 This module is the continuation of the fat batch culture kinetics. So, this module is the fourth module of fat batch culture kinetics. So, as we discussed in previous module of the various strategies of fat batch and then how we maintain the quasi steady state during the fat batch. So, when that mu is equal to D. So, the D is directly effect on mu and different other parameters of the fermentation process. So, as we already discussed that part expressed the change in product concentration in a variable volume especially in fat batch culture. So, the D P over D T is equal to Q P dot x minus D P mean if there is a product basically this equation is the continuous culture equation, but also utilize this equation for the fat batch culture too. So, we will discuss in detail in later on. So, if we talk about the product concentration change according to the balance between the product rate and the dilution by the feed. So, the dilution rate. So, if we say that fat batch quasi state change over the time of the fermentation mean if mu is not equal to D. So, then there is a drift in mu or a D with respect to D. So, if we cannot balance between these two rate production rate as well as the dilution rate then the steady state can be disturbed. So, the product concentration in fat batch system over the time of the fermentation depend on the relationship of Q P and mu which we called as specific growth rate. Hence, we can say that it totally depend upon D which we called as dilution rate. So, the F Q P is strictly growth related mean our product is growth related then it will change as mu with D. So, if mu and D is disturbed or a change then we can say that our product associated with the biomass will also change. So, the product concentration in such contains fashion when there is mu is equal to D and there is a constant increase in the product as we say when our product is directly associated with the biomass in previous module we see that when there is a variable volume and mu is equal to D then there is a constant concentration of the biomass. So, we can say here the same way the product concentration also remain the same. So, as much as the product concentration increase what happen due to the dilution volume also increase as an example we see if there is a fermentation vessel and here is a 5 liter volume and there are a 5 organisms and the 1 liter of the addition of the medium and that become a 6 liter total volume and during that the addition of the 1 liter medium into the fermentation vessel there is the increase of 1 cell and then the total number of cells is 6. So, when we see that 5 organism in 5 liter so, 1 organism per liter. So, when there is addition of 1 liter volume so, by the same time there is 1 more organism. So, the 6 organism per 6 liter. So, the ratio remain the same by the same way if the product concentration remain the same in fat batch quasi-state. So, we can say that the Q p is constant and independent of mu specific growth rate. So, then the product concentration well the start of the cycle when D p is greater than Q p x, but will rise with time as D decreases. So, as the D will decrease mean dilution will decrease then the product concentration will increase. So, the if the dilution will increase then product concentration decrease. So, it directly associated with the D. So, we can easily say that if our product is directly associated with the biomass. So, the same way when the dilution is equal to the mu then x remain the constant and the p will also remain the constant. If the D will increase then the biomass concentration also decrease and the product concentration also decrease. But if the D will decrease mean dilution rate will decrease then what happen x will also increase and p will also increase. So, if the Q p is related to the mu in a complex manner then the product concentration will vary according to the relationship as I already told you. Thus the feed strategy of the system would be optimized according to the relationship between Q p and the mu. So, overall to run the fat batch culture in a variable volume our main focus on the addition of the limiting substrate by knowing at what time what substrate will be the depleted. Keep in mind a very less change in the volume. So, mostly when we say in as an example when we have a culture of a baker yeast fermentation in the start we having us small amount of the medium and we have the inoculum. And there is a continuous feeding of the medium and the yeast grow with respect to the mu we are adding and there is a gradual change into the medium. So, as well as the fermentation volume will increase in the fermenter what happen the biomass will also increase. So, that we can run the fat batch under to that limit up till the fermentation vessel allow us. So, as I already told in previous module that we can only use the 75 percent of the total fermentation vessel volume. So, the remaining is needed for head space which is very critical during the fermentation process.