 In this module, we will talk about the microbial growth kinetics, which is the 5th module of fat batch culture kinetics. But in this module, we will talk about the second type of fat batch in which the volume remain fixed. So, as we discussed in previous module about different strategies in fat batch. So one strategy when we utilize the concentrated amount of the substrate while feeding. So when such condition when there is a fixed volume, so the fixed volume kinetics is discussed again part 1975. So he described the kinetics of the fixed volume fat batch culture. So he considered the batch culture in which the growth of the process organism depleted the limiting substrate to a limiting level to a certain level. So when that limiting substrate is depleted to a limiting substrate and then you add because when sometime is depleted that is the deficiency of that. So you fill that deficiency in the medium by adding those limiting substrate only. So if there is a such conditions in which you only add the limiting substrate then added in a concentrated feed such that the broth volume mean fermentation volume remain constant. Then we can say that the dx over dt mean change in substrate biomass concentration with respect to time is equal to gy. So where the g is the substrate feeding rate and y is the yield factor. So if we are feeding in such a way and the volume remain constant and the change in biomass with respect to change in time is equal to the feeding strategy and the yield factor. So what is the yield factor and what is the feeding strategy? So by this equation you can easily mention as you can easily see that in fixed volume fermentation during the fat batch that how the change occur. And we know that dx over dt is equal to mu x. So by putting the value of this you can write this equation mu x is equal to gy. So if we directly say that if we want to calculate the specific growth rate during the fat batch in a fixed volume then this equation can give the solution of that. So we can calculate if we know the feeding strategy rate and then know the yield factor and divided by that biomass then we can easily calculate the specific growth rate in a fixed volume fat batch provided that gy over x does not exceed the mu max. So the mu which we call that gy over x is equal to the mu in a previous slide. So that does not exceed the mu max. So then the limiting substrate will consume as it enters the fermenter ds over dt is equal to 0. Because in fixed volume and our feeding strategy directly based upon that we are only adding the substrate when that is depleting no more availability of that. So if the substrate is available there then there is a room for the increase in the mu. So if the change in substrate concentration with respect to the change in time that becomes 0 then only we can say that dx over dt may not be equated to 0 in this case in a fixed volume because the volume remain fixed and the in result of the mu what happened there is a continuous addition of the biomass in the substrate and then that culture broth fermented broth become concentrated with the biomass. So as well as the total amount of the biomass in the fermenter will increase with time biomass concentration you can see by this equation. So xt is the biomass after operating in fed batch. So x0 is replaced by x epsilon. So this xa are known that can be donated at that biomass at the time when we add something at the time of the feeding. So the g we already know that is the feeding strategy and y is the yield at time t. So by this equation you can easily say that we can determine the amount of the biomass that is present. So that we only determine if we know the existing biomass in the fermenter vessel. So as we know that when there is a feeding and during the fermentation period we are having three or four time feeding and then there is a four to three time then in the start the fermentation fed batch can be called as the batch culture and then become the fed batch. So initially all the fed batch fermentations will be considered as the batch culture. But later on that come into the entry of fed batch strategies. So as the biomass increase then the specific growth rate will decline according to the equation. So sometimes when there is we can say that a feeding strategy and we can say that our existing biomass become the base of the further increase in the biomass. So sometimes the mu cannot be same because if the feeding strategy somebody say that the feeding strategy is not equal to the mu then what happens sometimes there is a minor fluctuation in the growth rate. So by keeping the detailed record of the change in the biomass and the screening strategies when then we can say that there will be a good fed batch fermentation otherwise then fed batch can lead to the loss of so many substrates because we run only the fed batch in order to utilize the maximum utilization out of the substrate because sometimes in batch fermentation sub substrate when we add in excess amount in the initial time then that become a toxic. So due to which if there is a continuous residual substrate during the fed batch that can lead to the same threat as we have in a batch culture.