 So what we have seen so far is mainly regarding the shape of the Berkshum and diffusion flame but what about its structure and I have clarified in the past that what it refers to the shape is the overall flame shape but what is meant by structure is how do the concentration profiles of the reactants and the products and the temperature profile and how does the reaction rate all those things vary across the flame right so we should be looking at that but if you look at how the equations were solved it all becomes like a mystery in the sense we just got the flame shape by considering only the mixing field between the reactants the fuel and the oxidizer without having to worry about reaction rates and the energy equation which will dictate the temperature and so on so we never really solved these things strictly speaking now or rather rather as a matter of fact we have not solved for a reacting flow at all right so how what is what is it what has happened now so how can we actually reduce this well what we what we will see now is we will at least look at qualitatively how these things are going to go and we will worry about quantifying this next in fact many times we just we just goes left unsaid without having to be bothered about explicitly but there are lots of problems like in unsteady cases perturbations and all those things where we need to know what this flow field is or the combustion field is so it is of interest in some cases so what we are talking about is if you now have a flame shape like this question is if you now have R and Z go like this you now pick a particular Z and then start varying your R from the central line and go radially outward how do the concentrations of reactants and products and temperature and reaction rates vary so we have fuel in the middle slot and oxidizer in the outer slot now if you want to actually look at the flame structure we have a little problem here because this is a Berkshuman problem Berkshuman flame and the Berkshuman analysis assumes a flame sheet that means you now have just a sheet in which all the reactions are taking place infinitely fast right but that is not the reality so you are you are better off actually thinking about the structure of the flame to start with intuitively if you are now thinking about it qualitatively you are better off relaxing the infinite rate chemistry assumption and thinking about a realistic picture and then what we will do is expect what would what it would be for a infinite rate case all right the reason why I am saying that is because we will now begin to see a parallel between what we will do for a finite rate chemistry flame and the premix flame that we have the structure of a premix flame that we are already accustomed to right and where does that come into picture some is with what we will see now finite rate chemistry how is that going to actually make the flame look like first of all it is directly related to the thickness of the flame right so when we said infinite rate chemistry that directly went with a flame sheet assumption and therefore what we are expecting is if you now have a finite rate chemistry we expect a certain thickness for this flame what is meant by that what is meant by the thickness right so if you want to find out what that what that means we have to now zoom into this region and then look at it in a much closer way so let us suppose that you now have a thickness of the flame that is about this thick right what it means to say radially as we are going is this is actually where the reaction rates are beginning to be significant okay so you now have a reaction rate that goes like that now why it is the reaction rate fall on either side it is not because you are actually having a fairly low temperature okay it is because you are running out of one of the reactants on either side so on this side in this particular picture you are going to have a fuel rich composition on this side you are going to have an oxidizer rich composition and these are the these this is actually diffusing in and there is a region where they are meeting in stoichiometric proportions right in the middle of this region on either side the reaction rate drastically falls down because you are running out of one of the reactants on either side if you now recall when was the last time we actually had a thin region where the finite thickness though where we had a appreciable rise in the reaction rates and then a fall within this region this was in the reacting reaction zone of the premix premix flame the premix flame we had a preheat zone and the reaction zone and the preheat zone you did not have any appreciable reaction rates it is only in the reaction zone you had appreciable reaction rates so the reaction actually rates grew very rapidly and then fell back again because you are running out of a deficient reactant again on the on the on the downstream side right so here again on either side you have a deficient reactant because you are you are here your fuel rich and by the time you go there you run out of fuel here your fuel oxidizer rich you by the time you come here you are running out of oxygen there is a deficient reactant all the on either side therefore we should now anticipate that if this is like the reaction zone right as we had seen in the preheat the premix flame there must be something like a preheat zone so the preheat zone there was a convective diffusive balance alright and similarly what we are looking for here is if you now have this region where most of the heat is being released right then that heat has to be conducted on either side in the case of premix flame you now had a flow only in one direction and you had hot products on the other side so you did not really have a temperature gradient in the product side for a for a adiabatic flame okay so you did not have a temperature variation in in the product product side beyond the flame but in this case the flow is going in this direction right therefore you have hot region over here relatively cooler regions on either side okay so what that means is you now going to have a a a region where you have appreciable thermal or heat diffusion that is taking place on either side so the temperature is going to actually rise from from far away on either side and then locally become locally attain a peak in fact you should in fact you could you could even expect that this is sort of like that you have a curvature just like how in the preheat zone of the pre-premix flame you had a temperature rise with a curvature you can expect the same thing over here now if you are in the middle of the burner you are going to have a certain let us say fuel fuel concentration right and as you now coming closer to this the fuel concentration begins to fall pretty much like the way the the fuel concentration began to fall as it approached the reaction zone because there you had an upstream product diffusion but here just like if you know and then and then of course when you now look at the product concentration profiles in the in the preheat in the pre-mix flame structure it mimicked the temperature profile in a in a non-dimensional sense or normalized non-dimensional sense right here again that is what is going to happen you are getting lot of products that are being formed right and the products are all being formed in the reaction zone and once they are formed they look around on either side they now find that they are less in concentration therefore they diffuse so there is a radial diffusion that happens on either side for the products even as a convection is going on in the axial direction therefore you expect a product concentration profile to look fairly similar to the way the temperature profile is right so because you now have a high concentration of products near and then it falls rapidly on either side as you as the fuel is now diffusing into the flame it is progressively getting diluted by a product concentration that is higher therefore you should expect a transport zone for the fuel that is that is coming in like this and in this region the fuel concentration is looking exactly like how it was in the reaction zone of the pre-mix flame right and similarly for the oxidizer maybe at a different starting from a different level if you're plotting in in dimensional terms and comes down and as these things come down to nearly zero you have the reaction rate drop down to zero this is how this is happening so this is your W temperature Cp its concentration or you can say yp mass fraction and this is yf this is yo you can figure so much right but now the question is what if my makes this burnt approach is adopted what if my my infinite rate chemistry assumption is adopted what does it really correspond to in reality right what it basically corresponds to is in the in the case of the premix flame we were talking about a flame that is getting thinner and thinner when the reaction zone is getting thinner and thinner particularly when you have a very high activation energy right so in the case of high activation energy the reaction reaction rate actually begins to be very very low for a long distance within the preheat zone and then suddenly shoots up to very high value within the preheat within the reaction zone over a very thin thin region and the thinner the reaction zone region is higher is the higher the value to which the reaction rate goes because all of the reactions have to happen within that small region right so essentially what was what it meant for a high activation energy situation was that the the the reactions were waiting for the temperature to be raised to a fairly appreciable level before which they would become significant and once they became significant they would rise very rapidly with any additional increase in temperature right so as I said at that time the activation energy then is a marker of the sensitivity of the reaction rate of temperature higher the activation energy the reaction rate becomes more sensitive in the sense it is it becomes the variation becomes more and more non-linear it remains fairly low for wide range of temperatures at a lower level and then with a with a temperature rise beyond a certain level which is which is very high then it is even a slight increase in temperature will cause a huge increase in the reaction rate right and correspondingly your reaction zone would be very small very very thin so that is exactly what we are expecting over here as well right and as you see what it means is if this reaction zone is now going to become thinner and thinner then we expect the reaction rate curve to actually go shoot up to the sky right so that essentially comes to a limit where if you have a thin reaction zone that is a flame sheet then it should correspond to a infinite reaction rate right so from here we should now be able to deduce if you now have a flame sheet assumption the flame sheet assumption should correspond to an infinite reaction rate that is your W right strictly speaking you should you should keep drawing this line vertically up and up and up to the extent you can right it is it is it it is infinite then question is what happens to the rest of the curves right and then what is meant by what are we talking about like the fuel anoxidizer should be at stoichiometric proportions the answer is if you now look at the temperature what it means is we have basically squished this region right and that means this particular curve does not really exist okay or in the limit of high activation energy it to a higher order if you now relax this thin as some thin flame sheet assumption you will see this thing happening in a very very small region okay but outside in a larger picture it essentially is like our picture is starting essentially from somewhere here and then you get to see only the preheat zone counterpart okay which is the transport region for the temperature so you now get the temperature to go like that so in this case for example you could now say the temperature reach reaches a peak somewhere somewhere here and then falls back again right and keep in mind in this in this picture you need to have the temperature go to a zero slope over there for for symmetry consideration it has to probably go to a zero slope if you now have an adiabatic or insulated wall right so you have to keep those things in mind and trying to construct these temperature profiles in the global picture and this is actually what is called as the outer zone picture in the vicinity of the flame sheet right and this is actually a inner zone picture so you now have two or three levels into which you have to go to this is like the global picture this is the outer zone in the vicinity of the flame sheet this is the inner zone of the flame sheet that's how we have to think about it so if you now think about so the product concentration as I said will mimic the temperature so I can say this is your T and yp then look at how the reactant concentrations would look like what it means is this is going to be there because the product concentration is decreasing as you go away from the flame sheet so as you go in near the flame sheet in the two word radially the fuel concentration is getting contaminated by the by the product right therefore you are going to have this part of the curve intact so it's going to go like this and what happens then does the fuel fuel concentration cross cut across the flame sheet where the where the reaction rate is infinite no because all of the fuel is getting consumed there right so you now have a step jump into the fuel concentration so first of all we notice that you had a slope discontinuity in the temperature the temperature is continuous all right right but it is having a slope discontinuity what does it really mean it means that heat is actually being released over here and this heat is spreading on either side depending upon the slopes you have a temperature slope on either side corresponding to a heat conduction away on either side okay and and obviously you need to have the temperature go like that because you won't have heat go this way as well as that way and that will correspond to having like a cusp in the temperature profile that's a slope discontinuity but as far as the fuel concentration is concerned you actually have a value discontinuity as well because you are you are having the fuel concentration arrive at a particular level and similarly you can think about for example let us say that is your oxidizer so this is this is your yf and let's suppose that that's your oxidizer and comes in like this and then we are not squished that this region right so it comes in like this so what is meant by and then it drops to 0 because within this narrow region it just rapidly falls to 0 but now we have even squished this narrow region to a sheet therefore it has to fall to 0 within that sheet so what is meant by saying you have fuel and oxidizer in stoichiometric proportions the answer is very simple this is the value of the fuel concentration at the flame sheet this is the value of the oxidizer concentration at the flame sheet and if you now look at the ratio between these two it would be a stoichiometric that's how it has to turn out right but how did we figure that by just doing the mixing analysis without a flame strictly speaking the answer was if you did if you didn't have a flame you wouldn't have this curve you wouldn't have to worry about the temperature of the products so you're still going to have something that goes like that something like that that that goes like that the moment you found them at stoichiometric proportions you now said that's my flame surface and that's where the flame is but if you now go back and look at look at look at it in the in reality this is how it turns out to be so you don't have these things the fuel and oxidizer get consumed these are some of the some of the issues that you don't find very explicitly stated in textbooks and you get confused what exactly is happening in the diffusion flame as you now move for a little bit farther away from the flame on either side or how did we get to locate the flame using the stoichiometric surface assumption and just solving the mixing field so this is the connection between the mixing problem and the combustion problem in the context of a finite infinite rate chemistry which is actually a idealized high activation energy or infinite activation energy version of the realistic finite rate chemistry case you see so we will we will see later on next as in what is how do you how do we how is it possible for us to actually get these get these profiles but right now what we want to do is to stick with the theme on finite rate chemistry we want to now look at the situation with respect to finite rate chemistry here because that's what we started doing the question we have to ask is are we going to have this kind of a very thin in fact this is an exaggeration this picture is an exaggeration it's not even as thick as this right is it going to be like this everywhere the point was the flame sheet assumption or the infinite rate chemistry assumption essentially meant you have mixing rates that are rate determining when compared to the reaction rates so you didn't have to worry about how fast the reactions are happening because they were just waiting to happen they instantaneously happened once the mixing happened and the mixing was the one that was slower therefore we are waiting for the mixing to happen so when would we have high mixing rates and when would we have sorry when would we have low mixing rates or low or high mixing rates when would we have low or high reaction rates right mixing rates depend on concentration gradients reaction rates depend on temperature and of course of course nonzero concentrations okay so given reactants given that they are available if the temperature is low the reaction rates are going to be significantly low right if the concentration gradients are high the mixing rates are going to be relatively high whereas the infinite rate chemistry assumption is primarily based on low mixing rates and high reaction rates okay what we need to examine is when would we have a situation corresponding to high mixing rates and low reaction rates does that happen anywhere in the flame it's not too difficult for us to figure out starting from looking at the mixing rates as I said mixing rates are depending upon concentration gradient and as the fuel comes in and the oxidizer come comes in at this particular lip you have a high concentration of fuel here a high concentration of oxidizer here and there is a steep gradient of concentration of the fuel and a steep gradient of concentration of the oxidizer right it's almost like a step and it's almost infinite concentration gradients there so if you have infinite concentration gradients they are going to try to rapidly mix right there further down a little bit maybe you have the the concentration gradient smoothing out and therefore the mixing becomes sluggish all right but right there you have infinite concentration gradients pretty much and therefore the mixing must be very very rapid okay but maybe the constant with the reaction rates were even wrapped more rapid yes so many times you know when you're looking at these mathematical limits it's a question of whether if two things go in infinity which one goes to infinity faster right but is that right we are now going to have you to see we never really worried about the energy equation right therefore we never had to worry about the boundary conditions to the energy equation if we have to worry about the boundary conditions to the energy equation what would you do of course we pointed out that this this this is this temperature profile should go to a horizontal slope there because you're going to have an abatic wall but that's that boundary okay and then of course we have a symmetry boundary though those are the boundary conditions in R for the temperature but what about the Z boundary condition right so the Z boundary condition that you would apply is I am going to have cold reactants entering this domain that's what I would do if I just open my tap for my fuel to come in or my oxidizer to come in right I am not going to heat the fuel an oxidizer to the flame temperature and send them in so I am going to be sending it at cold temperatures so my my T0 is going to be less than my flame temperature so as the fuel and oxidizer are coming in and rapidly mix what would happen they are still cold they are just beginning to get heated up from the flame therefore the reaction rates are pretty low low when compared to what suddenly the mixing rates because the mixing rates are certainly high so right there you have a gross violation of the flame sheet assumption even if you had infinite nearly infinite activation energy right because the temperatures are fairly low and the the the concentration variance are infinite you see so both of them are actually working against each other in in satisfying the assumption that was made so what happens then right so what we want to do now is look at this region a little bit more carefully so let's do that so if you now go and look at only that region and I am going to now say let's have like a thickness of the burner wall right the inner pipe and so that's not at the moment that's not very very significant but we could think about using the thickness at some stage soon but at the moment what we are interested in is you now have a f coming this side and o coming that side right if I were to worry only about the mixing problem the way I was trying to do the Buxchumian solution I would now be able to locate my stock hematric surface going like that this is the stock hematric surface in the mixing region right so on this side of this the surface you are going to have a fuel rich region on that side you are going to have a oxidizer rich region all right of course this is actually for a Dirichlet boundary condition in in in the in the fuel and oxidizer concentrations right you could allow for flux boundary conditions when you permit axial diffusion to happen in which case this curve doesn't have to actually come here could be somewhere here a little bit away and so on okay but but but but in this in this region you have a stoichiometric surface emerging out from the domain upstream boundary somewhere right it's not very important that it is actually come in right at right from the for the discussion that we are doing now but this is just the mixing field okay and you you're having a mixing going on the gases are as they mix trying to get heated up from a flame so that the reaction rates will become appreciable and they can constitute the flame right what is a flame it is essentially where the reactions are happening reactions are have reactions happen where the reaction rates are significant reaction rates are significant when the temperature is high so the heat is getting released and then it now starts heating up those reactants that are cold so that that temperature can be raised up to the flame temperature and therefore they can react right this is how this is how it's going on so therefore we are expecting the flame to be there somewhere with a standoff distance okay and reaction rates are not very appreciable within this region because the temperature is just warming up to wherever the wherever it is wherever it is reaching the flame so this dynamics of heating up the reactants right to the temperature at which they need to exist for the flame is going to dictate the standoff distance right so it's essentially based on a thermal balance between of course you can now begin to factor in some amount of heat going to the burner wall by heat conduction there are also analysis that have been done where you take into account radiation losses okay so again you can think about these things but even without that even if you were to consider this to be an adiabatic wall you have to still heat up the reactants in the first place from their original room temperature let's say to the flame temperature that much bit is going to require a certain distance over which it can happen as the flow is getting convicted right so as this flame is now going to be there and heating up the reactants the reactants are mixing and they are mixing pretty fast here because the concentration gradients are very high right so when they mix by the time they reach this flame what is that flame that's no longer a diffusion same what's going on very cheating ourselves what kind of a premixed flame are we going to have right it is stoichiometric right there along that surface okay because we have the standard of distance now we can see why I wasn't really worried about whether the stoichiometric surface comes all the way back to here with a with a initially boundary condition or whether it would go somewhere else for a flux boundary condition that that's not that's not very important for this discussion because you have a standoff distance over which you have to figure out how the flame is going to look like right so it is the premix that there is a premixing going on right it's not quite like a premixed flame it's a it's a it's a premixing flame so typically people begin to talk about this is what's called a partially premixed flame right and what happens here is you have a stoichiometric mixture here so you would expect the premixed flame to propagate at stoichiometric speed but as you go little bit further out your stoichiometry drops drastically into a fuel rich fraction and on that side you're drastically going on as you go further out you're drastically falling into oxidizer which we have to think about a premixed flame propagation into this what you have to think about is like a mixing fan where these edges of these contours might correspond to a rich flammability limit and a lean flammability limit for a premixed flame beyond which you're not going to have the premixed flame exist this is pretty rough because we are talking about it's rough in many ways and we will we will see why this this this edges don't really have to correspond to that very precisely as we build the build up the scenario but at the moment if you're now thinking about a premixed flame that is propagating there we could think about like edges to this because beyond which it can't propagate and essentially what we are talking about now is a premixed flame that is trying to propagate against a a reactant stream in a what's called as a strained atmosphere ambience what has been by strained is you now have a premixed flame propagation with a concentration variation across that is to say if you now went back to your one-dimensional premixed flame picture we had this premixed flame all right but that was for a particular mixture ratio question is what would happen if your mixture ratio continued to vary across can I now have what's called as a mild stratification that means can I now say well this is supposed to be yf plus yo right but can I now say that roughly my yf was like this a profile like this that means I had progressively more fuel here and less fuel there and like my yo was like that we had more progressively more oxidizer here what would happen to that flame right so if you had a given uniform mixture ratio between fuel and oxidizer for a premixed flame it would propagate at a particular speed and that speed would be the maximum if this uniform mixture were to be stoichiometric on either side of equivalence to unity-equivalence ratio you are going to have the flame speed drop right so if you now think about a more and more fuel rich situation here more and more oxidizer rich situation here the flame speeds for the flame are not going to be the same everywhere right somewhere in here you are going to have a stoichiometric proportion in which they are they are existing and that is where the flame speed is going to be the maximum therefore the flame is now trying to actually propagate the fast test along the stoichiometric surface and it progressively is slowing down as you go further out this is similar to how we were looking at a fuel lean premixed flame established in a Bunsen burner with entrainment of air further out or even as a matter of fact if in even if you think about a fuel rich flame if you now entrainment there you now have a mixing region and the flame speed varies because of the constant because of the reactant concentration variation spatially right so here what is going to happen is the flame is now beginning to bend right this is of course a very blown up picture strictly speaking we should now go back to our G equation kind of approach where we now thought of a premixed flame as a flame sheet which contained all this information about the structure and all that information was packed into simply a flame speed variation right so if you had a flame speed variation then how would that look like if you if you had a stratified flame SL now is actually a local function of the equal equivalence ratio or see SL is now a function of the local equivalence ratio and it is now having a maximum over here and elsewhere it is now trying to propagate perpendicular to itself at a lower flame speed and therefore it is now going to shape itself in such a way that it is balanced by the local normal component of velocity whereas the maximum flame speed is going to counter the full velocity right there right that is exactly how we are thought about shaping shaping things like premier Bunsen burner flames and so on and that is something that can happen over here as well so now we now have to progressively go back to where we where we start right so in this picture which is here we would now like to think that you had a premixed flame that was like this right if we now had a premixed flame and at this particular point you are going to almost like 0 flame speed so you should actually expect this to trail off and DK right as more almost like extinct extinct becoming extinct and what happens on this side this is a fuel rich premixed flame right so this is rich premixed flame and this is a lean premixed flame so when you have a rich premixed flame you have a fuel excess fuel as part of the products right and when you have a lean premixed flame you have excess oxidizer as part of the products which can now diffuse to form this diffusion flame they are pretty hot right so the diffusion flame now no longer does have to wait to get ignited right so you can now have a diffusion flame that is actually emerging out of this stoichiometric surface where the premixed flame is trying to propagate against the flow the fastest and then trail off all right so this is the diffusion flame so this kind of a structure has now been variously called originally it was it was called by Buckmaster is what is called as a tri brachial flame meaning that it is a flame with three branches all right but subsequently most of the literature refers to this as a triple flame and the literature basically sides the first time the triple flame was published was in 1962 in an experimental work where you are looking at a diffusion flame with kind of a geometry but essentially with a very very mild stratification that means you have a mixture of fuel and oxidizer of varying proportions that the that a flame is subjected to and that gives rise to a triple flame structure so if you now go back to this picture we now have to expect that this is happening somewhere here right now that looks very small when compared to the rest of the diffusion flame no wonder Burke and Schumann never have to worry about this right because if you are thinking about like the height of this flame forget about this you know don't don't don't don't even worry about this right so the the the flame sheet assumption leading to the flame shape for a diffusion flame is fine for certain purposes of looking at the big picture view right so that is what we are expecting for the flame to look like so if you now go back and look at a candle flame very carefully let us suppose you had a romantic candlelight dinner with your girlfriend right and then of course forget about the girlfriend and look at the candle right now you know why I am a professor right so you now look at the candle very closely and you look at the base of the flame and you see that to be blue and sort of like a bulb and how would we try to sort of I exaggerate this picture like how do we get to see this more and more the answer is the closer this part is to the burner you can see as it comes further and further closer the mixing fan is actually not over right so if you were to have this stabilization happen somewhere here it is going to be much smaller so it means it is not going to be very apparent right so correspondingly if you now go back and see it is going to be somewhere here so it is not going to be very apparent all right so what you would want to see do is to take a for example a Bunsen burner and then shut off the oxidizer supply from the base and now allow for a diffusion flame to be established and then keep on increasing the fuel flow velocity so and we talked about this we said as the fuel flow velocity is increasing energy diffusion flame the length of the flame is going to increase but in addition to that you know also going to have this pushed up and when this gets pushed up you are having a mixing fan that is actually broader right and therefore you are going to have a larger region where you are going to have this flame so in the literature when you now are getting down to something very close you do not really see these three flames separately in fact you can again think about these three flames if you now go back and think about how we got these flames right the three flames this is from the G equation right the G equation kind of approach the G equation kind of approach is assuming a flame sheet and a flame sheet for a premixed flame is valid typically in an infinite activation energy kind of or a high activation energy limit and this diffusion flame is a sheet again because of an infinite rate chemistry kind of idea right in reality it does not like it happen like that we know we saw that it is actually take in reality right if you now translate that is now going to be like this and then it is going to come like that is like where reaction rates are going to be appreciable right and if you now allow for this to actually come progressively closer and closer these two branches now begin to close more and more right and of course there is no reason to expect that they will close simultaneously together. So there are conditions where you have stratification only on one side for the oxidizer or the fuel where you can get into what is called as the double flame structure or a hockey stick kind of flame shape and they call it double flame right where one of the branches is actually merged with the diffusion flame the other branches still sticking out but eventually when you get closer and closer you are going to have both the branches essentially merge with the diffusion flame and it is essentially going to look like a bulbous region of high reaction rates and that is that read that kind of a flame structure in general is what is called as a edge flame because it is actually relating to the edge the leading edge of the entire flame. So this entire flame you see when you had a fully diffusion flame you never really had to worry about propagation of the flame because it exists wherever you have an interface of fuel an oxidizer at stoichiometric proportions it does not propagate anywhere right but the moment you have to worry about a mixing region in which you are having a premixed flame that is propagating right you worry about propagation of the entire flame so it is as if like this flame is trying to eat into the reactant mixture with a certain speed at which the reactants are coming at it it is exactly the same kind of thinking as in the case of a premixed flame with curvature effects and so on as a matter of fact all the all the things that we talked about for flame curvature effect and flow divergence effect or valid in this region so you can think about here as you now look at a flame sheet that is there for the premixed flame you see the reactant that is going here is actually partially refusing and partially convecting so you are now sending out heat this way to a reactant that is not necessarily participating in the in the reaction therefore this region is not necessarily corresponding to adiabatic flame temperatures at all you will have a a two dimensional heat loss in this region and if you now get closer and closer to the burner you are also going to get heat loss to the burner right and therefore this that is another reason how this flame could actually shrink the region could shrink further and further as you go closer. And the second thing is as you now have a flame that is curved like this and the flow goes like this you can see that it is it is it would tend to actually go up and then converge because it is actually convex facing the reactant flow. So since it has to converge it locally diverges and then converges that is what we saw for a for a flame so in fact go back to this what we saw was we should expect this to happen so since it is a subsonic flow in reality what happens is you now have a flame tube this is now a faster flow that can be handled by a curve flame because it is actually diverging locally decreasing its velocity right so relative to the far upstream velocity this this is actually slow so it the flame tends to slow down the flow as it approaches so that it can get established right that is the flow divergence effect similarly you have a fairly huge flow divergence effect and you will if you now solve like the momentum balance associated with the flame you will now find like a small pressure hill around which the flow the flow has to go around and which has been created by the flame right so effectively what that means is this flame can propagate against a much higher velocity than even a stoichiometric premix fling because it curves so steeply and it causes the flow to diverge and then converge and therefore the far upstream flow is that actually a much higher velocity when compared to the flow at which it is stabilizing so it is not the local stoichiometric velocity that matters it is actually the far upstream velocity that matters which has been altered near near the flame by the flow divergence effect on the flame curve which all those things that we talked about for premix flames is valid and as we as it gets closer and closer to the burner you are getting into what is in general called a edge flame and the other thing that we can also point out is if an edge flame will correspond more and more to a infinite concentration gradient at the splitter plate whereas if you had a smoothly varying concentration gradient you will have more and more of a triple flame right so even for the same distance from the burner lip if you were to rig up the concentration gradient in a smooth manner you will get a triple flame structure whereas if you had a very drastic variation in the in the in the concentration gradient then you will have more like an edge flame right so the edge flame then is a is a more general picture of which a triple flame is a particular structure right and this is typically the destabilization mechanism for diffusion flames in general so the diffusion flame is essentially getting stabilized because of this and then of course because of this reason it it goes through what is called as the lifting process right as you now keep on increasing your your velocity at some stage the flame the destabilization mechanism does not work over here in this region and then it lifts off and you now get a diffusion a diffusion flame that is far away with a fairly broad premixing region and of course it is it is turbulent and you have to worry about those aspects also will stop here.