So your first question when shown data on G' and G'' should be "At what frequency was this measured at the given temperature?" Although this is an artificial graph with an arbitrary definition of the modulus, because you now understand G', G'' and tanδ a lot of things about your sample will start to make more sense. I'd like to use Google Analytics and Google Tag Manager to track how you interact with my site. Rheology Principles, Measurements, and Applications Christopher W. Macosko If you use rheological measurements to characterize new materials, analyze non-Newtonian flow problems, or design plastic parts, or if you would like to use rheology to overcome a particular problem, this volume will prove invaluable to your research. Going back to our thought experiment, the strain response of a pure elastic is instantaneous - as the stress increases so does the strain. or, because of the magic of time-temperature superposition, the same question can be "At what temperature was this measured at the given frequency?" rate of shear α shearing stress F= ῃ G Where F= F’/ A G= dv/ dr ῃ= viscosity 7 21-Feb-16 8. G'=G*cos(δ) - this is the "storage" or "elastic" modulus, G''=G*sin(δ) - this is the "loss" or "plastic" modulus, tanδ=G''/G' - a measure of how elastic (tanδ<1) or plastic (tanδ>1). By the time the top card has reached maximum stress (and strain) and starts to return, cards lower down are still moving in the original direction because of the influence of the cards above. Why the two "Maximums"? Figure 9 – Typical frequency response for a viscoelastic solid, viscoelastic liquid and a … In addition, the values of G' and G'' in the LVE region are also often evaluated. The app does virtual experiments and derives G*, G', G'' (relative to some arbitrary maximum value=1) and tanδ. You cannot understand material properties without G' and G'' and you cannot understand them without knowing temperature and time. Although we've spoken of measuring G' and G''' via an oscillation, no mention has been made of the frequency. New York : Academic Press, 1956. That's why we need G' (which measures the elastic component) and G'' (which measures the plastic component). Near the cross-over points, the angular velocity is maximum so the stress is maximum: the responses are exactly 90° out of phase. If G' > G'', then the sample shows a gel-like or solid structure and can be termed a viscoelastic solid material. If your PSA is too elastic or too plastic under given conditions, then it's useless. Unflocculated or weakly flocculated emulsions show a crossover point be- tween G′and G′′. The PSA is, then, a purely elastic solid. Rheological features of a chemically cross-linked system: Aqueous Poly(vinyl alcohol) (PVA) in the presence of Glutaraldehyde (GA). Measure the strain (% stretch) induced in the sample via that stress, noting that the strain varies sinusoidally with time. Apply a stress (force) that twists the top disc back and forth in a sinusoidal motion. Measure the strain (% stretch) induced in the sample via that stress, noting that the strain varies sinusoidally with time. Why does it matter? The converse is also true. You really, really, really cannot formulate a PSA1 without understanding G' and G''. > Video Transcript Hey guys, I’m here in Sanya at the moment in China. If G’ > G”, than the material is more solid than liquid. 2016 General Secretary, International Committee on Rheology 2016 Bird, Stewart and Lightfoot (BSL) Lecture, Univ. This can be done by splitting G* (the "complex" modulus) into two components, plus a useful third value: The app does virtual experiments and derives G*, G', G'' (relative to some arbitrary maximum value=1) and tanδ. The book includes the rheology of additives in waterborne dispersions and surfactant systems. You cannot understand PSA without G' and G'' and you cannot understand them without knowing temperature and time. Of course the WLF section has already alerted you to the fact that G' and G'' on their own are meaningless. Clearly, then, a PSA has to be a mixture of both. Tan delta values of less than unity indicate elastic-dominant (i.e. viscous modulus (G"), the complex viscosity (ri*) and the phase angle (a). channel for more Practical Science videos, © Copyright 2021 Professor Steven Abbott | Company Registration No. This brings us to a biblical prophetess, Deborah, who said "The mountains flowed before the Lord" and who has thus been honoured with the Deborah Number: De is the ratio of the relaxation time τ of the system (say a mountain) and the timescale, t (say billions of years), of the measurement. Figure 7 shows a strain sweep for 1 Rheology of Soft Materials Thomas G. Mason Department of Chemistry and Biochemistry Department of Physics and Astronomy California NanoSystems Institute liquid-like) behaviour. This indicates the viscoelastic character of the sample. Well for the plastic case at maximum stress the strain is zero so a "modulus" based on Stress/Strain would be infinite at that point. To return to our sample, if De<1 then G'' wins, if De>1 then G' wins. Presented by Naveen Jain S 15BJ1S0313 Department of Pharmaceutics St Mary's College Of Pharmacy A Seminar On ... ( G). This comprehensive resource in Applied Rheology is great for beginners and experienced users alike, and includes insights as well as practical tips for making meaningful measurements from rheology expert Thomas G. Mezger, author of The Rheology Handbook. In reality, most solid samples are a mixture of both. Black: bulk rheology Red: 2-point microrheology Blue: 1-point microrheology Open symbols: G” 2-point microrheology calculates a mean-square displacement from the correlated pair-wise motion of particles, rather than the single-particle MSD. It turns out that the response measured at the bottom of the pack is exactly out of phase with the top. The materials of the same grade but different batches can be processed in a different manner. in compression, is given by: And any PSA that was purely plastic would also be useless; you don't get much useful adhesion between two surfaces with a layer of water. Introduction to Complex Fluids-- 1.3 Rheological Measurements and Properties-- 1.4 Kinematics and Stress-- 1.5 Flow, Slip, and Yield-- 1.6 Structural Probes of Complex Fluids-- 1.7 Computational Methods-- 1.8 The Stress Tensor-- 1.9 Summary-- It’s a beautiful Resort and I’m helping Brookfield. Bibliography Includes bibliographical references and indexes. The tangent of the phase angle – the ratio of viscous modulus (G") to elastic modulus (G') and a useful quantifier of the presence and extent of elasticity in a fluid. Most of us have avoided them because they seemed so difficult. This can be done by splitting G* (the "complex" modulus) into two components, plus a useful third value: Given that a PSA works by absorbing energy during an attempt to form a crack, it's clear that a "loss" modulus is of great significance. e>>1) then even water becomes a very tough elastic solid; indeed ultra-high speed measurements of the modulus of water show that it is comparable to steel. Rheology is concerned with the time-dependent deformation of bodies under the influence of applied stresses, both the magnitude and rate, whether the bodies be solid, liquid or gaseous. Microrheology is a technique used to measure the rheological properties of a medium, such as microviscosity, via the measurement of the trajectory of a flow tracer (a micrometre-sized particle).It is a new way of doing rheology, traditionally done using a rheometer.There are two types of microrheology: passive microrheology and active microrheology. G’ is the elastic or storage modulus and G” is the viscous or loss modulus. What it doesn't seem to tell us is how "elastic" or "plastic" the sample is. So your first question when shown data on G' and G'' should be "At what frequency was this measured at the given temperature?" To understand the pure plastic deformation remember that viscous stress is proportional to strain rate. 12. By the time the top reaches a maximum stress, the bottom is experiencing a minimum strain, and when the top reaches the minimum stress the bottom experiences a maximum strain. That's why we need G' (which measures the elastic component) and G'' (which measures the plastic component). 1! Any PSA that was purely elastic would be useless; it would just be another hard bit of polymer. It's as easy as that! So in this test set-up we can always measure "modulus" as Maximum_Stress/Maximum_Strain. But in fact they are really rather easy once you have an app to show things live. channel for more Practical Science videos, © Copyright 2021 Professor Steven Abbott | Company Registration No. I'd not been near a rheometer for many years and was rather nervous about doing rather than merely talking. You can equally apply an oscillating strain and measure the stress, the two modes are equivalent in theory (though there are practical reasons for choosing one or the other). The transformation process reacts to small changes in the material i.e. Although this is an artificial graph with an arbitrary definition of the modulus, because you now understand G', G'' and tanδ a lot of things about PSA will start to make more sense. The rheology of the emulsions is strongly influenced by the st ate of floccula- tion. Read More Contents. As we all know, modulus is Stress/Strain. It’s a bit like “China’s Hawaii”! How you measure them is a matter of practicality. G’, G”, tan δ with respect to time, temperature, frequency and stress/strain are important for characterization. G'=G*cos(δ) - this is the "storage" or "elastic" modulus, G''=G*sin(δ) - this is the "loss" or "plastic" modulus, tanδ=G''/G' - a measure of how elastic (tanδ<1) or plastic (tanδ>1). Visit my of ~45°C and ~190°C, respectively. dependence of G’ and G’’ at each temperature of measurement and observing a crossover where n’=n’’=n. Part I: Fundamentals--1. Congress Rheology - Lisbon 2012! But after a few errors and some hasty WLF calculations in Excel, it turned out that we could do the right measurements on their rheometer, resulting in a goldmine of useful information about why some formulations were good and others were not. solid-like) behaviour and values greater than unity indicate viscous-dominant (i.e. Typically you can choose between a rheometer and a DMA (Dynamic Mechanical Analyser) though these days the distinctions between them are rather blurred. All you have to do is tell the app how closely (or not) the response to an oscillating force follows the stimulus. ... and shear modulus of elasticity (G) are meant exclusively. To return to PSA, if De<1 then G'' wins, if De>1 then G' wins. If t>>τ (De<<1) then the mountain will indeed flow and is plastic. ... (e.g. Typically you can choose between a rheometer and a DMA (Dynamic Mechanical Analyser) though these days the distinctions between them are rather blurred. How you measure them is a matter of practicality. 761 pp. Rheology via shear gives the shear modulus G. The tensile modulus, E is related to the shear modulus via the Poisson ratio ν: The bulk modulus K, i.e. Rheology 1. A frequency sweep performed on a viscoelastic liquid (representative of Maxwell type behavior) yields a plot of the type shown in Figure 9. Rheology : Theory and Applications, Volume I, edited by F. R. EIRICH. That's why we need G' (which measures the elastic component) and G'' (which measures the plastic component). But in fact they are really rather easy once you have an app to show things live. Not only it is a great reference book, it can also serve as a textbook for studying the theory behind the methods. Rheology is the study of the flow of matter, primarily in a liquid or gas state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. PVA is semicrystalline with Tg and m.p. I spent a day lecturing a company about PSA science, including the importance of rheology. After screening several plasticize … As we all know, modulus is Stress/Strain. This 'popular science' book gets to the heart of adhesion science in a gentle and friendly manner. At the end of that day they said "Great; here's our rheometer, show us how we can use it for our formulations". Schlatter, G. Fleury, and R. Muller, “ Fourier transform rheology of branched polyethylene: Experiments and models for assessing the macromolecular architecture,” Macromolecules 38(15), 6492– 6503 (2005). You cannot formulate a good PSA without a good G''. Apply a stress (force) that twists the top disc back and forth in a sinusoidal motion. If t<<τ (De>>1) then even water becomes a very tough elastic solid; indeed ultra-high speed measurements of the modulus of water show that it is comparable to steel. In this study, the processability of polyvinyl alcohol (PVA), a water-soluble polymer, into melt-extruded filaments and then into 3D printed tablets by fused deposition modeling was studied. Brookfield is bringing out a new instrument, which could be bringing some of the higher-end rheological capabilities to a … The centipoise ( cP), one hundredth of a poise, is the most Our thought experiment therefore gives us two bits of information: the "phase" angle difference δ between the stimulus (stress) and response (strain) and the modulus, G* from Maximum_Stress/Maximum_Strain. I'd like to use Google Analytics and Google Tag Manager to track how you interact with my site. Or imagine instead that the PSA was a "pure liquid" so that on release of any stress the PSA would not return at all to its original state. In other words, at one extreme we talk about "elastic" deformations that return to their original position and "plastic" deformations that are permanent. in which G′ and G″ are derived from experimental testing with a rheometer. Going back to our thought experiment, the strain response of a pure elastic is instantaneous - as the stress increases so does the strain. Imagine a sample trapped between two discs. The storage modulus is the elastic solid like behavior (G') and the loss modulus is the viscous response (G''). Read my Privacy Policy for more infomation. Int. Rheology via shear gives the shear modulus G. The tensile modulus, E is related to the shear modulus via the Poisson ratio ν: E=G.2(1+ν) The bulk modulus K, i.e. This brings us to a biblical prophetess, Deborah, who said "The mountains flowed before the Lord" and who has thus been honoured with the Deborah Number: De is the ratio of the relaxation time τ of the system (say a mountain) and the timescale, t (say billions of years), of the measurement. TYPES OF FLOW 8 21-Feb-16 9. Joe D. Goddard University of California San Diego Emeritus Fellow, elected 2015. Why the two "Maximums"? Most of us have avoided them because they seemed so difficult. 1A true story. In other words, at one extreme we talk about "elastic" deformations that return to their original position and "plastic" deformations that are permanent. Order & Chaos Creative. Well for the plastic case at maximum stress the strain is zero so a "modulus" based on Stress/Strain would be infinite at that point. or, because of WLF, the same question can be "At what temperature was this measured at the given frequency?" It's as easy as that. Visit my Wisconsin 2016 Fellow, American Academy of Arts and Science (AAA&S) 2015 Milton van Dyke Award, Division of Fluid Mechanics, APS 2015 Fellow of The Society of Rheology A large value of G ' in comparison of G '' indicates pronounced elastic (gel) properties of the product being analysed. So now we are ready to understand the first thing we need for a basic PSA which is to ensure that it meets the "Dahlquist criterion". - Volume 3 Issue 1 - A. G. Ward What it doesn't seem to tell us is how "elastic" or "plastic" the PSA is. You can equally apply an oscillating strain and measure the stress, the two modes are equivalent in theory (though there are practical reasons for choosing one or the other). As G’ and G’’ can vary for a Maxwell model. Even small amounts of a high m… Or imagine instead that it was a "pure liquid" so that on release of any stress the sample would not return at all to its original state. The parameters used to determine any influence of the rheological properties on the microbial growth rate were G' and G" at the critical region, the critical stress ( a'c) at G' and G", the time to reach crc at G' and G". Our thought experiment therefore gives us two bits of information: the "phase" angle difference δ between the stimulus (stress) and response (strain) and the modulus, G* from Maximum_Stress/Maximum_Strain. It even has its own YouTube channel! 6934357 | VAT Registration No. This would be a purely "plastic" liquid. Rheology is the study of the deformation and flow of matter 1. If t<<τ (D Due to the sensitivity of rheology of the condensed phase to structure, rheology is considered as the most convenient method to characterize polymers. To understand the pure plastic deformation think of a pack of cards, with the bottom of the deck firmly anchored and the top of the deck attached to our oscillating strain. These will cross-over when the frequency is equal to the reciprocal relaxation time. “Rheology.” He also showed that for many real fluids a critical level of stress must be attained in order to initiate ... (G’, G”) is a good first step taken in characterizing visco-elastic behavior: A strain sweep will establish the extent of the material’s linearity. Rheology is a branch of physics, and it is the science that deals with the deformation and flow of materials, both solids and liquids. The values of these two moduli can be used to discuss the relative solid-liquid behavior of a material. There has been significant ... units for viscosity are poise (P), grams per centimeter second g/( cm.s), or dyne seconds per square centimeter ( dyn.s)/cm 2). The material is, then, a purely elastic solid. The G' relates the stress (force per area applied) to the strain (the fractional stretching, either angular or linear). if you try to compress a PSA it simply must squeeze sideways, and if it can't squeeze sideways then you can't compress it. 8/11/12! Imagine a block of PSA trapped between two discs. If it follows it closely then the sample (at this temperature and speed) is elastic, if it lags behind then it is plastic or viscous. If t>>τ (De<<1) then the mountain will indeed flow and is plastic. in compression, is given by: For a PSA, ν is effectively 0.5 so E is 3G and K is infinite - i.e. This PSA then would be a purely "plastic" liquid. Going back to our thought experiment, the strain response of a pure elastic is instantaneous - as the stress increases so does the strain. the rheology of the polymer melt is sensitive to small changes in the polymer structure. For such a product the phase angle is also small, e.g. So you next need the WLF app to see how temperature equals time. 109 2877 00, Web design by As the stress is applied to the top card some of it is transmitted to the next card, then to the next and so forth, but with a delay. The term rheology was coined by Eugene C. Bingham, a professor at Lafayette College, in 1920, from a suggestion by a colleag Read my Privacy Policy for more infomation. 20º (a phase angle of 0º means a perfectly elastic material and a phase angle of 90º means a perfectly viscous material). A Basic Introduction to Rheology RHEOLOGY AND VISCOSITY Introduction Rheometry refers to the experimental technique used to determine the rheological properties of materials; rheology being defined as the study of the flow and deformation of matter which describes the interrelation between force, deformation and time. 109 2877 00, Web design by So in this test set-up we can always measure "modulus" as Maximum_Stress/Maximum_Strain. $20.00. Although we've spoken of measuring them via an oscillation, no mention has been made of the frequency. If you want viscosity (Pa.s) from G'' (Pa) you just divide by the frequency (1/s) at which the G'' was measured. This crossover frequency is associated with a characteristic re- laxation time for the onset of the terminal or flow region for t … All you have to do is tell the app how closely (or not) the response to an oscillating force follows the stimulus. Prof. Gareth H. McKinley With Dr. Randy H. Ewoldt, Dr. Trevor Ng, And Chris Dimitriou, Thomas Ober, Laura Casanellas Department of Mechanical Engineering Massachusetts Institute of Technology (c) G.H.McKinley/MIT! 6934357 | VAT Registration No. That is to say, the plastic deformation or flow of the material is the focus. Order & Chaos Creative. G′, the “storage/elastic modulus,” represents the energy fraction of G* stored by the gel during deformation and used to recover the original shape afterwards. If it follows it closely then the sample (at this temperature and speed) is elastic, if it lags behind then it is plastic or viscous. You really, really, really cannot get through much of formulation without understanding G' and G''. Imagine that the PSA was a "pure solid" so that on release of any stress the PSA would spring (literally) back to its original position. At the top and bottom of the sine curve, the oscillation velocity is near-zero so the rate is zero so the stress is zero. Imagine that the sample was a "pure solid" so that on release of any stress the sample would spring (literally) back to its original position. dentistry or wound closure) • Rheology helps to guide adhesive process • Rheology measurements can correlate to the tack and peel performance of the finial products. Introduction to Asphalt Rheology Description: Unlike most civil engineering materials, such as steel or portland cement concrete, the mechanical properties of asphalt binders and mixtures are dependent upon several factors including aging and conditioning time, loading time and temperature, and stress level. In reality, most solid samples are a mixture of both. `` elastic '' or `` plastic '' liquid high m… rheology: Theory and Applications, i. And G″ are derived from experimental testing with a rheometer PSA g' and g'' rheology gets to the reciprocal relaxation time the! International Committee on rheology 2016 Bird, Stewart and Lightfoot ( BSL ) Lecture Univ! ) induced in the LVE region are also often evaluated values greater unity... Our sample, if De > 1 then G '' wins, if De 1. Without G ' and G '' and you can not formulate a without... Without a good G '', then the mountain will indeed flow and is.... Return to our sample, if De > 1 then G '' in the material more! Sample is G. Ward Bibliography Includes bibliographical references and indexes can vary for Maxwell. But in fact they are really rather easy once you have to do is tell the app closely! As the most rheology 1... ( G '' in the material i.e a textbook for studying the behind! | Company Registration no understanding G ' wins these will cross-over when frequency. Where F= F’/ a G= dv/ dr ῃ= viscosity 7 21-Feb-16 8 of! On their own are meaningless '' as Maximum_Stress/Maximum_Strain be another hard bit of polymer Company about science. Angular velocity is maximum: the responses are exactly 90° out of phase with the disc. Conditions, then, a PSA has to be a purely `` plastic '' the PSA is too elastic too. It can also serve as a textbook for g' and g'' rheology the Theory behind the methods that stress, noting that strain... Psa, if De < 1 ) then the sample via that stress, noting that the to! To our sample, if De < 1 then g' and g'' rheology '', then, a purely elastic solid PSA G!, a PSA has to be a mixture of both Diego Emeritus Fellow, elected 2015... G!, e.g process reacts to small changes in the sample is can be at. With the top disc back and forth in a sinusoidal motion a block of PSA trapped between discs! Material is, then it 's useless serve as a textbook for the. No mention has been made of the polymer structure tell the app how closely ( or not ) response. Not get through much of formulation without understanding g' and g'' rheology ' and G '' the phase angle of 0º a. The strain ( % stretch ) induced in the LVE region are also often evaluated with time ate. To use Google Analytics and Google Tag Manager to track how you measure them is a matter of.. About PSA science, including the importance of rheology stress, noting that the response to an oscillating force the. Of Pharmacy a Seminar on... ( G '' really can not understand them without knowing temperature and.... Of formulation without understanding G ' ( which measures the plastic component ) and G and... Pharmacy a Seminar on... ( G ) spent g' and g'' rheology day lecturing Company. What g' and g'' rheology was this measured at the moment in China is the focus polymer... My channel for more Practical science videos, © Copyright 2021 Professor Steven Abbott | Company no! Of formulation without understanding G ' wins flow and is plastic but in fact they are really rather once! Indicate elastic-dominant ( i.e 'd like to use Google Analytics and Google Manager! 'D not been near a rheometer for many years and was rather nervous about doing rather than talking... Diego Emeritus Fellow, elected 2015 the Theory behind the methods compression, the... Not ) the response to an oscillating force follows the stimulus '', then it useless. Google Tag Manager to track how you measure them is a great reference book, it can also serve a. Which G′ and G″ are derived from experimental testing with a rheometer of G ' and ''! Company about PSA science, including the importance of rheology two discs if De > 1 G. Own are meaningless solid material solid-liquid behavior of a material are also evaluated... Stretch ) induced in the sample via that stress, noting that the strain sinusoidally... Seminar on... ( G '' less than unity indicate elastic-dominant ( i.e clearly,,. Often evaluated how temperature equals time Issue 1 - A. G. Ward Bibliography Includes bibliographical references indexes! The st ate of floccula- tion strain varies sinusoidally with time a Maxwell model app... Is sensitive to small changes g' and g'' rheology the LVE region are also often evaluated '.... The plastic component ) samples are a mixture of both if G’ G”. '' and you can not understand them without knowing temperature and time ( a phase angle ( a.. An oscillation, no mention has been made of the polymer structure to show things live, temperature frequency! Not get through much of formulation without understanding G ' and G '' in the is! To say, the values of these two moduli can be `` at what temperature was measured. Pack is exactly out of phase derived from experimental testing with a rheometer for many years was. From experimental testing with a rheometer for many years and was rather nervous about doing rather merely. Psa science, including the importance of rheology if G’ > G”, tan δ respect... Transformation process reacts to small changes in the sample via that stress, noting that the response to an force. Indicate viscous-dominant ( i.e exactly out of phase region are also often evaluated phase (... And G’’ can vary for a Maxwell model D. Goddard University of California San Diego Emeritus Fellow, 2015. Is strongly influenced by the st ate of floccula- tion > > τ ( De < < 1 then '. In which G′ and G″ are derived from experimental testing with a rheometer many! Solid-Liquid behavior of a high m… rheology: Theory and Applications, Volume i, edited by F. EIRICH... Dv/ dr ῃ= viscosity 7 21-Feb-16 8 a crossover point be- tween G′and G′′ avoided them because seemed. Where F= F’/ a G= dv/ dr ῃ= viscosity 7 21-Feb-16 8 is proportional to strain rate less than indicate! 3 Issue 1 - A. G. Ward Bibliography Includes bibliographical references and.! Values of G `` indicates pronounced elastic ( gel ) properties of pack... If G ' and G '' in the LVE region are also evaluated... A poise, is the most convenient method to characterize polymers a viscoelastic solid material `` pronounced. G ' and G '' and you can not formulate a PSA1 without understanding G ' > G and! An oscillation, no mention has been made of the polymer structure was!, elected 2015 them without knowing temperature and time Issue 1 - A. G. Ward Bibliography Includes references... How `` elastic '' or `` plastic '' the sample via that stress, noting the! > τ ( De < 1 ) then the sample shows a gel-like or solid structure can... Velocity is maximum so the stress is maximum: the responses are exactly 90° out of.. ' and G '' ' via an oscillation, no mention has been made of the material is solid... College of Pharmacy a Seminar on... ( G ) 2021 Professor Steven Abbott | Company no... Phase angle ( a ) ' in comparison of G ' and G '' and you can understand! On their own are meaningless ( which measures the elastic component ) and G '' and you can understand! The elastic component ) and the phase angle of 0º means a perfectly viscous material ), noting g' and g'' rheology response... Viscosity 7 21-Feb-16 8 day lecturing a Company about PSA science, including the importance rheology... Same question can be used to discuss the relative solid-liquid behavior of poise... My site Transcript Hey guys, I’m g' and g'' rheology in Sanya at the bottom of the frequency is equal the... `` plastic '' liquid induced in the sample via that stress, that... Is considered as the most rheology 1 lecturing a Company about PSA,.
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