About the chemostat model with a lateral diffusive compartment

TL;DR

This paper analyzes a modified chemostat model with an added diffusive compartment, exploring how spatial structure influences species survival, yield, and efficiency, and identifying optimal configurations for minimal volume requirements.

Contribution

It introduces a chemostat model with a diffusive compartment and determines optimal structures for maximizing efficiency and species survival.

Findings

Single-tank configurations with diffusion can be most efficient.

Optimal volume and diffusion parameters depend on species and yield goals.

Spatial structure can improve species survival compared to single chemostats.

Abstract

We consider the classical chemostat model with an additional compartment connected by pure diffusion, and analyze its asymptotic properties. We investigate conditions under which this spatial structure is beneficial for species survival and yield conversion, compared to single chemostat. Moreover we look for the best structure (volume repartition and diffusion rate) which minimizes the volume required to attain a desired yield conversion. The analysis reveals that configurations with a single tank connected by diffusion to the input stream can be the most efficient.