I'm wondering how I can derive the return time of the culture cell concentration back to a steady-state in a chemostat after a small perturbation of the bulk culture cell concentration.
More specific, I have the following situation. I have a very small chemostat with a working volume of about 200 µL. Influx is achieved via a very small needle which drops fluid in the reactor. At this small scale, the influx cannot be seen as a continuous stream, but rather as points in time when the next drop is added. Consequently, when a new droplet is added, the culture concentration in he chemostat drops slightly, which is seen as a perturbation from the steady-state situation. Now, I want to determine how long it takes for the system to recover and again arrive at the steady-state situation.
The chemostat is assumed to be perfectly mixed, and the working volume of the reactor is constant over time (efflux is removed by overflow at a certain level in the reactor).
Any answers or suggestions how to calculate this are very welcome!
