Mathematical analysis of the effects of particle retention efficiency on determination of filtration rate

Morphological, ecological, and behavioral aspects of filtration of small, inefficiently retained particles by benthic as well as planktonic filter-feeders are of current as well as historical interest. The exponential model applied to determination of filtration rate was originally conceived for filter-feeders clearing suspensions of large, efficiently retained cells. Therefore, applicability of this model and its assumptions to filtration of small, inefficiently retained particles merits critical re-examination. Derivation of the exponential model historically used in calculation of filtration rate is reviewed and shown to be inappropriate when filtration efficiency is less than 100%. Box models are constructed for filter-feeders that act either as sieves or aerosol filters in suspensions of small inefficiently filtered cells. The models predict a complex or double exponential decline in cell concentration that cannot easily be translated into filtering or pumping rates. The models further predict that apparent filtration rate will decline over time because of physical limitations, rather than behavioral changes, with respect to filtration efficiency. Compartmental analysis of filtration of inefficiently retained particles in a turbidostat system predicts a similar artifact in determination of filtration rate.