non-trivial stationary solution. To our knowledge,
this work is the first to derive precise existence and stability criteria for
such a generalized model. Lastly, we also provide an illustrating application
of this criteria to several flocculation models.
