26 Nonlinear viscoelastic phenomena

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26 Nonlinear viscoelastic phenomena
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30 (Lecture 2 missing)
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Lecture 26 - Nonlinear viscoelastic phenomena. George Phillies lectures from his book "Phenomenology of Polymer Solution Dynamics"
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glasses in polymer dynamic based on
George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011
ends today this lecture is lecture
26 nonlinear this going elastic phenomenon I'm professor
facilities today we're going to continue our discussion of policy dynamics were going to talk about nonlinear effects of followers but if we ask what sort of effects are the 3 sorts of things there is powered by General Motors not only the issue is involved fractured Hanser which describes the courses within the language the issues involved in memory namely Falmer solution here somewhere along relaxation times you can see experimentally and there than there are a lot somewhat vaguely described as modern methods things there and now the done were not going story so the starting point for discussion is water forces within the flu so we have and we have here a small you will does not have to be accused by make 1 of the favorites is extremely small relative to the other 2 and we have axes so here is taxes and here's why I'm here is and we asked water forces on the way the general statement is we have this object and across each service for for example this service there is Of course across the surface but the force across the
service as a component of the direction and involvement while directions and component the director the component is the interaction is that compression lower fractional worst across the blue exceptional costs the sideways forces are short of How can we represent his force all we do is we introduce an object of was pressure tests and the prejudices destined for use in excess of the explore on the next of the you what that's the while I was the same he's the facts he's alright the state they want the prejudices describes the forces led describes forces 1st of all this with cancer it's 3 by 3 matrix that and what we do ask that those forces are in terms of pressure to answer is we got the pressure answer when the unit vector parallel 1 of the Senate's perpendicular States so for example here is high I on the unit vector perpendicular to the wise playing with his and her over the phone and so for example I have that he is I have the statement are there is slight mixed mathematical symbolism here this is 3 by 3 got back here and was and what we we get we get out worst and its effectiveness is vector forced perpendicular to the x-axis that's not the same as the next vote force and that are forced next next time they have lost the next line change plus the next the that some of the forces across next service and the forces across that service next alive this the compulsory for those of you
want to see this in unit vector for you right after the accident fantasies I can't pesticide that got the ax ax that's the power of products from the affected areas plus the that's a lot of time during the act was to that's the I think and there you have pressured and might say that vaguely recalled having heard about pressure someplace back in the 6th grade and you don't remember pressure being intensive the answer is that if you were simple with the isn't doing it currently the pressure sensor here's the 0 hour there are the 0 0 euros euros euros 0 of that is there is a pressure is a single longer I gives the force across the axle the y and z faces an acute and the the same on such doubters 1 ,comma additional issues that guests skipped over and the book might confuse people others have regrets the issue is as follows during you we said of course across the excess space is given by this object you might legitimately ask Is this next phase the next phase of the other side the answer is if it's a very small then 1st approximation its pressure is the force on both surfaces is sense that it's clearly imprecise because if we have pressure have worsened across the surface the offers no necessary obligations that the ball force cannot be changing his position goes on that is we could have on whole the effects of the the question is how they got those forces and the
answer is the true waste the differences between the 2 places can in the significant the 1st right where forces reasoning is if the object the volume is being accelerated very rapidly and then the difference we have said acceleration in the x-direction all the method of all of the x-direction forces across all 6 faces had better not be 0 that there be however for the most part we talk about commercial systems inertial less systems in systems that so that we can but we do not have to worry about ownership and in that case the of some of the faces forces against the 0 further in saying some of the forces that cast the 0 I don't always take the volume approach being yes and if the volume has approached the issue on the volume the think becomes very small in the area of the society faces is having fallen like this in the area of the site faces becomes very small relative to the top of the box and therefore for this very thin volume the top and bottom forces are almost all force and effect force to solve 0 the forces here and here at the 2nd best approximation saying there's no inertia similarly in addition to their being no In all inertia you also want to say that the bottle forces in the small that this is a Lakewood someplace where the force of gravity on crop presumably because there is a force of gravity on there's a wave and the lifting the downwards here and the forced words there had better be arranged to match the white because think that's all and therefore there will be pressure gradient as you go downward but under normal conditions that's also language you should realize that just
approximations framework you must be the case since the volume small saying in there she is negligible but a moment of inertia should also be treated as negligible and angular momentum stored inside this object should be neglected that's again approximation however the angular momentum has to be negligible let's look down and lost the ball in the hole in that box of and look at the door angular momentum relative to this well an hour for the angular momentum to be negligible at work on the object must be negligible and therefore the call to work this way across this is the work this way across the service had better in 2 0 that's again approximate however within minutes approximation were saying that work is working 0 this is saying let's see this is the x-axis business to apply access this is the worst In next direction across a lot taxes that the wanted and this is the 4th across the axis of the plane perpendicular to the axis accident wider direction and this is the effects of all those who have varied therefore the explored and his wife and their 2 now that's fine as long as the angular momentum is negligible and in the 100 m problems that's typically a safe assumption 1 can go for stray into other areas that in their worry about whether urged that the assertion is matrix of the world Africa and our social full of liquid P 0 0 is that we now ask what happens to pressured cancer if we made life a little more complicated now introduced a event the tension there actually is a real article organization the People's attention important things that have the following them it is true that a fluid velocity and the fluid velocities the ex directory if we have Shearer capital for future firms can't go on a greater displacement the direction in which we live velocity is changing as the wider action I grew up in here is a tough place to here is .period played the final play stationary hot plate has velocities so the X the assumption of and we're going to get the validity of this song that Is that invite all the pieces of 1st how you see something like this and the southern expert and some distance why between the 2 places to places 0 and held in the southern access is going to to be and why on capital also represented here not that is fluctuating explains why it's .period and this is provided by the capital the distance Place now if you love them moving this way gradient is this way and there is a neutral directions seat OK and directions so we now take the lead with to share of and some several things on the wall or going to talk about her looks only a diagonal components pressure the expects the lore I wise use it said and in equilibrium slower those components are all the same in Apollo liquid waste were sharing baby become policy on the whole audiences not equal to each other and therefore the defiance of the catalog of the expects since he was Y and end to did the water on time he see that having introduced the 2 analysts we you don't need this anymore and just the direction in which we're are getting lot here they have names namely and 1 and 2 are the 1st 2nd you marvel give found description of these things is being moral stressed differences means that pressure the liquid is certainly is
not the same policy with respect to the 3 principal axes excellence if you go through the literature and go far back far enough you can find people and to identify with 0 and the best that can be said for the preservation of old and is known to be involved there are a lot of things to normal stressed differences are not 0 there is 0 if there's no sheer but if we increase this year the on normal stressed differences become all on equal if you think about this although there is a cemetery issue the cemetery was strongest here's here's here it is the velocity had some money so we we have some capital which his is velocity gradient and as a result of the velocity gradient fractured this way and the pressure out of applying the company yes that's suppose I reversed direction of the sheer yes I have reversed the direction of the sheer and so the alliance why the CCC is this way by itself because I want to be I have reversed the direction of the sheer are however if you think about the cemetery for a bit odd do should we reverse the direction of pressure difference well probably not because if you walk around the forests of the robot behind the wall and looking again you're going to be be seeing the picture right back that is the system has really should have reflection and variants and you can confirm that this view we imagine this blackboards transparent yes people sitting on the far side of the wall looking at season's mirror-image picture and they had better agreed with as to whether he lied while he's easier relatively larger or smaller and therefore we are going to work following the both of these he said as capital square now there's another set of forces which I will simply dropping briefly which are terms ,comma it because there's a viscosity and the point that there is a viscosity is let's see little of appears to leaving little doubt there is stationary so if we imagine this plane perpendicular to the Y axis there is a force across it the next direction because the liquid is biscuits and therefore well this is the worst the x-direction what he y axis and therefore more CDs while acts has since moved to the all the actual I heard about 0 . 4 per down from those those 0 if there's no fear of America was the argument saying it's that it to be 1st yes or no if the Shearer if the food is going that way the dragon forces also in that direction if I reverse direction of the arms flow of followers by standing on the other side of life were looking at the force also reverses direction and therefore these 2 terms were the 1st OK so that is distressed and that those to normal stressed differences I oversimplifying appreciably however from the standpoint of what we're going to do with these I have said not USA OK we have a solution because of this policy and it has not 0 normal stress difference what currently in use he is in danger of this foreign policy and the severity of the problem they also have flow properties that involve not just the normal stressed differences but also involved for example fair system has a memory and I'm not going to show what some
of these peculiar flow properties are not from the flow properties of the simplest 1 the was on so what is the nature of experiment the symbol permanently Our mixing bowl full of creating and I think in stirring and I start stirring China which brings the rain and with great well-defined experiment and you do this work this week just as true water for some time to work through water flowing moves away from the storage costs engine Tania certainly the normal expected to the case In the polymer solution see exactly the opposite of the year using a liquid plan plans useful role that's why is liquid finding of rock and natural 1st of all the answer is but we're doing sharing the liquid because we're spending and we're sharing liquid therefore cap is not 0 and the normal stressed differences are not 0 she would want to arrange things so the past surfaces has surface of constant pressure and there is a service of constant pressure you have to hire only put off because the normal stressed differences between the 0 or less rot rock-climbing haven't explained have details at all the important issue is that Ron Klein is actually fairly demanding test on any model Paul Revere the other is a nice paper passengers the reference book and the point of the book reference you he he's there on the try compare his prediction of rock climbing against models of polymer dynamics and you discover that some of them don't interrupt that's a serious flaw let us consider a few other exotic phenomena this 1 is a little more complicated so here is high yeah pushing polymer solution all melt out the and of and if you've ever done this slightly longer homes basically if you do this with water the water flows out and it has offered moralist straight line if you do this with Paul rebelled the text the will investigates swell referred the issue of feeling comes out of the place and bulges and gets wider this is getting wider and also of course must be slowed down well that's extra dates well that's certainly not something you see in conventional OK there is a traditional profits so we have until the later of the walls and recently good writing and if you do this with water the liquid surface is flat across the range of the system if you use the polymer solution you discover there's a bald just as certainly primary wealth and influence in the middle of the trough is higher than the flu with the edges Of the last fall by on Kurdish and following book collects some dozens of these different strange effects are less consider another 1 all this is not against some of these are not easily understood is just saying all normal stressed differences that normal stress this is normal stress on the other hand there's always direct reduction and if we say there is direct reduction what we mean is we are pushing liquid down and if it's going fast there tends to be turbulence corners and this increases the resistance so what we do here is we drop into the liquid trace quantities were criminal in quantities of all suddenly the director reduces great the there have been military experiments for the idea was you all don't stuff out of prowl share with injection fluid out of proud of ships and this will reduce because you eliminate turbulence although I haven't heard that this was put into effect ,comma actions but it was
an idea that someone Foxworth spending money what is music director reduction will that may be related to the here we have a very large family of and open the drainage holes all of this for example the enlarged and having dropped the late William we then let it drain what you observed after that there's a new momentum but the annual madam cannot easily escape down the drain and therefore especially if he got a little bit you see import export forming Lucien training parables of America's interesting things right where it's great yes drops and Marie makes and this effect disappears completely you see no it has seen no entrainment bearable that's not true that again she wouldn't fall over and the basic qualitative flow properties just changed appreciably alone Oh there is flexible enough of a photograph a famous photograph and all and this is what seen here as the father of the editors where molecules what he goes as follows the hero and we're more and polymer solution out of beaker yes so I was following very slowly they very the solutions and now we go in with a pair of scissors and because the liquid which you can knew you could not do do this with a lot of ways that we can come and what happens while the sound here goes where it's going piece of here tracts they give it the pieces of the adjoining pieces of liquid be of the connected to each other by little spray is storage model this time to this the last recourse Thursday a it's actually sort of the same phenomenon here we have the speaker and would like to get polymer solution however to will contain them here so we will use signed except for right she to both sides now ordinary watering to because it has to do anything but what we do is we take this and we it's liquid and stretches of has an extension of the stocks and we all have after carefully the position changes so they can still be dreadfully with flows over the top and that like this In the law containers and it's being siphoned out even tho it is not because there there's nothing there that is America liquid behaves tho it's connected with itself over extended regions curiously the physics is entirely different you can get exactly the same phenomenon using superfluid helium you provides the walls trees down and flown to the lower container without artificial intervention well over the official intervention needs he believed so fluid on this planet so there is elastic recoil and this object is to win sigh now issue here is there are a lot of blood flow which you would like to explain the challenge is that some of these are a little difficult to want take so for example if you say I thought it redirects but what do you want to measure and how far it retracted how fast it retracted what happens scissors went through to Cerveceria phenomena for instance the nonlinear some of them were offered quantitative therefore offered drop trivially into theoretical models but that doesn't mean they're really just seems to be a little different from the sort of phenomenon that talking about so far and that is that what you're flow of on we will now push ahead and we will talk about memory effects but the but the there are a bunch of these the simplest when sketch this is that we have and streamlining of surgery to infinitely long flights and 1 is moving with respect to the other and therefore in the space between there is a sheer range you cannot go we run the system run it for a long time and we measured force on the lower applied forcefully or the worst of the opera place we have to put forces on the 2 places to get them to move with respect to each other and the forces determined by the sheer rate it's also determined by the viscosity the sensible thing to to talk about the worst screen area now we go
in and we make a sudden change in the Shearer at the and so plot USA Simon answers I'm flattered the island of comes along now chairman so there is some change this year I increased maturity and now having increased the Shearer I asked what happens to the spring there is a force per-unit area we need to do all this and we ask What is this what does the AMA stressed the ex-wife he if you do this for the answer is nothing at all happens until change and then distressed pops up and problems again and there is in this region you know it's it's gone amok this is all versions that is we have all the solutions that was habituated to being cheered him particularly rate and we then suddenly increased year we eventually get back to a steady state but before we get back the steady state we have this transient was over she followed the current spot suggests that sometimes you can get oscillations but the Our however you can also proposed several experimental artifacts on related to the inertia of the apparatus said that would give the illusion of those oscillations even they were not current that is it would be in can a machine artifact of physical or once you go in the other direction well finances and here's our charade I am not slow things down and we what what forces are involved in doing this the history's worst comes along and it does that and recovers and we have on issue that is once again on fears of memory affects the system takes a while to accommodate to what is going on around all the effects that I am describing can be also be business this is all the stress you can also see the same sort of thing you measure 1st stressed that is you change share raid the polymer solution ,comma days but it does not accommodate instantaneous but if you want you can also do more complicated experiment mentioned going no more of the mainly you can take all of the sheer rage you will say we will have to replace it have gambled on but oscillating place their work for which he is solved a "quotation mark homemade sweets also yes and that is the next the law and that he can had to with a 2nd year which constant and becomes the 2nd constant power would involve no emotion in the directions parallel or it could have involve almost out of applying of board perpendicular to the 1st year and now we have liquid with being subject to fairly complicated said displays the also this way that no less compression late in the Lo would would have to to escape of science and that we get a little messy so you want to do this so that the volume of fluid doesn't feel some obligation OK we have now describe what goes on in the city so we will not push on a different set of experiments in these experiments were we set control the sheer rate move on played with respect to the Of the idea constant speed or oscillating there are several actually will agree with the sort of experiment figuration to inspiring Icesave mathematics began to infinitely large plates however they wouldn't fit in a laboratory and then strain sodas several traditional arrangements which means that anyone arrangement used to say this is a soldier coming out on board this is another cylinder sitting here and I will rotate cylinder with respect to the US difficulty with that is that we're doing constant angular rotation as you go out on the radius on the sheer rate is obliged to change for the sum the parts of case another investors saying will have a small this year we will have another this year the little goes out forever is part of the 2 guests and we rotate 1 disk with respect to the UK and the distance between 2 disks is cast doubt that also has a problem
because the title on the surface here the it only part yes rotating and that means the top surface here is moving much more quickly than the top surface here and if I calculate the the there's a velocity stay out of my work invite calculated the velocity gradient is proportional to our because distance the distances are the same glossaries Ramada Inn where waiting this this cold :colon and place instrument and the notion of the played instrument is immediately ,comma while playing like this we have flat plate .period that we rotate once played with respect to the other and all that stuff and the X that's the velocity perpendicular the of all the horror yes however tell the separation between the 2 is also a proportional and therefore the ratio of the X over all the family the origin the whole and is in the market In order to avoid complications were joining pieces of liquids are moving in different spaces in the sky ,comma becoming series shall so I sort of had the experiment and that if you want more complicated the OK ,comma talk about something different story the bottom-place dessert about Blade and the around like this and then displays the top flight with respect to the bottom place through this yes gambling is strange and what we do is an experiment by law cannot resist the while resembles 1 we start off with no strings and then suddenly displaced long plagued with respect to to the other In well-defined experiments not trivial to do this you have displaced the top place with respect to Parliament very quickly get off to a high-speed were among the non stop again in such a way that doesn't oscillator source but it can be done and we ask what is the response what is that Austrian area appropriately normalized you know the answer is the worst on placed in the liquid is 0 until we do need of strange displacement and then the 1st and later time the case downwards this trace the beginning of this year yeah it's a function of time because if we wait 1 of the worst peers it is also a function of again because this is not only a year therefore we can measure achieves the again what shaped as if he had well approximately speaking same sold to exponential at the realize so if you say it's a sum of 2 exponential 2 exponential within a lot of things even if there is quite perfectly right so you should all really be insisted that if we don't the concentration of people and way the shift from something that looks like this is something that is done bigger and has a neutral vary the durable therefore you change the concentration of molecular weight and something happens and now we have the a question of what behaviors she is the began all you will notice against several literature references but I decided to stop the ball without doing a detailed study of nonlinear response there were several reasons for this 1st of all I was running up against page I was also running against time limit because I had to get booked public I was also running out into something of an exhaustion with been going on for 5 years and some 1 bring projects it was also very clear that the literature on this topic was very much in a state of flux as opposed to most of the rest of what we have discussed where all if I had done a literature search and didn't cut off the year to later for a year or 2 earlier gathered the lasted more figures but there wouldn't be anything very new there that is there that might be so additional measurements but people would agree on what they were and what they said the nonlinear stuff is currently in a state of all its ability to give birth on and therefore on decided to stop
I shall however illustrate growing disgust you need a lot and we're going to have this kind of I'm going to tell you what interest suppose you apply .period clearly began that is this part stressed that the if you do most of the strange size as the worst period various time goes well there is the analysis which use part I don't everyone agrees correct there also these everyone agrees is correct difference and what collaborated with reason I stayed with the show is without that March and face the gamble over some functions of that is if you multiply proposed by some constant at large reports for the 1st time a large Chinese multiplied in occurs all lying on top of each other and therefore are longtime there is the assertion is a common relaxation process which some people might think not and I don't believe it's a disagreement if you do the math and that the current moving around this way you can see this however there is also a nice set experiments like the stadium and the analysis by to carry shows what happens if you start with the measurements themselves and look at the measurements themselves and don't over process them before you look at because what they did is a lot this is the future of the pair of forwarders contract what they did was to go the meeting of the yeah it was the best thing saying they're going to have to what have you got and what they demonstrate Is that gambling is not among entirely yeah yeah there is yes you can make curves agree with each other but this division factory on I have is a bit more complicated than say 1 over an hour on the issue there is that there are a number of models that predict 2nd behavior but if you ask them what they would say about half of you would think you would have in the Model Town in Indiana and the result is that it is not new OK there's a further cut his post this is supposed to be a critical test of polymer right now and we get to a nice review by the errors you will know don't that system and what is to say that we please look at it before almost all of these years about 2004 for about a year and for the about 2 dozen studies that about half of show predicted behavior about half of them don't and so what is going on is due you very thoughtful and careful analysis and love for artifacts there is an extremely long list of artifacts that could cause various deviations from the expected theoretical behavior and therefore the proposal is that in fact sometimes you see the theoretical behavior and sometimes you experimental apparatus is uncooperative causes a problem if you read the paper carefully there is 1 bit that does not yet not I'm not faulting the author and maybe it really was that just missed the point but the question is where those artifacts Place in the studies which did not find expected answer or the studies that did find the expected answer and it is as completely sorted out now costs this would be a little more delicate to do because if you're saying X is wrong because he painted his apparatus the call it may be years before the paintings hang in there it's legal but if you say X is wrong when nor a certain number of your colleagues and therefore there is a certain matter delicacy here nonetheless all the question in all of which experiments with good which would be a shortly the author does describe the oscillating response which you can in fact find in some experiments that really is artifact and people that actually seen indeed more experiments but it began operating system relating areas will be completely toll call them strain so we have a strange again and we have another strain again and 5 plot straight emotional 1 played with respect to the other here is the on and here is again and we ask what is the system do after I displays the 2nd time or if you want the for the year University of pride of the 2nd displacement is the direction opposite to the 1st those are very demanding experiments end To be predicted by many it's on system experiment extensional viscosity the core issue here is extremely it's important commercial we gave Paul is is usually the terms and what we can do because the polymeric with we stretch so we have to find out something here for example we attach it to real there and we stay in the real very very quickly and therefore if I look it said Mark hypothetical markers lately the slowest gets stretched out the fire observers sitting here but the observer here is the tourist murder and here's something going this way here's some of them have you thinking about this for a moment they realized what was happening all the system if you do this and the answer is this physics and problems with a wire brush problem as stretched the while gets narrower and this is how to convert a very thick cable into a very thin thread is threat very important commercially important feature of this I'm work here this era here that is the top and bottom surfaces of the will be at the the same speed on way to the Lakewood is warning part so there's words compression but there is no significant share trading in 2 years so as not share Garcetti's there is extensional viscosity father however a series of interesting
experiments due to weighing way bring on people and what they demonstrate is that even if you're extremely careful you get localized regions were nonlinear things are happening the notion that you can just say it's a uniform thread being stretched the same way everywhere along its length at the same time I does not hold offered detailed experimental costs this J which allow portion of which was discussed what I very loosely described as moderate experiment further really modern well some of them are in the sense that it wanted to give them much harder to do all kinds of some of model the sense they have only been known so let us take a few these and 1 of these is them the issue was followed a year of polymers the foot between pair flights and this could for example be to repay the rotating columns played I described in which the center axis of Collins and blackboard there are other ways and means there was that the system to share so we just share the system and we ask what happens and the answer is that if we had not only here we had a problem with stock we had coming in from the DAX the July it's going to be constant across the high seas so the sheer right the skeletal where here is high here's a gamut of atmosphere is a little unusual and unique axis vertical and what you have is the Security Council however if you can actually be used real the solutions the air we concentrated etc. etc. etc. and do the experiment why is discovered it tends to be defined fairly narrow bands as opposed to being the same everywhere it's a tho the fluid had formed the old planes and was yielding near those plants the security be equilibrium assured fans that if you do things for a long time and everything just sits there yes now the actual experience where Japan is due to the it's a very clever said experiments you was respond with all our annual in year to get their moment so in fact latest going back and forth with respect to the bottom plate and 1 from end instead they used their fans you get these cells inside the zones fluid is yielding and between them and the sheer rate is much lower well that's not always you would expect to fight From the usual discussion but there is in fact what you find experiment we will get some of the more dramatic form of this moment on the more dramatic form this fall instead oscillating things we will look at the relaxation of restrictions that and more dramatic form this is no 1 will yesterday "quotation mark for re-election the issue was halted work on the Microsoft here place I'm just glad it's 1 life with respect to the other of of the and so what was originally this morning ,comma Ramon after I'm gone this the lake would presumptively his movements and the form of promotion is the phrase sometimes used and not a lot for replied that he did not know mathematicians issues that are displays and that resulted from in Poland originally like this turnout here and there is a risk that there's a status of forces solid to place to hold them in place because we displays things because of the old and the other is not 0 and we now ask what happens what we always do after you governments and the answer is the polymer is more than local banks this following rotator as the rotate on this 1 that stretched and as time goes on to retract and all of these in the context of these this model the fuel and because they can use their move relative to their immediate neighbors the forces between them and their neighbors are we doing this and therefore because the forces between them and their neighbors are reduced but at the time those 0 today however when you're done with all this I was carefully whose bright green always along this line I suppose I waited a long time and G-15 gamma goes to Europe while polymers diffuse sideways the widest worries but during the relaxation ,comma facing the and not were they started at the moment gamma per then as you move things to the side and they had sent there they refused but they don't move over any significant assistance and this is a core part of the so-called relied on words that's the except you can actually do the experiment I describe you can actually go in on you he also are actually used brief came as the ideal solution but you could actually ask what followers will do and the answer is at 1st they're doing some sort of relaxation but then keep waiting until times seem be fairly along with respect to any of all relaxation times and what you discover is that there is matters "quotation mark N and the sheer history sorted itself this year is now confined to fairer more confined to a more limited regions of space now it's not there is no stranger than strange but the amount was the strain here despite agreement destined mainly Jose 7 times toward strings yes so there is 1 OK that's not likely as flocked there are large numbers of models of polymer over dynamics most of which will only produce we acid flow this is a serious problem in the palm of own they also allow the end of the day 2 finals well 3 final OK Laura angle possible during the year miles looking at from played that's supposed to mean this and we rotate out with respect pot ended an Tory experiment there actually to the actual vary and 1 is because the alarm bell the fate of this sort of 0 "quotation mark only the theory says there's oscillation frequency and the other variable is dealt the fatal many is how far back and forth are you taking 1 plate with respect to the upper hand in standard experiments don't think that is small and agrees and there were 5 looking like this have played his worst problems because of this process is going back and forth but this displacement is very small relative to this system so that is the angular displacement of the top promises of human greed sex morning however there is nothing mechanically requires you do that you could also you invest and we therefore have what is called medium and larger and more hostile toward each year it really is sideways displays the wealth years the sideways displacement of about the same as and if you're under this plan this medium a loss for its latest if go out here you have a large colossal Tories placed the point of medium and large angle is the polymers sitting here now have to rotate quite considerably if there's been a whole lot and therefore the amount of the level of rotation gets to be quite substantial West margin loss Tory here In could actually do the experiments you can also do experiments were you measure the of dielectric relaxation at the same time we were doing this you should realize you know the frequency which is doing the dielectric relaxation measurements on the frequency at which you doing the oscillation and the 2 frequencies are independent and therefore life is a little more complicated than it was before the last at the end Noriega transformed the picture is as follows we have for example the flat disks and the copyists oscillation back-and-forth only the mentioned the force on the bottom of this yes and we can use piezoelectric elements and we can use electronics and we can be very clever and we can actually get a recording of this time on the bottom line is that it's very precise and what we say is willing 48 transforms time records Madison Wis 1st foray transformer we have this object oscillating back for forth an old and therefore the force on the we will have some confidence there will be in the I've already this season -minus Delta the old man sees the worst of year oscillates same frequency the oscillation of years earlier but there is a phase difference in the face difference corresponds to the fact that there a story as well as lost it's like any other driven harmonic oscillator these quite happily Dale the harmonic oscillator imaging OK let's true however the fact that a longtime record I can look for all the frequency components not just the 1 only and I look at the response as a function of frequency held yesterday by the people responsible later that turns out the response also has the real that financial and so forth that is you were seeing a nonlinear response because the system is not so yourself frequency in this case it's frequency trip 1 of the optical versions of the same frequency doubling the theory that trip down experiment could be made considerably more elaborate I had not seen found this in literature in there and the notion is set driving at 1 many I have some gadgets doing the driving its computer controlled by the drive with 2 frequencies at the same time and then I could look for all the harmonics in combination frequencies and this is what you do in model year laser optics will this happens to be a mechanical system that you can do the same thing in the world for the responses of of frequency and now the yes it's 2 different things and it was always going to different free I mean the fate of the angular position of top-flight this song played a 0 "quotation mark commented on the last day of the identical the 1 fated to co-sign all made too he also health that is I think drive plate at 2 different frequencies ran just 1 and if I do that I can look from Hamas and combination free but the bank now in return cash rate because Chapter 3 gives us some additional nonlinear phenomena but that you're looking at capillary alone electrophoresis so we have a huge area general theory loss of polymers polymers and we put things in order with the problem and we measure the the velocity of things down the capital and the velocity of the measured velocity coming back lost the Cloister everything you're saying and down here you really factor and the sector sees the things come about 5 and so you can measure the length and time therefore Oregon for a velocity In you divided velocity by the implied yield you have way of frantically you well new shows got some not only in your property I think we freeze the electrical field you discover new becomes a function of driving you know that is status of mobility just being number the mobility status on the applied field it is unclear from in my reading of literature I suspect very there's someplace where the nonlinear transport effect costing about some of the old or just becomes too small to measure however you do have a very controlled his change the field of lot system in which you get non-linear responses promo and therefore you have a nonlinear all this stuff lasting response which your program director I can bother you purchased from all sides what you see in the measurements the new falls exponentially stretched exponential growth size until you get to a critical broke silence yes the following critical size which he plans on Polish concentration there is a very unique drop off which is close power on the transition operate not be perfectly shock you can certainly some of the of less prone to the same concentration you can see what appears to be around now from the standpoint of the analytical this is good but this is very bad because he's the mobility that we have very weakly on probe size and you can get separations out here so as not call however since this crossover and this crossover the pure perhaps at the same time say they were the same I'm not positive but it looks like they're the same received the same month in case you're getting good separation is getting good separation you know goes will lower the fees and because you go lower the yield on Mindanao of higher-margin probes before you run into problems and by varying the field strength as you go you can get rapid separations and you can also get separations might work at higher fees margin approach perhaps I have no comment expert however this is very clearly a nonlinear change if you ask yourself what is the variable that is determining the nonlinear change the answer based on a probe size field behavior etc. I used to be With this transition corresponds to how much force you putting on Palma's solutions and the polymer solution be cases that as yield .period OK we're almost out of the way I would like to know the answer is we discussed working in for the care of everything that goes on in your facts and we talked about 3 sorts of issues we talked about things that were clearly to normal stressed differences 2 do you didn't talk about the instrumentation problems that come up trying better moral stressed that's is there that we talked about things that arise because the system has memory the real molecular relaxations which take place on time scales so long service and finally we talked about some new methods and observations such as Shearer abandoning our not be acid flow electrophoresis the discussion Jr was really 11 caps on the day's last supplied them over the weekend tried described on so there is that for all the different types of love of life and I still have a suspicion that there is some sort of experiment I missed in the not too but I did try the next lecture will review all of the experiments and high points of what found and then we will have about 1 2 lectures in which will actually trying to interpret this in terms Paul box but that's it for today


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