Effects of spatial structure and diffusion on the performances of the chemostat

TL;DR

This paper investigates how spatial structure and diffusion influence steady-state nutrient concentrations in chemostat systems, revealing thresholds and conditions where configurations outperform or underperform compared to perfect mixing.

Contribution

It provides a comparative analysis of different chemostat configurations and identifies conditions under which spatial structure and diffusion improve or impair performance.

Findings

Existence of a nutrient input threshold reversing configuration benefits.

Non-monotonic dependence of output on diffusion rate.

Conditions where diffusion enhances chemostat performance.

Abstract

Given hydric capacity and nutrient flow of a chemostat-like system, we analyse the influence of a spatial structure on the output concentrations at steady-state. Three configurations are compared: perfectly-mixed, serial and parallel with diffusion rate. We show the existence of a threshold on the input concentration of nutrient for which the benefits of the serial and parallel configurations over the perfectly-mixed one are reversed. In addition, we show that the dependency of the output concentrations on the diffusion rate can be non-monotonic, and give precise conditions for the diffusion effect to be advantageous. The study encompasses dead-zone models