23 Viscosity, viscoelasticity

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23 Viscosity, viscoelasticity
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Lecture 23 - Viscosity, viscoelasticity. George Phillies lectures from his book "Phenomenology of Polymer Solution Dynamics".
December Weight Viscosity Day Scale (map) Scouting Starter (engine) Measurement Order and disorder (physics) Crystal structure Ship class Viscosity Relative articulation Kette <Zugmittel> Potentiometer Ship class Spare part Polymerlösung Linear motor Star Progressive lens Typesetting Molekülmasse Field strength Hall effect Year April Power (physics) Locher Concentrator Metal Quantum fluctuation Aerodynamics Direct current Series and parallel circuits Hour Book design Noise figure Water vapor Stock (firearms) Model building Volkswagen Golf Last Firearm
Prozessleittechnik Quality (business) Effects unit Dielectric Scale (map) Light Ring (jewellery) Kette <Zugmittel> Phase (matter) Bird vocalization Pattern (sewing) Separation process Knot Solid Roll forming Constraint (mathematics) Electricity Cylinder block Linear motor H-alpha Reaction (physics) Electron Molekülmasse Year Command-line interface April Hydrogen atom FACTS (newspaper) Specific weight Isotope Quantum fluctuation Belt (mechanical) Autumn Series and parallel circuits Universe Cartridge (firearms) Book design Noise figure Volkswagen Golf Near field communication Ruler Afternoon Hot working Cosmic distance ladder Measurement Viscosity Radio atmospheric Ship class Commodore MAX Machine Rutschung Orbital period Spare part Month Material Angeregter Zustand Star Microform Typesetting Paper Chemical substance Kopfstütze Concentrator Collar (clothing) Sizing Gamma ray Absolute zero Theodolite Power outage Synthesizer Stock (firearms) Model building Firearm
Universal <Firma> Quality (business) Eisengießerei Scale (map) Measurement Cash register Viscosity Bird vocalization Roll forming Spare part Video Book cover Atmosphere of Earth Material Angeregter Zustand Star Typesetting Space probe Will-o'-the-wisp Sensor Protection Molekülmasse Key (engineering) Kilogram Year Train April Power (physics) FACTS (newspaper) Chemical substance Concentrator Series and parallel circuits Autumn Theodolite Relative dating Water vapor Stock (firearms) Last Movement (clockwork)
Prozessleittechnik Liquid Cosmic distance ladder Hot working Measurement Force Viscosity Negativer Widerstand Spring (season) Flap (aircraft) Bird vocalization Arbeitszylinder Colorfulness Ship class Crossover (music) Spare part Month Color charge June Engine displacement Stress (mechanics) Molekülmasse DVD player Inertia Year Bending (metalworking) April Power (physics) White Drehmasse March (territory) FACTS (newspaper) Cogeneration Concentrator Universe Series and parallel circuits Cartridge (firearms) Fahrgeschwindigkeit Plating Theodolite Remotely operated underwater vehicle Relative dating Gradient Stock (firearms) Week Riser (casting)
Spread spectrum Physicist Cosmic distance ladder Hot working Photography Audio feedback Bubble chamber Measurement Force Negativer Widerstand Fire apparatus Spring (season) Ring strain Energy level Phase (matter) Screwdriver Separation process Roll forming Alcohol proof Ship naming and launching Video Hose coupling Engine displacement Hyperbelnavigation Striking clock Langwelle Typesetting Stress (mechanics) Tiefdruckgebiet Electron DVD player Electronic component Year Machine Vise April Lead FACTS (newspaper) Series and parallel circuits Schwache Lokalisation Fahrgeschwindigkeit Plating Book design Remotely operated underwater vehicle Level staff Model building
Acceleration Hull (watercraft) Scale (map) Order and disorder (physics) Spring (season) Kette <Zugmittel> Particle Teleprinter Rigging Atmosphere of Earth Engine displacement Audio frequency Tiefdruckgebiet Electron Year Kette <Zugmittel> Black April Railroad car Power (physics) Leyden jar FACTS (newspaper) Control rod Perturbation theory Cartridge (firearms) Fahrgeschwindigkeit Food storage Book design Level staff Pistol Liquid Hot working Bottle Stufenversetzung Bomb Day Summer (George Winston album) Access network Viscosity Microphone Mitsubishi A6M Zero Cell (biology) Caliper Spare part Orbital period Video Engine Shock wave Langwelle Typesetting Car seat Stationery Machine March (territory) Drehmasse Concentrator Gentleman Ground effect vehicle Theodolite Remotely operated underwater vehicle Water vapor Model building Analemma Sailing (sport) Last
Concentrator Hour Orbital period April Viscosity Model building
classes in polymer dynamic based on
George Phillies book phenomenology of polymer solution dynamics Cambridge University Press 2011
ends today this lecture is lecture
23 viscosity introduction to this last day city the tempo oral scaling on his ups and
festival is they were going to finish off our discussion viscosity and push on to discuss discovered last December let me where we left off roster speaking we left off the chair 12 thousand figures 12 . points to welcome you the authority to her treatment of pot molecular weight dependence of the viscosity the solution now there is a bacteria actually fairly considerable number of measurements of the East and they're actually fairly consistent namely what they find what is fine with considerable consistency many systems is the viscosity depends on the left with this precious metal weight and asked brought out up quite emphatically by for example Figure 12 . 1 4 of 12 . 1 4 ,comma measurements they actually here in doorway and Edwards who report them as measurements done by almost nobody at all on the measurements are little more complete and amendments of the original paper on although having said that the an interesting feature here is that if you go back and literature and asked what people said about this these measurements you can find people who say they have measured the molecular weight and its viscosity and asked predicted we see how a lot dependence of the molecular weight there actually are measurements that find Powell molecular weight because it's sets off for example as we discussed earlier how all adults measurements which pushed out to the Mets find close to the melt a towel on the dependence of viscosity on molecular weight in volume fraction water the plot where rapid clearly straight lines viscosity changing his a towel on em and if you actually say will stay fairly close to the melts and we will explode points that seem to be deviating from the region's on you actually qualified but how on the reading however most of the you find which are down considerably lower concentrations do not find out how power lot behavior they find stretched exponential but any interesting example of this is provided and this is also the Onassis stretching over to the next section which is in discussion of policy part of that supplied gracefully and gracefully looking at polymers and they look at leading changes and they look at foreign stars and they look 6 hours starters and if you look here at the results they show as a function of concentration for linear change and earlier changes of molecular weight of on the 1 . 6 6 that is going as a function of concentration wall lot they find what is very clearly a straight line and look at it it's clearly a straight line and it's quite clear that the Army you were seeing Powell on the other this for the 2 Armstrong linear chain to our stock on the other hand for FC war and for athletes and say very clearly on the same plots Lisa chains of about the same molecular weight all this is about 190 5 polymer and the other is about what it was about 1 . 4 World Golf Hall of end for the other 2 very serious clearly see stretched French exponential molecular weight dependents concentration you're fixed molecular weight of concentration is if you look at the molecular weight depends where they have a considerable number of samples they were looking at concentrations of about 300 rampantly extremely concentrated systems and the molecular weight and a straight line from linear they are was a fresh exponential To stretched exponential said actually for we all stop all as a thought taken as a function of concentration in the upper figure the linear change showed the strength of our law behavior the stars should stretched exponential behavior the viscosity of the stock was for the most part unless the viscosity of linear all are however if you look carefully at the measurements against concentrations can seem quite up here and so is the old concentration was stated the kind of eventually sold the stock always as the obliged to give the functional behavior they shall viscosity that was higher viscosity structure Out of linear chains all the however for the most part start polymers comparable molecular weights all are all fairly high concentrations less viscous linear chains and it faced concentration as a function of molecular weight against the stars are less viscous Emily changes in but you can also look at the results of all laughter you can the results of era collaborators they looked at 3 the story the stars were appalling health volunteers styrene on the day look a series of concentrations and molecular weights on you can see the results in all my years 12 . com 6 and what they found was that again if you about the same concentration at about the same molecular weight the viscosity all stock owners to get the priest is left for viscosity all know why is the statement that the stock holders have a lower viscosity linear changes and all the number of models of polymer dynamics which serve the linear chains have extra loads of motion that are in principle not accessible stops off in particular for example often reputation type models say that if you have a linear polymer he can creep through holes in a transient that's like snake in the world but if I am a Stockholm were in order to make forward progress when I have to do is introduce retract by fluctuation 1 of my arms that's difficult to push it out a new direction and now I can take a very modest step forwards on the Net result is that 1 would expect and it is harder for star move with respect to each other than at least if they're very concentrated than it is
for linear chains that does not appear to be quite near observers question can and also the possibility the the all that could be an issue in the after however In the solution the amount of happiness determined by the concentration and the answer is that the constant were make comparisons people not concentration for struck you go there you recall with respect to to let us have changed into that is they have high and start all over I have 1 point where there were 3 chains coming together there is an equals 3 stock there is a narrow region around this where there were 3 of my chains close together however found large stop Oliver over most of my life and look exactly like lineages therefore that this sort of infected you might find interesting facts small chains with large ones you would not expect OK we advanced the theory the whole discussion around figures 12 months can issue around figure 12 . 28 configured 12 . 7 2 years to produce the polymer and we changed the solvent what happens if we change well the expectations but if we are in favor of solvent or closer to which means we also have the right to weed out a policy change solutions although he would rather see some of his neighbor than see something else too and therefore we increased concentration at nothing terribly interesting will have to change rates they didn't say nothing at all because the fate of it you can get a perfect cancelation affects approximately on the other hand over the goods sold we see what we saw the chapter on dielectric relaxation which is what this been means for most of the time namely as increased concentration look charities the change radius falls with increasing concentration all so there'd be these however stacked properties there probably is the chain of command take this step were talking about viscosity here viscosity is a dynamic property and we ask what happens to the on the behavior of the system if we change solvent quality such but the 1st answer is if we look at a series of changes different molecular weight the viscosity as this case of most other the systems not all of the systems are not sufficiently high molecular weight concentration but the gold concentration dependence is stretched exponential and what we can to find as we increase polymer molecular weight and were measurements we find the parameter alpha increases and the parameters all right so there is also there is new and both parameters ,comma molecular weight and the 2nd thing this is the comparison parameters In good solvent In the latest and what we find is that in a state of solvent patterns us here parameters movies from the whole point of the 120 5 work and if we go however take the same material over to good insolvent the parameters movies Poland . 6 of a point that great there is we're going in to and we change the solvent quality when we make you go into their solving the parameters new falls obviously model derives this equation in fact predicts this behavior we will eventually get to later but if you look at the figures especially 12 . 28 this change of new was physically quite visible if you look at his son-in-law "quotation mark a lot viscosity concentration for a evaders solvent B on concentration and the data is fairly close to a straight line because the firm boast was stretched exponential but if you look at the measurements and good solvent you typically see a more tiles curvature because you were looking at a stretched exponential red purists in the now having said this let us push ahead and consider the general features of viscosity it will take a lot of specific measurements and what we do for fun and viscosity depends on polymer concentration in polymer molecular weight not to mention the so-called 1 would the apology and 1 could put in solid quality With respect to the apology are there was a very long dispute this goes back a considerable piece about the viscosity of ring followers are in bid that was mostly belts which the book is not covered all the issues there was well you can try to make melts you have asked army in trying to make it rains and put them in melts here is a ring is a a nice or during years and synthesis process didn't get itself all tied knots so that its fall all under modern conditions if you want to answer that question you can resort to using DNA tests since home you can synthesize DNA is with the absolute molecular weight control but absolutely mean we have something that's 180 thousand base pairs meaning its molecular weight is tens of millions on the molecular weight is while the fluctuations because the several isotopes of carbon period nature and carded an interior hydrogen I say nature all but the molecular weights are totally exactly control no fluctuation you can also synthesize things this synthetic DNA not stuff that occurs in nature that is a star are completely 1 his 1st you can also synthesized happens naturally some viral DNA students are the enemies of the ring polymers there again we want Spurs the electron micrograph of those readings indicate the rings are completely open their are tied up in in knots although however having said the rating polymer is are home Mom's 1st stop all merger truly model 1st in synthetic that the comes their way there is the significant practical issues that people have not gone studies of DNA viscosity there is extensive it as the viscosity studies at the demands the all OK having said it let us
look at the question the 1st quake which are going to emphasize significantly more than was emphasized this data is not universal function policy that is if you think that you can take your viscosity measurements and yes there will be some chemical dependence Constance and there will be things that depend on the concentration of molecular weight or maybe even 1 strands of molecular weight some representation of amounts to Uriel all sizes chain although if you think that all of the changes are the same because of that and therefore there should be a universal functions that is to viscosity is a function of concentration on you're going to be disappointed instead it is quite clear from the literature the viscosity is not universal function of CEO instead there too distinct phenomenology and 1 of the terminology you see is simply a stretched exponential which in measurements data goes up data from other people go out more less and another set of systems stretched exponential all afternoon .period and then the I'm going to see a powerful but it is worthwhile to recall that the same phenomenology this class it is occupied by satirical Hall spherical show the same being the the hourlong the hands on the exact material for spherical College the slope is considered is appreciably steeper than from any other chains and if you look at the many arms stock polymers this slope creates all makes the transition from linear change behavior of very nearly parts security what it should be clear that any model that explains this phenomenon is subject to the constraints that must also be work for cervical collar voiced serious concern about number of things but on Form entanglement lattices is not really wonderful and former Albany wrapped a is certainly not so we have the issue viscosity behavior of light up quite what you would have expected from some of your reading from some here yeah OK through work if you were shocked to viscosity of all files and in the rest of the year over it's your above about as he and most of those measures are literature studies to revolt but the bites were holding out however if you look at that it doesn't appear that if you you get involved here instead of continuing along on power loss there is all words deviation the nature of the upwards deviation is not quite certain all what might however for example proposed to do since were extremely high concentrations that some sort of jailing transitions in which things actually mechanically get in each other's way and the chains cannot slide across each other because they came after all the rigid over short distances they can't move sideways is easily enough to get through him however that is a fairly specific that's a fairly rare exception was not a lot of studies look on the look for a predictions that the conditions on the effects of what all that prediction is very generally not true Paul Merson options there are some exceptions to this rule this family but predictions that you can simply assumes scaling do not sustained other than if you wanna say saying we have scaling need to explain why some of the guys in the scale and sometimes you don't all otherwise you can't just so OK so that is the sort of behavior we get all we might then asked Well others generalizations and and what the answer is for a very large family if you have the we have created over a 0 is song constant golf sees the new and now I'm on all of them like the native and Alpha Tau both actually see brass their tendency but if we actually look at the measurements and they asked OK we get this thing fear what do we see well beyond what is usually In a range of around but I can't be more precise than their best reasonable approximation called in .period affair with so I should have something to go from faded you go from various solvents solvents the parameters you and what I would call the health care because it's helpful to him what I call on all the animals and the animals it's not seen increases as we know from there solvents to resolve its generalization context what behavior we see or any answers seen In the year 12 . areas where we plot helpful to which the terms of this the way to his health of him and gamma coefficient seeking to block health against Baltimore the way now I just show you why it's your reaction the G that was a nice piece of graph paper professor abilities at least it was very nice before you way back and started firing the shot and points are all over the place however if you look carefully at this points I have labeled .period 5 chemical family of the polymer so we have a serious I identified separately each set of philologist Paul holders that are chemically identical differently and if you do that you see the strategic single-family ophthalmologist polymers alkalis variable interest rate .period the straight line has slowed so there is a lot lot plot so we say Alpha goes is important Our earmarked and what can we say about gambling if we look at all of measurements that is also measurements were the same way out of the a large number of different polymers electric rates and all the bad things were consistent and the answer is the other this typically in the range of of people . 6 0 . 6 seconds on the final phase of the whole way that called for an old . 9 4 words quite largely confined spaces where it holds .period want on if you look at this he knows there are different slopes Nunavut materials and therefore were not fighting universe the slope is not
quite universal constant but for a given set of samples the power a lot friends is actually fairly shot on this result is also this result is also listed In the past the systematic review of all the collaborators and all the wonderful Russian data piled in 1 place for us because we have also use this another is a good reducing very that is if you take all these measurements and plot was functions of sea times the intrinsic viscosity rayon Sea we have a lot of the here you find a suitable series different polymer molecular weights measurements in Ireland the same person downward for the expansion and still lie on the same when you are doing a lot must be in place in some form of seeing all of which means that all of the molecular weight independence of viscosity casting built into the molecular weight depends of the intrinsic viscosity you can't get any of the molecular weight hands out years of place because if you didn't want plot this vast city for a series of holders of different molecular weights they wouldn't lie on the same line by line along the same lines because viscosity is also times the intrinsic viscosity that statement Universal function goes all the way up to however it is important there this viscosity the intrinsic viscosity depends on him power therefore this equation says viscosity use of function of 1 of the functional see NYTimes News constants and the air and example of a function that has properties that viscosity has this tendency is given by this fall now you would have to say is is the health care c and b the power and therefore the Diskin the need to date times new yes phoned the next following paid by multiplying the the experts say therefore this equation and then waited only consistent so long as the announced a new related like this novel last year false results are entirely consistent with everything he said I would be delighted to say that I enjoy protection from movies movies and of molecular weight solve quality the event really is quite different from the 1st obstacle is that if you look at this formula for the viscosity data from rhetorical use since you know is the exponent of the Expos which means bigger than for a more neutral doesn't change a whole lot if we send is almost always in the range of 1 here and 1 that's correct all and therefore there's not a lot of range and if there's any difficulty at all measuring you accurately you run into problems with Brossard scale there are some other recent parameters however that have been sort of hearing tonight can point to that fueled 1 we can talk about you know the answer to the youthful is the the transition concentration in the key transition concentration yes we're not limiting ourselves to systems that show solution like smell like transition a transition they are in charge of like this and there is a concentration of the substance solvency and trends in contemporary and correspondingly there is discussing leaders of the when we discussed this call a well 1st serious there's it's always really only 1 per cent volume fraction is the area and finds he was about to take off more the higher and viscosity of registration provided by the discussing the insolvent about and also going willingness on that's very clearly not trained concentration and viscosity which can start getting space them an question is that of a linear polymer is how the transition concentration and the answer given in 12 . 3 3 Europe on points of the warrantless calls for a willing and the transition concentration of and my told 1 of . 1 overs so that is as you increase the polymer molecular weight the concentration of the transition faults the quality of course you need a set of measurements where the same material that shows the transition has been studied for a lot of different polymer molecular weights otherwise you should be hesitant about leaving the fish and the results that do exist are on holy and fossilized inside they discussed for and on you look at those and she roughly this behavior state you might OK so that's the transition concentration I you might also say Well gee that's the transition concentration and maybe we should really express transition concentration in natural and when I say the actual concentration for Paul Merson and with people generally need to see the Stasi now there are people who say the old ceased were the stars the overlap concentration but in fact the overlap concentration is usually inferred from the intrinsic viscosity mainly the stock he equals holds strong numbers range from what I've seen in almost all foreign water over distinction but not yet OK so we look to see and we will ask out loud transition concentrating natural movements received transition and if you go through all the accumulated evidence to find transitions as high highest 80 you can find things that heard about the implies that more technical but you can also find transition concentrations below for example hydroxy probe cellulose which Urals philosophy United others studied for and so if you look at the transition concentration and natural units in covers a very wide range of values you should realize this is a significant part of the way now often meld concentrations in revolves idols analysis were not only about 300 columns all the transition concentration for war on hydroxy probable cellulose all the intrinsic viscosity was 1 over all wanted to GM leader in the transition occurred around 6 grams
per liter sup the if we say will put the concentration of natural units you don't see any tendencies measurements flaps on there is however something you can do which destinations not perfectly but actually pretty well and the answer is if you look at all those curves where you see something like this linear polymer not years for the wrong measures for people spoke of a lot of different molecular weights you look at the graft you realize the crossovers occurred about the same viscosity and in fact is the use of approximately monitored the at part of on a date to hear the song on her way to the that is there is not a concentration which ensued cross over but there doesn't appear to be a viscosity universal viscosity which the crossover says accepted parts fiercest many different and the crossover and viscosity occurs when data over a 0 reduced viscosity is if you months save produce something that's fairly viscous not completely impossible Oh yeah you said the politics of behavior of year you might legitimately Westernized awardees expert and the ouster of for referral systems is in excess of 5 3 in however in confinement systems in which more to Florida of well I mean much larger somewhat larger for example and hydroxy probable cellulose answers about 4 . 4 and therefore there is a power locks from making even tell you how a lot let us give From the systems that do show transition which well it is universally universal transition as function of transition viscosity it's not universal transition function concentration all in all it doesn't even hear that song system so let us go go back unless look at the system would not see a transition which is 1 of going out in some cases Farenheit class and I still to to reduce costs and talking about him so in cases in which no transitions OK so there is a curve and 1 of the things you might legitimately ask is well she couldn't we manage described this measurement perhaps humbled Powell and if you go through literature you find people from Holland comparable year which is sort of tangential goes to points over some distance and you find out here typically linear curve and in between the song transition was
sort of talked over as feeders transitions Abroad and therefore you might propose yes the measurements actually show a crossover from 1 side of the behavior the other but the crossover is a little hard to see because there are other things going on not the there's not a clear transition away there would be a phase transition I don't think anyone has proposed that the letters White almost no 1 who goes the system so there's there's a transition but it's clearly not a phase transition not the only question is is this a reasonable restrictions and will answer I think is that if we look at in the office he knew he'd here the stretched exponential behavior marches out health and move currently and the concentration of portion C 0 rate and extra long the whole purpose and therefore viewed from this perspective there is no transition there is a single smooth curves just shrugs OK I have just run out of jail you don't want to be in this market stocks I am now going to advance discussed this week unless this story that brought pictures the idealized picture of Europe infinitely long plates now that's a little dangerous because place earned infinitely long and there are several ways around this for example then plates in circles and have sent cylinders where you have a flat plate you have a rotating called you may say what you want and rotating color and the answer is the velocity of Europe's only a quarter past velocity of parallel plate this distance distance out from the center increases heart and therefore at this distance has this distance is proportional ,comma and therefore violated velocity of the plate over the distance from the played part 2 and there is a velocity gradients here and the velocity gradient is uniform this it's not you have to be a little careful with this because it is all going to be some question of whether the uniforms he said this way the potential complication nonetheless we should persevere and I should draw this spring and this despite the bottom plate stationary and top players being moved back and forth and the top place as displacement all told the removal and displacement is song Young would "quotation mark that is we haven't displacement and the extent of the displacement oscillations is the harmonic you can do that equally with either work the displacements were fairly small now you might say Well gee we get information out of him displacements Florida and the answer is yes and there's an object and experimental method called charge hanging over possible to every year and we shall reach Laos In the next chapter Chapter the however we just read Chapter 13 which talks about linear last year OK so we have this displacement and the resultant reported get this placement the have to apply a force on the upper plate back for now if you think about this for a moment you realize that if a player has inertia you're also accelerating the slated for saving time and you I have to deal with this Texas basically an experimental work and the inertia of the place has to be made small enough in some sense that you can measure the Kurdish forces the fact that the liquidation I'm going to call this a 0 the offered to oscillation comeback on compensation for all the reason is that look at the system if you make plays a bigger and bigger he amount Fortuny goes up but it's basically a linear process and therefore do interesting things forced review and the the area is known as this breasts In the 1st forestry unit area which by the way is going to be isolated as a function of time in the stress determined by
the amount of oscillation the displacement divided by distance held in that is fighting his whole apparatus made twice as big vertically the amount of oscillation seen locally by by all there is and it starts out Neighbors along this line and we increased the lead to its maximum this possibly the neighbors displaced sideways 1 way or the other in mosque back-and-forth banter and the amount of local displacement is determined by the ratio of the displacement of applied to the distance between plates and this is known as the spread version yeah
supposedly actually do this experiment there are a couple of different ways we can do 1 thing we can do used to apply an Tory foresaw here and there in the motion and so we have force which is very precisely controlled Houston's back on and we asked how the player moves we can also have a driver and feedback electronics and the played back and forth through a fixed distance and we instrumentally determine how much force were having to users so the play actually does those 2 experiments ,comma level that is are they at that measure series of curves were certain about the cost per unit area certain stressed and certain strain on matched with each other 1 from 1 bowl you were actually experimentally creating stress measuring strain vise versa doesn't matter if there's 1 curve and the distinction there is purely how you build your machine OK no having said all this not only that but the measure this question this is the news the it's only because he wanted to this is all about it seems to me the answer is no that statement is more general than its linear response that is you have stressed you hear strain identified double espresso what happens to the strike will strain may or may not bubble many years as responsive thoughts but however the statement is there's a stress strain relationship would be true whether it was when you're not the only places where you would get into trouble with this is that you can have a history cessation where on if we will apply different for example different strains and stresses changes someplace or vise versa you might not be able to to reach every point on her instrumentally very easily by biden 1 1 now this is linear response in the sense that the theoretical analysis that is going to linear is going lasted city assumes that if I apply a series of forces at different times the food has a response at later times and I can just 2 linear response that is add up all the responses of fluid the worst fire fighting force several times research finding ladies and I'll get the answer will get too many years so what is the net result there is all this the actually look looked at the spring stressed work too In here and we compare it with the story we find ourselves and what we we can find that because this is a year we can get the worst we can provide out the 0 we have cost per unit area per unit of strain and that forced turns out to have 2 pieces there is 1 piece terminated by function the prime of all that and she crime of all there is now multiplying the displacement traditionally signs co-starring all right "quotation mark photos there is 1 component where response has a response that is being phased With the displaced so you have displacement and there is restoring force that's what areas that grows linearly and displacement here the oscillating Peter and then we we have another component In other components In is 1980 agreed however that what and so there is a response that is 90 degrees out of phase 2 the displacement meaning this is a force that is the largest displacement is 0 National very odd but you dampening phasing out of phase sponsors you might ask what does this all mean why is the worst in our phase displacement is liquidate after all if you made the displacement stopped and sat there after a while the force would disappear because they really just that's a little more complicated the answer is the low share Stasi years it it was relatively low frequency pw Prime Minister over many these 2 objects when she crime for model energy prime lost I complaint legitimately 1 gene that seems like to to represent things and I will now show something that makes much clearer physicists pointed to what we were looking at I'm going to multiply each of these objects by 1 and of course where a physicist says I'm going to multiplied by 1 you know it's going to be some huge object that is in fact 1 of the books but not the book and multiply despite warnings were all that where over and I got this 1 by 1 in the form of overhaul that's perfectly legitimate notice this set like the staff but now I ask you OK I have something that goes as Omega science but the displacement it it's not the result of phase with place and I have something that goes gold-medalist where times displacement Wahabi have looking at your role if you think harmonic oscillator you realized this object is to velocity and I have determined the forest that is determined by the velocity Gee that's a lost and here I am term that goes all Madison Square times the
displacement nasty acceleration and the explaining that goes of the acceleration is restoring enforceable system looks like it has long springs and in fact there are Arizona math models blamed on home if I recall correctly Maxwell and this whole picture be modeled as as a system and it has a sprained and calls the spring is something known as -dash hot -dash parts various works Japan's people had Helen types the -dash thought that the fate of the what course moving objects in the teletype comes back very fast and you don't want to wear the foreign cars because it does the vibration damage that is so that the school system like object and moving objects coming this way Johnson has Vermont coming out as of March this year the year and the robber disputes this saying and there is a little here and the this is the case but it's a pistol result you compress the air slows things down and then when it's done compressing the air here blows out the end and continue the opening this a little sliding and so eventually Africa's small fraction of a 2nd the moving object on the teletype is flocked to the end here it's brought was stopped at exactly the right location and with no unpleasant shock acceleration of damages all well yeah those that and it doesn't fire high high-quality Victorian engineering you know essentially parts of this the object private stuff was nowhere to the advanced system known electron it's sold on him and there is a national and you can feel the dance partners do solemnly was so you have this hanging objects in liquid and the hanging objects in the Lakewood it's just a really good with the viscosity and no frequencies and some or it has frequency bands and this object represents storage was Tennessee's represents the lost 1 so that is a picture of the bomb this last parameters Lanier in terms of storage model was lost on and you notice that I have read parameterize them starting here with assistance days and once I've done this we lost lot looks exactly like the viscosity there is however dislocation qualitative for years however the consequences of if I had a lot cheaper were achieved crimes police you remember that contains something I divide up momentum which I can safely and therefore prodigies don't from both going to 0 this is a little hard do a lot of thought they both got down and low frequencies is more typically want lots and never really yet this year there is a link their behavior which is contaminated from power and then the things that happened out here and perhaps the Kurds across the divide the making of America marjoram a dramatic herbs Vermont again I'm not going to drop this in any detail to find standard texts the important issue is that if you talk about she prime orgy double prime cells themselves all of you find that they have heard that looks sort of like this and there is a region where things are reasonably flat a low-frequency bring him high-frequency region introduced terminology will get that next time all the main issue is that there's a shape 1st if I instead said I'm going to go away and I waited plot to keep trying to overcome clear word she stole from over Bloomberg provided that I divided out leaving slope and if I do provide out leaving solve that says that low-frequency the behavior that I'm looking at this frequency and which is sort of what you would naturally expect any speakers although as you can see from a book about the same in leaders last year there a wall over and then here there is at least at 1st at powerful the lady something interesting happens at large and question we asked given that I have drawn these pictures is well how life derived from rationalized curve explains its and so I will do you think that follows us based on a variety of theoretical while we have not yet discussed in detail and renormalization group apart and so we're going to actually involved in the life of 1 of the high dynamic scaling on the mind on and we are going to want to be involved renormalization group part of the renormalization group argument being involved is much more general and qualitative and many renormalization group argument although it will be clear what it is we're going to start out here is a straight line represented concentrate we will match viscosity is plotted perpendicular black war of words and what we find is the viscosity increases his idea of a higher concentration and eventually at least in some systems we reached the transition concentrate Of the and down here is the solution like and the solution like regimes he stretched exponential in concentration in the year and hot here is smell like reading and through seat Best secure phenomenology now what I say is I didn't do something called all over smaller positive functions renormalization man and what I and I applied this in the context of the hydrodynamic sailing and I said I can calculate a certainty behavior at lower concentrations and the Altenburg a dollar renormalization group lessons turned
lower concentration calculations into the stretch exponentially and we're going to assume that's true now I'm waiting for another little bit time the PFR achieved all over coloring positive function normalization method actually predicts 2 sorts of functional behavior the functional behaviors predicts the pence on where water all thinks points all of the of renormalization group In particular if you have a fixed point at 0 then near-zero day stretched exponential behavior as stop on the other hand How years old if you have a way of fixed point that is way out there and that is the dominant fixed .period we several 6 points but as we go along here there always a dominant fixed point is the dominant fiction points out here you would get power behavior as sir next trip the viscosity is low-frequency lives all of you don't try that Over all red list after the has the function of concentrated and so is the dynamic lost loyalists and therefore what we say we are looking along this discusses the I can also say put another exercise in handling user certain vertical axis skipped over finally called vertical axis frequency but I'm going to say this velocity is what we measure along the Omega moralist maybe not quite 0 so we measure at all but low frequencies and we get the viscosity secede 0 frequency however it's 0 frequency with the wrote as Ada I could just as well that Britain has cheated on you prime by the way concentration for the moment and therefore I now have to variable function and I have used the the renormalization group argument to work along with that since 0 now comes the somewhat I would start here but I march sideways and at 1st I didn't machine when the station .period zeros presumably still there and then at some point I went sideways and often these other fixed points about which I know very little become dominant therefore I moved from the solution lies we don't like however I am emerging along and see the all matter as the variable designed sideways on career and I am looking at something that really is really only a function of give this picture is correct there is is a great deal of extrapolation this it's obvious spots on the the that Mullah frequencies this explains is dominance and therefore I should have a stretched exponential frequency power eventually I crossed this line and one-time across this line I am in region where the life the explains out there somewhere and I should have known that it would hold this summer really to calculate what power is at all In order to do do the extrapolation even the low-frequency I would need some something previously viscosity is 0 plus presumably some intrinsic starts at the age of C plus some data that it is I would need some way to generate a model gives me the low-frequency frequency bands so I move or lost 0 at all and after I have moved off 0 and all I can then use the old bird dollar renormalization group to say what happened frequency however I have not found working on things I have not yet found the frequency yes and therefore this is the assertion is that you find this linear staff and then fill in the low-frequency behavior that has not yet done and cross over the fixed points out there not concentration OK come so that is the rationale and you notice was predicts that days stretched exponential and frequencies at lower frequencies end and predict how long frequencies higher however there is an interesting if you look carefully there's a little bit scientists you run and 1 that I have skipped around around is what it says about frequency dependence way out here that is if you are way out there all you're not like reaching all the way and therefore you see simply Powell on frequency behavior will that actually pointed data that looks like this and the question is how long are you really going to see that the worst case that there is a very low frequency stretched exponential frequency reading and correspondence that is possible this that is over and very very close to 0 frequencies get out the sufficiently low frequencies the CDs behavior disappear and answered on the other .period but if we go off to a very high frequency this is all going to be the case but we have got into the only extra genes at very low concentrations orders this current trend over so that very very low concentrations were we can just barely see particle interactions at all are we are still in the concentration next that stretched exponential dentist who all was not handled this very does not discuss this a lot of water bottles around there it covers the slot jury now you could say of course she this picture explains why some systems show all although the solution like not like transition and some not namely depending on exactly where the fixed points out here are it might be a case that the soul of the system to along concentration access always melts this
purpose not only invented stops at the and even at the mouth of the details numerical parameters going in the calculation saw you can get all the way out here in the faced pointed 0 is still dominant but the other systems and all you needed differences in encountered least dependent parameters such that these 6 wastes the pond dominant and some concentration that out here see Powell and therefore want universal physical model plus chemically dependent parameters that the tournament where we face .period his dominant predates both behaviors will last 5 the on hydrodynamic scaling model which actually allows you to have to behaviors in 1 general model is not also good for models that assume scaling because they assume that you always get scaling out here which it seems that you not OK that is the UN's Aaron of having given you the answer us we have now reached experiment we have also reached approximately the in the hour and therefore we have reached a natural .period stopped therefore I am going to stop so this is lecture finishing off my treatment of viscosity and advancing to my treatment of the hydrodynamic scaling model and its homicides for predicting linear this but we Lester said I'm George Phillies This is the end of the lecture


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