Introduction to Microbiology in Wastewater Treatment | Biological Systems

[00:00:05][Music] [Music] oh oh sh sh sh on [Music] in the last class we discussed about the wastewater treatment that is we discussed about primary treatment secondary treatment and tertiary treatment in fact uh we also discussed further on the various units that are present in the primary treatment and certain design aspects the systems that are the units or the systems that are present in the primary treatment are that is screens then grid chamber and sedimentation tank these are the very important uh parameters these are very important uh units these units are designed and some of the design aspects we have seen in today's class we will discuss about the secondary treatment secondary treatment is very very important because the objective of the secondary treatment is to the objectives of secondary treatment is number one to remove biodegradable bi biodegradable organic matter and this biodegradable organic matter is in terms of two things one is uh collidal form as well as dissolved form so the secondary treatment is aimed at removing the organic matter which is biod gradable okay and that organic matter which is biodegradable may be present in the form of a collidal collidal form or it is in the form of a dissolved form so this organic matter if not removed from the waste water and if we discharge the waste water with this organic matter into the rivers then there will be oxygen depletion so discharge of uh waste water containing organic matter is not permitted we have to remove it so in order to remove it what we do is we employ biological waste treatment systems biological waste treatment plants the purpose of biological waste treatment plant is to remove the organic matter that is a collidal form as well as in the dissolved form so the biological waste treatment plants obviously employs the microorganisms microorganisms are important or most important uh components of a biological wastewater treatment system so as the micro mic organisms do the work for us that is a cleaning up of the environment so we should know something more about the microorganisms or the microbes and uh in fact the microbes are used microbes are used to clean up the environment we are using the microorganism to clean up the environment the environment could be okay I will write environment okay EnV is for environment I could you environment could be three types of En environments one is what is called uh it could be lithosphere it could be hydrosphere it could be atmosphere lithosphere means land okay uh the three components of the environment are one is lithosphere that is a land environment where we live in and then hydrosphere is a water environment which use for uh you know the water for various beneficial uses and also the third component of the environment is atmosphere which is the air we breathe and so on so that means if the environment is pollut uted that polluted with biodegradable organic matter what we try to do is we clean up the environment okay using the microorganisms if I clean up the lithosphere land clean up of land if I call it using the microorganisms again everywhere I'm using the microorganisms for cleaning up then it is called bior remediation bior remediation is a process by means of w I can clean up the pollutants present in the land using the microorganisms if I uh in the river waters if I want to uh clean up the river now next is the clean up the the river so I employ what is called a waste water treatment plants waste water treatment plants are designed to clean up the uh waste before it enters into the rivers so cleaning for the river is by employing uh the waste water treatment plant treat the waste water treat treat the waste water and discharge into the rivers that is a cleanup of the environment uh as for as the lithosphere that is the hydrosphere is concerned the river is the hydrosphere third type type of thing is atmosphere so air pollutants that are present in the environment air pollutants that are present in the atmosphere can be uh removed using the microorganisms in such a case we use what is called a biot trickling filters using biot filters we can uh sort of clean up the air so the air may contain like socks oxides of sulfur oxides of nitrogen socks and nox so socks and nox can be removed using the biological reactors so in other words the microorganisms are very versatile they can be used to remove the pollutants from the land they can be used or to remove the pollutants from the river from the water they can be used to remove the pollutants from the air all three things are present so now it is a basic requirement for us since we employ the microorganisms to do work for us to clean up the environment we should know more about the microorganisms so now that particular thing microorganisms are to some extent I will say that microbiology we should know something about the microbiology I will give a brief introduction for the microbiology so microbiology that is required for the waste treatment or for cleanup of the environment we will discuss only that particular uh microbiology that is required so the microbiology means in this particular thing what I will be discussing is the types of microorganisms types of microorganisms we like to employ in the wastewater treatment or in the treatment of the land or in the treatment of the air so the types of microorganisms we'll discuss and then their nutritional requirements Nutri nutritional requirement of microorganisms which is important that we'll discuss and the environmental conditions we'll also discuss about environmental conditions which affects environmental conditions which affect the growth of microorganisms we'll discuss we'll also discuss about what is called biokinetic parameters for the microorganisms biokinetic parameters for the microorganisms these B biokinetic parameters are required they are required for the design of the treatment system for the design purposes this is required so for the design purposes the biokinetic parameters that are required are the following so for example I would like to know the growth rate of microorganisms that is again writing biokinetic parameters that is growth rate rate at which the microorganisms are growing of microbes in a given uh organic matter M microbial growth rate uh bod removal rate will study and Decay rate of mic organisms we'll study all these things in the biokinetic parameters all these parameters ought to be found out in order to design effectively the treatment system design of treatment system so in a series of lectures we are going to discuss these things and finally I also would like to uh discuss in this particular thing the microbiology the bioreactors types of bioreactors that are employed that are employed to treat the waste water okay and also the type of bioreactors is one thing and also we'll say that the oxygen requirements by the microbes will also be discussed in this particular thing and finally I'll discuss the uh treatment systems like treatment units like activated sludge then trickling filter and thirdly anerobic systems we'll discuss the design of these things at the end of uh the series of lectures you should be a in a position to design given the was Wast water and its characteristics and the quantity of waste water or the flow rate of waste water I should be able to choose uh which of the treatment systems I should employ and how to design that particular treatment system that's what we are going to do in series of lectures from today onwards so now let us see coming back to the type of microorganisms taking the first thing the type of microorganisms I there are many ways by means of which the microorganisms can be classified okay there are several ways and I will use a method of classification which is based on the nutritional requirement nutrient requirements any microorg or ISM for that matter any living System including us would require the following things number one we require an energy source in the food we eat we require energy source energy source is required in order to produce the energy for the microorganisms so we also required what is called a carbon source that means the food we ate we eat should contain a carbon compounds the food we eat should contain a compounds which produce energy so this energy that is produced from the energy source will be utilized for two purposes one is for the maintenance maintenance and for the other thing is for the biosynthesis maintenance and biosynthesis M maintenance energy that is uh the energy required for the cell to move around tell cell to conduct certain activities so that is the maintenance energy this is a biosynthesis for producing the more biomass so this is a carbon Source carbon source is required for the growth of microorganisms growth of microbes okay growth of microorganisms we require the carbon source that means the food we at or the organic matter I am providing to the microorganism should contain a carbon Source it should contain energy source Suppose there are different types of energy sources are the microorganisms can utilize different components different compounds for the energy source for example for energy if microorganisms use microbes use organic carbon compound organic compounds for energy if it is use if it uses organic compounds for energy then it is called heterotrophic organism it is called heterotrophic organism is anywh there it is heterotrophic it has it will use organic compound for energy and this heterotrophic organism uses organic compound for energy it also uses organic compound for biosynthesis as carbon source so same organic compound same organic compound can be used as a carbon source as well as energy source by heterotrophic organisms these are the majority of organisms present majority of organisms we encounter in nature majority of microbes we encounter in nature are of H this heterotrophic in nature in fact heterotrophic organisms are those organisms or the organisms who employ mostly in the wastewater treatment so these are employed in the wastewater treatment plant wastewater treatment plant these are employed so suppose if uh you if the microorganisms utilize instead of organic compound for energy purpose if they utilize inorganic compounds for energy purpose they are known as chemo autotrophic organisms so the second group of organisms are chemo autotrophs chemo autotrophs autotrophs is self- dependent so they are independent organisms they are depending on self only self-dependent organisms and they depend on the chemo chemo means chemical they depend on the chemical uh chemicals that is chemicals or inorganic chemicals for example energy source energy source for the chemo autr or uh energy source is inorganic inorganic compound so inorganic compound compounds like ammonia so this inorganic compound like ammonia is oxidized to nitrite and nitrate it is oxidized to nitrate and nitrate to produce energy so this produces energy this energy that is produced is in the form of atps ATP adenosin triphosphate okay this ATP is adenosin triphosphate adenosin triphosphate is a energy rich compound and it gives out the energy whenever energy is required so atps are produced these organisms which utilize this oxidize ammonia to nitrate to nitrate in the presence of oxygen oxygen is required for this and this organisms this is called n ronas and this organism here it's called nitrobacter it's called nitrobacter these are the two organisms which utilize the inorganic compounds for energy purpose okay second thing is that what is the carbon source for them carbon Source could be inorganic carbon compound inorganic carbon compound so the organism these organisms which utilize uh the inorganic compounds for energy and inorganic compounds as a carbon source for the carbon source is required as I told you for the growth of microorganisms this is used for the growth okay so the this carbon Source this is the energy source and this is the carbon Source these are known as autotrophic organisms these are special organisms we use them in specifically for the nitrification nitrification to occur in tertiary treatment because I discussed about the nitrification when I discussed about the tertiary treatment so in the tertiary treatment the nitrification occurs and I want nitrification to take place so this will happen you I mean this will occur because of these microorganisms the third type of organisms is what is called a photo autotrophs autotrophic organisms photo autotrophic organisms are those which contain which utilize sunlight energy sources in this case is sunlight they get energy from sunlight they trap uh energy from the sunlight and utilize the carbon dioxide as a carbon Source carbon source is carbon dioxide the simple reaction I can write it here is they utilize carbon dioxide plus water and this is the sunlight in the form of H new sunlight this is H new is sunlight plant constant and the this is a energy sunlight energy and the these are the photosynthetic these are photosynthetic plants and uh microscopic photosynthetic plant example is alal cell alal cell so with this reaction what would happen is that the resultant of this reaction H2O n plus oxygen H2O n n is nothing but a carbohydrate this is a carbohydrate they prepare carbohydrate a form of formula for carbohydrate and oxygen is produced by the photosynthetic cell this are photosynthetic reaction what we are writing so we have we utilize photo autotrophic organisms like algae in the wastewater treatment especially for the uh in in oxidation ponds the example where we use this particular thing is oxidation pond example of photosynthetic photo autotrophic thing uh organisms is oxidation ponds okay that's what we use uh the photosynthetic Auto organisms that means we use heterotrophic organisms we use chemo autotrophic organisms and we also use Photo autotrophic organisms for the wastewater treatment depending upon the type of reactors we are designing so basically most uh commonly used wastewater treatment or commonly used microorganisms in wastewater treatment as a already indicated are heterotrophic organisms okay heterotrophs are trophic organisms so again I re uh emphasize that the classification of these organisms are based on the nutritional requirement okay that is a carbon source and then the energy source that's what I have been discussing particularly these organisms there are certain other classification people have so many other classifications another classification I can tell you is one is that based on the temperature we we have what is called a cyrilic microorganisms cyrilic microorganisms are those microorganisms which grow under low temperatures for example these organisms grow in the refrigerators also they spoil the refrigerated food so the organisms that grow around 4° or to 10° cel s they are cyrilic organisms second type of organisms is mesophilic organisms mesophilic organisms are those organisms which grow in the medium temperature okay that is about say 27 to 35 27 to 40° C then we have got thermophilic organisms thermophilic organisms are those organisms which grow at a higher temperature that is about 40 45° to 60° C these are this is at another classification that is based on the temperature the tolerance of the microorganisms to the temperature however that classification is one classification this classification another classification based on the nutritional requirements so we'll move forward with the heterotrophic organisms because these heterotrophic organisms are employed very widely in the Waste Water treatment so these are widely employed in wastewater treatment and most of the treatment plants are based on the activity of heot trophic organisms and hence I should try to find out what is called growth cve for heterotrophic organisms for these organisms I should like to know what is a growth curve that means what do you mean by growth curve growth curve is that how with respect to time how the growth of microorganism take place in a reactor let me consider a batch reactor what is a batch reactor batch reactor is a reactor where there is no inflow or outflow that is batch this is a batch reactor no inflow or outflow or output from the reactor so let me consider a batch reactor this is a a a sort of a batch reactor where I have the liquid okay and this batch reactor is completely mixed I'm mixing it completely completely mixed reactor that means the contents of the reactors are uh contents are mixed thoroughly that means wherever I take the sample if I take the sample over here or over here wherever I take the sample the concentration of the contents will be the same okay that is what is called the batch reactor let us say in this batch reactor I have at time T is equal to Z to start with I have what is called a concentration of microorganisms concentration of microorganisms these microorganisms are heterotrophic microorganisms this concentration microorganisms is X so that means X not is the concentration of the microorganisms in the reactor and then there is also food the what is the food food is the energy source and carbon source that is the for the heterotrophic organisms organic compounds recalling this organic compounds are both energy source and carbon Source organic compounds provide energy as well as carbon to the microorganisms so such organic compounds which produce which give energy as well as the carbon for the biosynthesis for the growth of microorganisms is known as a substrate let us call this a as a substrate substrate is also biodegradable organic matter so substrate also can we say is a b biochemical oxygen demand oxygen that is required to decompose or to oxidize the organic matter organic matter here is a substrate under aerobic conditions uh oxyen required is nothing but the bod so the bod we can say the bod is same thing as a substrate so let us take that at time t equal to0 concentration of microorganisms is X KN and concentration of substrate I'll go back here substrate is equal to S not so in this reactor I have S and X at time t equal to Z the the conditions are X is equal to X and S is equal to s x is a biomass microbes concentration or biomass concentration that is also called as a biomass and S is a substrate concentration okay what I do is that I now bring in contact the microorganisms and the substrate in the reactor at time to equal to zero and I am mixing it completely and during this mixing what is happening is that I'm also providing what is called ation oxygen supply I am also providing Iration or oxygen supply is also there in this reactor so because of this particular thing what would happen is the organisms utilize the organic matter present in the waste water or present in this reactor so for example if I say that organic compound can be called as a glucose I'll take a simple example C6 h126 is a glucose so this is a representative of organic matter in waste water or this is nothing but the substrate for me now substrate plus oxygen this is mixing or Iration and air is providing the oxygen and then I have microorganisms and what type of microorganisms I have we can say that they are heterotrophic microorganisms the microorganisms which use organic compounds for energy purpose as well as for the carbon Source or for biosynthesis so when these things happen what will happen is that the reaction will take place with the production of carbon dioxide plus water that is a carbon is converted to carbon dioxide hydrogen to water okay plus we'll have energy this energy is in the form of ATP P adenosin triphosphate as already indicated so this energy is used by the microorganisms to produce more cells so that's what is going to happen that means now what is happening is I'm giving the food to the microorganisms I'm giving substrate to the microorganisms the microorganisms utilize the organic matter and increase in the number or increase in the body weight so as a result of which as you have as the time Pro presses that is the time is uh as the time increases what would happen to x x is going to increase the biomass concentration increases and S is going to decrease there is a decrease in the organic matter because microorganisms are utilizing microorganisms utilize organic matter and increase in number that is X is increasing as the time progresses so if I were to plot a graph of this particular thing this particular thing what is happening so time is on x- axis and micro will concentration on the y axis if I plot this particular thing what would happen is that at time T is equal to Z I have certain amount of microorganisms that is X not to start with in fact at time to equal to zero whatever organisms are present or are introduced in the the system they are called seed microorganisms seed present in the seed and if you uh if you try to find out the concentration of microorganisms as a function of uh time so initially you may have something like this and then afterwards it will move up and then it will go and then it will be some sort of a stationary and then over a long period of time maybe I'll break it here I'll break it here over a long period of time then it would be declining so there are four distinct segments of the curve this curve is known as bacterial growth curve this is a bacterial growth curve when I'm trying to grow the organisms in a batch process batch process is a process where we don't have inflow and outflow the organisms are growing within the closed environment so closed ecosystem the microorganisms are growing so this is let me call it as a number one segment this is number two segment number three segment here number four segment there are four segments in the bacterial growth car this bacterial growth curve uh indicates how the microorganisms are utilizing the the food and growing in numbers so number one is called you can see here in the segment number one segment number one what is happening if you see there is no increase in the number of microorganisms this is no increase the almost same microorganisms up to this time this particular period is called lag period lack period the lack period is there because the microorganisms are put into a new environment I putting the microorganism in the new environment and maybe the substrate the food is new to them as a result of which they take some time to get acclimatized to the new environment and also to new substrate so during this particular process even though there is no net growth of mic organisms lots of activities are taking place so the organisms are physiologically very active they're very very active physiologically what does it mean it means that they're producing the new enzymes in their body in the cells so as to act on the substrate and also to adjust to the new environmental conditions so this is physiologically active condition physiologically active State lots of activities are taking place enzymes are produced they know how to degrade the uh substrate that the food so that they can increase in the number so once having done that segment number two is called a log growth phase log growth phase log growth phase is the organisms are multiplying or increasing exponentially exponential growth they are increasing an exponential growth rate growth rate is exponential okay that's the reason why we have got a sudden increase here of microorganisms as the microorganisms are increasing very rapidly this is a number or this could I mean the microbial concentration is increasing rapidly what is happening to the substrate concentration the microorganisms increasing means substrate should be decreasing there is a decrease in the substrate concentration number one number two is that means what is happening because of this there are more microorganisms and less food so in this particular case what is happening is more microbes and less food that means there is a more competition for food I told you that is a closed environment a closed ecosystem in this closed ecosystem there is no new food coming in as a result of which the food is limited and the microorganisms are more and as a result of which there is a competition for the food and because of that competition then the growth rate starts decreasing so for example if you take there is a point of inflection here if you go straight like this if it is exponential it should have been like this but there is a point of inflection from this point of onwards point of inflection where at the point of inflection there is a change in the slope of this particular curve the slope of the curve starts decreasing so it goes like this so the point of inflection is occurring because of the depletion of food okay this is a depletion of food depletion of substrate or food second thing is again I will rest that it is closed environment so the toxic end product metabolic end product starts accumulating in the reactor so accumulation of toxic and product becomes you know harmful to the microorganisms we are not removing any material from this so toxic end products accumulate toxic end products and these end products are result of metab metabolis toxic metabolites toxic end products uh products or toxic metabolites I'll put it metabolites accumul H as a result of which the growth rate decreases the growth rate so as a result of these two things the net result is decrease in the growth rate decrease in growth rate and this decrease in growth rate yields what is called number three segment that is called a stationary phase number three is a stationary phase this is a stationary phase where there is no increase in the micro concentration so that means this micro concentration remains constant here it it has reached a plate it will not increase further so this is called a stationary phase stationary phase there is no net growth so no net growth of microbes now if you reach number four segment what is happening number four segment fourth segment is a segment where the microbial concentration is decreasing with the time as the time passes this is decreasing that means there is no growth in fact the the destruction of uh microbes this is result of destruction of microorganisms microorganisms are decreasing with time so that's what is what is happening in this particular thing so why is it happening The Food is Almost exhausted number one the reason for this is the substrate is exhausted is exhausted I'll put it here number one number two reason for this particular thing is that accumulation of toxic metabolites again accumulation of toxic end products so these are the reasons which are responsible for the declining growth phase so if you look at the microbial um growth rate or bacterial growth rate C you will have got this four segments depending upon these four segments are depending upon the availability of the substrate and the growth of microorganisms so these are the uh things this this particular curve is very very important for us in uh understanding what exactly is happening in the wastewater treatment plant now let us move forward with this after understanding the growth curve we'll uh try to follow this uh what exactly happens to the reactor try to put some mathematical equations for this for the growth curve so there are in fact there are several mathematical models to describe the growth rate for the growth rate growth rate of microorganisms okay number one is a simple model we'll use it what is called a sort of a based on mano's model and uh people also have applied another model which is what is called a logistic growth model growth model to describe the growth C or the behavior of growth of microorganisms now let us see we'll try to use the both the models and then see how exactly we can uh formulate some of the mathematical models so the fundamentals of the mathematical models I will try to look at it now now again I go back to this reactor this reactor at time t equal to Z xal to x s equal to s mind you both s and X are measured in the same units so it could be so the milligram per liter of biomass milligram per liter of substrate so both are measured in terms of milligrams per liter X and S are unit used measured in the same units so now let us say here I can write down that uh DX by DT rate of growth of rate of growth rate DX by DT is rate of growth rate of microbes is proportional to the microorganisms present at the time this is one simple equation that's what we are taking the growth rate is proportional to the x x is the microorganisms present at the time so in other words this can be DX by DT is equal to Mu into x uh removing removing the proportionality constant with the MU mu is known as the specific growth rate specific growth rate and the units of mu if you take it the units of X here x are same they cancel out mu will take a unit of team inverse time inverse mu has a unit of time inverse mu is a specific growth rate okay now this specific growth rate mu is not a constant I'll remove here mu is not a constant now what is Mu mu is the specific growth rate specific growth rate of microorganisms should depend upon the concentration of the substrate so in other words mu is not not a constant mu is a function of substrate concentration yes that's what I'll write it is a um function of substrate concentration and also it is a um function of environmental conditions let us say that environmental conditions are kept very conducive for the growth of microorganisms we're not going to change that particular thing so now what is happening is that this function function the relationship between with mu and S is given by mu is equal to Mu Max s multiplied by S over KS + S is given by this equation so suppose if I were to plot a graph between s that is a substrate concentration and then mu here mu is a specific growth rate and then the substrate concentration on this particular thing when the substrate concentration is is zero there is no substrate concentration then what is going to happen to the growth rate growth rate is also zero no food no growth rate no growth so then as the substrate concentration increases growth rate also increases like this and then finally what would happen is that it would go and then it will become sort of asymptotic or it could be stationary will come stationary to this as the x s increases this particular thing is almost constant so this constant thing is called as Mu Max this is called a mu Max maximum growth rate has occurred at this particular thing now again going back as the substrate concentration is increasing mu also increases and this follows this Stace of this cve this is a cve and then beyond this particular concentration of the substrate whether the substrate is this or substrate is this okay whatever is a substrate mu value is constant that is the MU value when it takes a mu max value then that is a independent of substrate concentration the up to this particular period up to this particular Point probably the MU is function of substrate concentration Beyond this particular thing it is independent of substrate concentration so that's what we can see this particular thing so that is a muax mu Max is the maximum maximum uh growth rate constant growth rate constant now I am putting it this is a constant really indeed a constant growth rate here it is only specific growth rate and here it is a constant because there is only one unique value for a particular microorganism for a particular substrate for particular waste water as well as for particular group of microorganisms mux will be the only one value that's why it is a constant and S is the concentration of the substrate and milligram per liter so this can also be called as a b whatever I have bod in the waste water and then KS now the ks is a term which I have to say KS is nothing but the value of s this is KS what is KS KS is the value of s when mu is equal to Mu Max by 2 half of mu Max so I know mu max value half of mux value I'll take it and corresponding s value is equal to ks so KS is a saturation substrate concentration sub State concentration when mu is equal to half of mu Max that is what it is okay these are all terms are indicated here so in other words mu is a function of the substrate so substituting back in this equation I have so DX by DT growth rate of microorganisms is equal to Mu into uh mu mu is given by mu Max multiplied by S over k s + S multiplied by the X so you can see here the growth rate of microorganisms is a function of depends upon a constant mux another constant KS KS is also constant so I can write it here this is also a constant KS is also constant it depends upon the substrate concentration and it depends upon the microbial concentration so this is a actual equation which GS the growth of microorganisms and then growth rate cve so now let us take one case case one I'll try to simplify this particular equation with certain growth certain conditions let us say case one case one is that when substrate when s is unlimited what does it mean substrate is unlimited when the substrate is unlimited means if I go to this particular graph somewhere here I am very high substrate concentration substrate unlimited means very high concentration of substrate so when is a high substrate concentration is present in the reactor during the initial periods during the initial periods of the of the bass reactor dur in the bass reactor during initial periods we have this particular thing so that s uh s is very very high compared to ks KS is small s is very high and hence I can say KS plus s is can be approximated to S I can in the denominator KS plus s can be approximated to S because s is very great compared to KS that means if I take that equation now and substitute this condition that the growth rate is uh that is substitute is unlimited DX by DT equal to Mu Max multiplied by S over s because KS + S is s multiplied by X so this S and S cancels out DX by DT is equal to Mu Max into X so can I solve this equation now yes I can solve this equation I could not have solved the equation DX by DT equal to Mu into X mu is the specific growth rate and mu Max is the specific growth rate constant maximum growth specific growth rate constant this is a constant that's why I can differentiate DX by X is equal to Mu Max into DT I can solve this equation when t is equal to 0 xal to X and when T is equal to t x is equal to X so that means the solution of this particular thing is nothing but um and applying the this thing X is equal to X into e to^ of mu Max multiplied by T so this is a solution of this so this particular equation is telling me that X is equal to X into e ^ of mu Max into T mu Max is a positive value so this is all positive value that X is a positive value multiplied by X not and hence it is a a positive value in other words this particular thing this particular equation describes the growth of microorganisms at exponential growth rate so that means this equation describes the exponential growth rate so or this is log growth rate of the curve log growth rate of the C suppose if I PL this graph again T versus X so I have this this is the curve what we have so this particular thing is represented by DX by DT is equal to Mu Max into X mu Max into X this is a cve so this this exponentially it goes so that means this is exponential cve that means this exponentiality is valid only up to certain level afterwards it is not valid we'll continue in the next class uh when the substrate is limited this unlimited substrate you have taken when the substrate is limited what is going to happen we'll discuss in the next class [Music] the [Music]