 This module is actually the second modules of the growth kinetics in continuous culture. As we have seen in a previous module that we can control our growth rate in the continuous culture with the help of the dilution rate. But now we will discuss in detail that is how this substrate concentration and thus maximum specific growth rate how they are associated to each other. So, as concerned the mechanism underlying the controlling effect of the dilution rate is basically essentially the relationship expressed as by the Monard equation 1942. We have seen in our previous kinetics modules that Monard equation is mu is equal to mu max S over k S and S. So, here we can say that the mu max maximum specific growth rate and k S which we called as substrate utilization constant these two parameters known as Monard parameters. So, in a continuous culture when we say that mu is equal to d mean our specific growth rate when we come to the dilution rate. So, as well as there is a dilution and then there is a growth and there is no more change in the cell mass concentration in fermentation vessel. Then we can transform this equation just by the change of mu with d. So, we can say here that d is equal to mu max S bar over k S plus S bar just a minor difference in a previous equation to this equation is that what is the difference between S and S bar. So, S bar is the substrate concentration when the culture in steady state. So, simple S is only the substrate concentration which we called as residual substrate concentration which we are. So, here we can say that S is the substrate concentration at steady state. So, by this equation if we can easily calculate if we know the dilution rate then we can we can easily calculate the amount of this substrate at the time of steady state by just transforming this equation into this. So, this equation can easily be so S bar is equal to k S d is a dilution over mu max minus dilution. So, this whole equation is basically just the retransformation of this equation we can use easily. So, when we say in this equation so this equation can predict that the substrate concentration is determined by the dilution rate. So, in fact, so when there is a dilution that can actually the predict the substrate concentration inside the fermentation vessel. So, we can say that that in fact, this occur only when the growth of the cells depleting the substrate to a concentrate that sport the growth rate equal to the dilution rate mean when we are adding something and growth will happen when there will be a growth as well we say that when there is a growth cells number will be increased as well as the cell number will increase their utilization of the substrate will also increase. So, in such case when there will be a more more growth more cell will be there then we can say that there will be a more utilization of the substrate. So, the actual the substrate concentration in such condition is directly related to the dilution rate. So, if we can say that the substrate concentration inside the continuous culture is directly related to the dilution rate. So, we can assume four possibilities that if there is a change either in a specific growth rate into the fermentation vessel or there is a change in the dilution rate what will the possible happening inside the fermentation vessels. So, these are the four different possibilities which we will discuss here that just we can see here that if the growth rate of the cells will be less than the dilution rate mean mu if the mu is less than D then what will happen. So, then they will washed out of the vessel mean when there is a less growth rate and dilution is more than mu then what happened we are harvesting the medium with the same rate what happened there will be a gradual washing of the cells. Then the total number of concentration inside the fermentation vessel will remain less than the initial one. So, by this case that the biomass concentration inside the vessel will be decreased. So, when the biomass inside the vessel will decrease it can effect what will be that. So, when there is a less substrate then there will be a more availability of the substrate because the relationship between the substrate availability to the existing cells what happen then there will be a more substrate and the present number of cells have the more chance to utilize the substrate. So, in the first condition lead to the second situation. So, when there is a second situation that can lead to the third situation what happened. So, when there is a increased substation substrate concentration it effect directly on mu. So, by this case when there is a more substrate then there is a higher rate of specific growth rate. So, by when in first condition when there is a washing out and then there is a decrease in substrate in a biomass concentration and dilution is the same what happen then the more availability of the substrate that lead to the higher rate of the specific growth rate. So, when we say that there is a high growth rate and with respect to the higher substrate that increase substrate's concentration in the vessel that result will growing the higher rate than the dilution rate. So, the biomass concentration inside the fermentation increase. So, this is the third situation which will occur as the result of the first one. So, in such case in a fourth situation we can say that the steady state will be reestablished. So, these are the four possibilities can happen when there is a change in the steady state or actually what happen then it is all the time that in a continuous culture that the reestablishment of the steady state will happen. So, thus the chemo state is the nutrient limited shelf balancing self balancing culture system which may be maintained in a steady state over a wide range of sub maximum specific growth rate. So, we can say that the concentration of the cell in the chemo state which we have already seen this by such kind of the equation in a batch culture that X is equal to the Y which is yield coefficient and that is directly related to the initial substrate concentration and as well as the residual substrate concentration. So, just by changing this that X into X bar. So, X is the biomass concentration in the fermentation vessel, but X bar is the substrate concentration when there is a steady state. So, in this equation as I already told when this steady state biomass concentration can easily be calculated by this by addition of in this equation we can say that the mu max and K s as the monod constant and D is the dilution rate and S r is the substrate concentration. So, by so we can say that the biomass concentration at steady state it determined by the opressional variables S r D. So, the S r is increased then X bar will increase, but the S which we called as the residual substrate in the chemo state will remain the same. So, because as well as we add the substrate then that will be utilized. So, if the D is increased then the mu will also increase. So, mu and D is very critical in this case. So, and the residual substrate at the new steady state would have increased to support the elevated growth rate. So, thus the biomass resulting in the lower steady state. So, in such case when there is a re-establishment of the steady state then that is totally dependent upon the dilution rate which can be controlled through the mechanical parameters in continuous culture.