 In this module, we will talk about the microbial growth kinetics in continuous cultures. As we have seen in our previous modules, the growth parameters, which we can say that kinetic parameters in batch culture fermentation as well as fat batch fermentation. In this module, we will take that what will be the continuous culture that is basically for changing the batch culture into the continuous culture. So, during the batch culture, when there is a exponential phase of the growth, when there is a continuous specific growth rate with respect to the time that affected sometimes due to some substrate depletion. So, we can say that the exponential growth may affect by the utilization of some substrate which we have seen in previous module which we called as limiting substrate. So, in fat batch we see which we only add limiting substrate into the fermentation medium during the fermentation period, but we have no harvest. But in case of continuous culture, as we can see that the exponential growth in batch cultures that can be prolonged by the addition of the fresh medium to the vessel. So, provided that the medium has been designed such that the growth sub that growth is substrate limited mean that growth is affected by some media component. So, that is not limited to the toxin produced in that medium, but that is affected by the depletion of any one substrate. So, we can prolong the exponential phase by the addition of the substrate that we know that that is utilized or exhausted. So, thus we can repeat it. We can maintain the exponential phase until we can utilize the full volume of the vessel mean working volume of the vessel as we have seen in fat batch. So, when there is no more capacity of the vessel which we have already told you that in state fermentation in deep fermentation we can utilize maximum 75% of the total volume of the fermenter. So, when there is a full capacity filled by that medium then we cannot have the provision to add the more substrate. So, if in such case when there is a facility of the overflow mean when we are adding something on other hand we are having some device to facilitate us to overflow then so when we add the medium that is displaced by the equal volume that we are adding. So, from this we can maintain the volume of the vessel. So, by this adjustment in which we are adding and we are something harvesting then we can call as the continuous culture. As we have seen in our previous module when we talk about the types of fermentation on the base of process. So, in that module we have seen with the help of different diagrams that we are adding on a one side and we are harvesting on another side. So, if the medium is continuously we can say that media is fed continuously into the volume into the vessel then there is a suitable rate of steady state mean on one side when we are adding some substrate and we are so harvesting something. So, then there is a steady state mean our flow inside and then and there is a fixed volume of the fermenter. So, in that case the formation of the new biomass so specific growth rate if the mu is equal to the dilution which we are adding that become equal then we can say that there is a steady state no change in the volume no change in the biomass concentration in that fermentation vessel so that is state in continuous culture referred to as steady state. So, you can see by this equation here that the dilution can be expressed with respect to the flow rate and the volume of the vessel that is already filled. So, the initial volume when we start addition of any substrate in the liquid form so the unit of flow rate can be expressed later per hour. So, here we can say that the volume will always be expressed in litter. So, then the units for the dilution is always should be in per unit time which is r. So, the net change in the cell concentration over the time period in the fermentation vessel can be expressed as we have seen that dx over dt is almost is a growth which we can say that mu x so this one we can say that mu x so as well as in a continuous culture that we are harvesting something so we are extracting something from that vessels which we can express as dx so this can be called as the equation that how the biomass concentration exist in the fermentation vessel while we are running the continuous culture. So, when we say that when there is equal dilution rate with the specific growth rate then the state comes when we say that steady state. So, the under steady state condition the cell concentration remain same mean there is no further change in the cell mass concentration so we can write here that dx over dt is equal to 0. So, by adding this dx over dt in a previous equation in a previous slide equation that mu x is equal to dx when we say that dx over dt is equal to 0 then by putting this value into that equation we achieve that mu x minus dx is equal to 0 and then obviously we achieve equation mu x over dx so this can easily be write down that mu is equal to d when mu is equal to d so this is the state when we say that that it is a steady state. So, under the steady state conditions the specific growth rate is controlled by the dilution rate. So, if we maintain the steady state we have our control over the dilution rate which is an experimental variable so when we are running the fermentation in a continuous mode so then we have to control our dilution as well as we have to control over the output. So, in this case we can recall that under the batch conditions an organism will grow at its maximum specific growth rate so therefore it is obviously then when there is a continuous culture that may be operated only at the dilution rate below the maximum specific growth rate. So, in a continuous culture when we say that here that in a batch culture that specific growth rate but in a continuous culture that can be operated through the dilution rate in order to have a below to that maximum specific growth. So, within a certain limit we can say that the dilution rate may be used to control the growth rate of the culture. So, by the addition and we can say that with the dilution rate in the continuous culture can be helpful in controlling the growth rate in a culture how it is it will we will see in the next slide that the growth rate that the growth of a cells in a continuous culture of this type is controlled by the availability of the growth limiting chemical components of the medium because when we say that continuous culture is going on and we are adding some media component which is actually chemicals which provide some nutrients to the organisms. So, we can say that state when that growth is dependable to that chemicals and then by the addition of those chemicals that steady state can be referred as chemo state and this chemo state we will discuss in detail in the later modules.