It is a bioreactor keeling Chemical environment is static

Fresh medium is added continuously and culture liquid is removed by keeping  culture and chemical environment constant 

 Originally Chemostat was the name given to a device that enables people to grow and harvest bacteria continuously, in contrast to the older batch culture in which a fixed quantity of nutrient was supplied and bacteria were harvested after a chosen growth period. In general, the chemostat is operated (as long as possible) in a steady state (for example in a logarithmic growth phase of the bacterial population). As Dr. Murugesan Muthu says, now chemostat is used in a wider sense to refer to a continuous flow bio reactor operated in steady state.

Now a days 'Chemostat'  used to grow microorganism in fixed quantity of a particular substrate rather then all supplements and only that quantity of particular substrate is maintained and cells were harvested along with product. 

use  the link below

https://en.wikipedia.org/wiki/Chemostat

http://bio.classes.ucsc.edu/bio117a/Novick%20and%20Szilard%201950.pdf

http://www.sciencemag.org/content/112/2920/715.extract

"During chemostat culture, the concentrations of cells and all substrates and products in the medium do not vary with time."

Page 664 from the book "Bioprocess Engineering Principles", by Pauline M. Doran. It's one of my reference books when I need something.

https://books.google.com.ar/books?id=Z-N4SNmsYnMC&lpg=PA809&vq=chemostat&pg=PA664#v=snippet&q=chemostat&f=false

A chemostat is a constant environment reactor where the operational parameters are constant and under control. These parameters include pH, substrate flow rate, mixing speed, temperatures and others. Other reactor is named turbidostat where the parameters are controlled by monitoring the optical density in the reactor.

The chemostat is an experimental apparatus where the chemical environment can be maintained static and nutrient availability can be controlled by the experimenter. This is achieved by culturing cells in a vessel subject to continuous supply of nutrients and continuous overflow of content exceeding the vessel volume (a glass under a dripping tap is good analogy).

Article The Use of Chemostats in Microbial Systems Biology

Chapter How Fast Can We Grow?