  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
floc size distribution 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, the mathematical
model considered in this work accounts for basic biological phenomena in a
population of microorganisms including growth, death, sedimentation, predation,
surface erosion, renewal, fragmentation and aggregation. The central objective
of this work is to prove existence of positive steady states 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 develop a numerical scheme based on spectral collocation method to
approximate these positive stationary solutions. We explore the stationary
solutions of the model for various biologically relevant parameters and give
valuable insights for the efficient removal of suspended particles.
