This document is meant to encapsulate the discussion from Thursday July 9 th 2009 on the review of the paper:

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1 This doumen is mean o enapsulae he disussion from Thursday July 9 h 2009 on he review of he paper: No seady sae flows below he yield sress. A rue yield sress a las? -Møller, Fall, Bonn (ArXiv: v1 ond-ma.sof) Addiional reading (in order of helpfulness): - The yield sress myh revisied H A Barnes appearing in: Moldenaers P, Keunings R (eds) Theoreial and applied rheology. Proeedings of he XIh Inernaional Congress on Rheology, Brussels, Belgium, Augus 17-21, 1992, pp Yield sress and hixoropy: on he diffiuly of measuring yield sress in praie Møller, Mewis, Bonn Sof Maer Leer o he Edior: a rue yield sress De Kee, C.F. Chan Man Fong Journal of Rheology 37 (4) July/Augus 1993 The following repor has 7 seions: Brief Overview of Paper Remarks on Claims in he Paper Furher Thoughs on Thixoropy, Yield Sress and he Aging vs. Rejuvenaion Piure Nex Quesions on Relaing a Time Dependen Visosiy o Previous Models Can a Rheomeer Measure an Infinie Visosiy Below a Yield Sress? Pondering Dimensionless Numbers o desribe Yield Sress Fluids Remarks on Presenaion of Paper Sarah Baes (swbaes@mi.edu) July 23, 2009

2 Brief Overview of he Paper The objeive of he paper is o address wheher he yield sress is a ransiion beween a solid sae and a liquid sae or a ransiion beween a liquid sae and anoher liquid sae (as advoaed by Barnes and Walers). This disinion is made by omparing wo differen ways of presening daa and assigning a value o visosiy o inaessible shear raes. Figure 1: η = Arifa from non-seady experimens -Bonn η = Consan A figmen of exrapolaion - Barnes Graph A represens Bonn s view ha he maerial ransiions from a solid (η = ) o a liquid and Graph B represens Barnes s view ha i ransiions from a liquid (η = finie) o anoher liquid, albei dissimilar from he firs regime. The auhors presen evidene for heir solid-liquid ransiion view by repliaing Barnes s rheologial esing proool on four arbopol based maerials. They perform reep ess, where a onsan low sress is applied o he maerial and he resuling deformaion and flow is moniored over he period of he es. They argue ha hey have eliminaed many ommon arifas enounered wih esing yield sress maerials, suh as wall slip, by using a variey of differen rheomeer/geomery ombinaions. Their resuls are onsisen aross hese many ess in ha hey do find ha here is a plaeau visosiy a very low shear raes. If, however, hey vary he amoun of ime hey spend olleing his visosiy, hey find ha his plaeau visosiy inreases indefiniely wih ime. They onlude ha he Newonian visosiy plaeau is an arifa of he measuremen being olleed before he sysem reahes seady sae. The auhors hen disuss possible mirosruural reasons for his visosiy inreasing wih ime. They noe ha his behavior may have been expeed if he maerial were aging and sruuring wih ime. However, he maerials in his sudy do no fi a radiional definiion of hixoropy. The maerial does no age when a res and he flow hisory (a high shear raes) does no influene he maerial behaviour. They sugges ha he very low shear rae ould hange he balane beween forming onneions and breaking onneions by supplying enough energy o bring pariles ogeher where for rue yield sress maerials hermal fores would suffie. Wih his, hey offer an alernae definiion of he yield sress as one beween aging and rejuvenaion. 2

3 Remarks on Claims in he Paper Maerials: The auhors sugges ha he four maerials ha hey have esed are a represenaive sample of yield sress maerials. However all four of he samples are in fa all arbopol based and fall ino a small aegory of non-lassially-hixoropi yield sress maerials. While he auhors exend heir onlusions o yield sress maerials in general we migh quesion his generalizaion. The auhors also ie ha arbopol foams and emulsions are normally no onsidered as maerials ha age and herefore explain all aging seen a res as due o low-shear indued. Furher work should be done o examine his assumpion as heir measuremen proool has an unusually long duraion. For insane, hey repor elsewhere ha heir foam oarsens over a period of 8 hours from a bubble size of 12 μm o 50 μm. This ime period is on he same order of magniude as heir 3 hour reep ess. Shear banding: The auhors laim ha shear banding, or shear loalizaion, in nonhixoropi yield sress fluids happens only if here is signifian sress variaion wihin he geomery. As hey used geomeries ha have very differen sress variaion profiles he auhors sae ha shear banding is no an issue in heir resuls. Cone and Plae Vane - Cup Small Sress Variaion Large However, in ligh of heir argumen ha he fluid ages during low shear flow experimens, i may be more aurae ha shear banding does our and is due o age inhomogenieies inrinsi o he fluid. Comparison o Barnes: In he Yield Sress Myh? Revisied, Barnes does sugges suspensions ha migh be expeed o have yield sresses. These suspensions, inluding simple non-ineraing suspensions and floulaed suspension, seem similar o he senario ha Bonn presens. Barnes suggess ha we an expe a yield sress when dealing wih suspensions ha may ahieve a phase volume of pariles equaling a maximum phase volume when he pariles are densely paked. Given ha his paper is wrien o address many of Barnes s findings, i would make sense o invesigae he model suggesed by Barnes o explain he appearane of a yield sress in a floulaed suspension. Infiniely Inreasing Visosiy: The auhors sugges ha he visosiy of heir fluids will inrease exponenially ( ~ ) wih ime. They furher use heir low-shear aging explanaion o suppor heir observaion of a growing visosiy. A loser examinaion of he physial piure however, does no suppor a visosiy ha inreases wih ime wihou bounds. Wih Barnes s piure of a yield sress being a sae of maxed paking, we an imagine ha here is a ime where he pariles reah he required paking densiy. A his ime we would expe ha he visosiy plaeau should be measured as infinie. The auhors mus deide wheher he visosiy plaeau and is ime dependene, is one of measuremen error from lak of paiene or from aual sruural kineis. The piure involving kineis suggess ha a some poin he maerial does indeed reah seady sae by he limi of he number of onneions ha an be made by a finie number of pariles. 3

4 Furher houghs on Thixoropy, Yield Sress and he Aging vs. Rejuvenaion Piure The following piure seeks o apure urren relaionships beween yield sress and hixoropy voabulary. Mirosruure in Fluids Resiss Flow Indued Rearrangemens Yield Sress (No hange in sruure) No Flow Aging Flow Indued Rearrangemens Thixoropy Wih Flow Rejuvenaion (Inrease in Sruure) (Derease in Sruure) This piure however is inomplee, as Bonn poins ou ha his piure does no allow for a fluid o age in he presene of shear flow raher han a res. Bonn s fluids are he firs repored fluids ha age when under low flow bu no a res. Bonn s mirosruural piure suggess ha he yield sress is no as an inrinsi variable, bu raher depends on he naure of he volume of fluid over whih i is evaluaed. This volume of fluid is experiening a balane of proesses boh sruuring and de-sruuring he fluid. Fluids made of very small pariles, sruure a res beause of hermal fores. However for larger pariles, boh he naure of how we probe he sysem and de-sruuring proesses usually dominae. We rarely observe a fluid ha does no hange is sruure or inreases is sruure while sill being loaded. A hough experimen ha would measure his alernae definiion of a yield sress ould be ha imposing a sress whih equals he yield sress would preven sruuring in a fluid, whih a res, ages. Mirosruure in Fluids Sruuring Balane σ y γ y y y De-sruuring Faors Flow Res Sress Thermal Visosiy, Maerial Funions If maerial is sruuring Inrease in visosiy If maerial is de-sruuring Derease in visosiy By more losely relaing hixoropy and yield sress, we ould seek less onroversial definiions of boh. 4

5 Nex Quesions on Relaing a Time Dependen Visosiy o Previous Models The mirosruural piure presened by Bonn is no new. Mujumbar summarizes models ha aemp o balane he kineis of building and breaking bonds wih he expression: dn d k n a b ( ) k ( n0 n)( ) n is he number of aive bonds n 0 is he number of iniial bonds k - is he rae of sruure breakdown k + is he rae of sruure build-up is he shear rae In a previous paper Bonn presens an evoluion equaion: d 1 d n 0 (1 ) λ is a measure of he number of onneions per uni volume τ is he haraerisi ime of he build-up of he mirosruure a res η 0 is he limiing visosiy a high shear raes α, β, and n are maerial onsans Solving hese equaions for he ime evoluion of he sruure parameer we find (respeively): a b b n n0 (exp(( k k ) k 2n 0 )) e Neiher of hese ime evoluions ombined wih assoiaed visosiy models sugges a visosiy ha grows as ~. If he ime dependene in he inse graphs, really refles aging under sress and no impaiene a nex sep would be o ompare his ime prediion wih an appropriae model. Barnes s piure of flos growing and pariles jamming o progressively form larger sruures provides a seond menal es o judge wheher he visosiy growing in ime wihou bound is physially realizable. 5

6 Can a Rheomeer Measure an Infinie Visosiy below a Yield Sress? The rheomeer has boh a smalles and larges orque ha i an measure. This limis he resolvable visosiies in a given amoun of ime. If here exiss a yield sress a whih he visosiy of he fluid beomes infinie, would a rheomeer ake an infinie amoun of ime o repor his visosiy? max max min Tmax max K geomery max K geomery min min T max sienis For he AR-G2 1 : T max =200e-3Nm θ min =25e-6 rad For a ypial one and plae (R=20mm, α=2 o ): 3 Tmax 3* e 3 max 3 3 2R min 2 (20e 3) 25e 6 sienis For a ypial plae and plae (R=10mm, H=1mm): 2H Tmax 2*1e 3 200e 3 max 4 4 R min (10e 3) 25e 6 sienis Maximum Measurable (Pa.s) sienis Visosiy Inreases wih Paiene Maximum Torque sienis Cone-Plae ( R=20mm, =2 o ) Plae-Plae ( R=10mm, H=1mm ) Minimum Torque e7 * 5.1e8* sienis sienis Duraion (s) Noe ha he rheologis may hoose any orque beween he minimum and maximum limis for various reasons, suh as no waning o desroy exising mirosruure. Given ha he ime evoluion of he visosiy seems o mah a rend relaed o proool more losely han rends relaed o mirosruural models, perhaps his phenomena is indeed a measure of paiene. 1 TA Insrumens speifiaions a hp:// 6

7 Pondering Dimensionless Numbers o Desribe Yield Sress Fluids Barnes s insisene on a rigorous approah of no allowing approximaions abou he maerial behavior even if he maerial does no seem o flow on he imesale of monhs seems disonneed from engineering appliaions. Informaion on he ime sales of use and load upon he maerial is relevan o seleing an appropriae maerial. An engineer migh argue ha he onroversy surrounding he yield sress does no hange he exisene of an applied sress below whih he maerial does no appear o flow. η large η small This engineer migh wan o desribe wheher his fluid is a suiable yield sress maerial, despie he onroversial naure of he definiion of he yield sress. Wha dimensionless number migh we equip him wih o desribe how yield-sressy a fluid is? y L The Bingham Number, does no seem o apure his desire Bm V Yield _ Sress Visous _ Sress We ould inorporae variables suh as Δη, η, λ, σ y, G, G, experimen, and desired applied sress ino a differen dimensionless numbers using Bukingham PI heorem. ~ L flow applduraionh One suggesion migh be: L L L appl h is he hikness of he film σ appl is he applied sress during he experimen duraion is he duraion of an experimen or appliaion is he visosiy orresponding o he applied sress appl L is a haraerisi lengh sale appropriae for he duraion of he experimen L ~ <<1 maerial is solid-like; no observable flow on he experimenal sale L ~ ~1 observable flow on he experimenal sale L ~ >>1 maerial is fluid-like; flow dominaes experimen This number ompares he disane he maerial will flow o a haraerisi lengh of an experimen. 7

8 This number may be helpful o desribe appliaion requiremens and experimenal resuls. Appliaion Case Sudy: Adhesive Loomoion The relevan lengh sale migh be relaed o he sroke lengh of he roboi moion or he lengh of he robo. The ime would be he ime assoiaed wih he period of he sroke. Ineresingly, his number ould be useful for fluids ha are ypially no desribed as having a yield sress bu an be used as if hey are yield sress maerials for experimens ha have shor ime sales or large haraerisi lengh sales (suh as he example deailed above). Experimenal Case Sudy: Bonn s Resuls This number ould also desribe experimenal resuls. For insane, Bonn s maerial ould ~ be desribed as having L 1 for haraerisi lengh sales up o 27 mirons. By using his number o desribe boh experimenal resuls and appliaions we an have inreased onfidene ha we have piked an appropriae fluid for a given appliaion. Finally, his number an help define a yield sress maerial even in more heoreial siuaions. If L ~ approahes zero he maerial would be a rue yield sress maerial. A maerial ha ages as ~ n : n 1 as Bonn suggess would no mee his definiion; maerials ha age faser han his would. ~ appl L 0 n 1 ~ L 0 n 1 n 1 appl 0 n ~ appl h L L 0 duraion appl duraion n duraion n ~ appl h L L L h 1 h L 1n duraion applh L 1n 0 duraion 0 Can a rheomeer experimen be haraerized by a range of observable L ~? For a given maerial and duraion of experimen, L ~ is bounded by he applied sresses (T min <T<T max ). Wihin his range, he duraion of he experimen will bound L ~. As explored previously, rheomeers do have a resoluion limied by a haraerisi lengh sale. The duraion of 8

9 he experimen should herefore be a leas as long as he maerial would ake o move aross he resolvable disane. This ime is: ma required 2 applied If we use his ime in our L ~ alulaion we find: ma appl h ~ 2 applied L L ~ h L 2L ma limis how well a rheomeer an evaluae he produ L ~. For insane for an Lh appliaion where he L is 1μm and he film hikness is 100μm, he AR-G2 ould no measure L ~ smaller han 4.0e-4 (for he duraion we alulaed above). Relaionship of his number o he Deborah Number The Deborah number is defined as he raio of he relaxaion ime sale o he sale of observaion. relaxaion De observaion L ~ is a reformulaion of he Deborah Number s inverse. L applied relaxaion and observaion is duraion. h applied The definiion of L ~ aemps o speifially separae ou experimen deails ( duraion, L, h, σ applied ) from maerial properies (η), where as he De does no speifially segregae experimen from maerial. 9

10 Remarks on Presenaion of Paper This series of graphs is a lassi example of rying o fi oo many ideas ino a small area. One suggesion is o reposiion he legend so ha he legend overlaps he norh-eas orner of eah graph o eliminae he unhelpful ik marks in his area. The inse graphs should be removed and perhaps ploed separaely as neiher axis shares he same unis wih he larger graph. Boh of hese graphs illusrae he auhors poins more learly han he graph below. Here he differen sresses are praially indisinguishable from eah oher. The auhors would be wise o relabel he differen daa series direly on he graph. Also he auhors would have done well o fous more on onsan sress measuremens beween 25 and 27 Pa as ha is where he Newonian plaeau visosiy develops a ime dependene. 10