Colby, R

Laurati, M

Vlassopoulos, D

Zaccone, A

English

Florence Research

Discussion of 010405JOR by J. Kim et al.Citation: Journal of Rheology 58, 1391 (2014); doi: 10.1122/1.4892817View online: https://doi.org/10.1122/1.4892817View Table of Contents: http://sor.scitation.org/toc/jor/58/5Published by the The Society of RheologyArticles you may be interested inDiscussion of 004405JOR by M. Laurati et al.Journal of Rheology 58, 1418 (2014); 10.1122/1.4892815 Thermokinematic memory and the thixotropic elasto-viscoplasticity of waxy crude oilsJournal of Rheology 61, 427 (2017); 10.1122/1.4978259A micro-mechanical study of coarsening and rheology of colloidal gels: Cage building, cagehopping, and Smoluchowski's ratchetJournal of Rheology 58, 1121 (2014); 10.1122/1.4892115Discussion of 019405JOR by R. Zia et al.Journal of Rheology 58, 1158 (2014); 10.1122/1.4892821Linking self-assembly, rheology, and gel transition in attractive colloidsJournal of Rheology 58, 1219 (2014); 10.1122/1.4878838 Direct observation of DNA dynamics in semidilute solutions in extensional flowJournal of Rheology 61, 151 (2017); 10.1122/1.4972236Discussion of 010405JOR by J. Kim et al.Question: Alessio Zaccone: How does the proposed structural breakdown mechanismdifferentiate itself from previously proposed mechanisms based on shear-induced sever-ing of weak connections between clusters?Author Response: As discussed in Sec. IV, we propose that the dominant microstruc-tural processes accompanying yielding are:1. In the initial stages of yielding, compression of the internal structure (and correspond-ing formation of large voids) of the particle-rich domains, which appears to dominatethe nonlinear mechanical response in regions I and II. Such a process does not requirenet breakage of intercluster bonds, but merely rearrangements of same in order toform a more compact structure. This could be seen as akin to the initial stage of the“two-step” mechanisms previously proposed, such as by Koumakis and Petekidis(2011), in which local bond rearrangement occurs within clusters. However, our meas-urements establish that these rearrangements primarily occur at length scales muchlarger than individual particles, and that the internal fractal microstructure of clustersremains relatively unchanged (as evident in the SANS data for q > 0.1 A˚1) for thecase of a heterogeneous gel.2. In the final stage of yielding (which dominates in region III), the network compressionsaturates and both decorrelation (indicated by a disappearance of the low-q peak), and“depercolation” (indicated by a maximum in the homogeneity of cluster-cluster corre-lations) of cluster-cluster interactions occurs. We think this process is indeed the sameas that put forth by others—including the work by Hsiao et al. (2012)—in whichbreakage of weak intercluster bonds allows clusters to be suspended and flow, butwith an associated length scale coinciding with the phase separated structure ratherthan the local particle-particle scale.To summarize, the microstructural processes we propose here to accompany yieldingare qualitatively similar to those put forth previously by others. However, our measure-ments clearly show that, at least for the heterogeneous gels studied here, these processesare primarily occurring at much larger length scales than the local scale of particle-particle bonds that is usually depicted in these hypothesized mechanisms. This is perhapsa subtle difference, but one that we believe has significant implications for the rheologi-cal modeling of these systems near the yield point.Question: Marco Laurati: In manuscript 004405JOR of this same special issue, weshow that concentrated depletion gels formed by hard-sphere like colloidal particles donot show the pronounced in-cycle yielding observed for these samples, i.e., the stressovershoot close to strain reversal in the Lissajous figures of Fig. 9. Still we speculate thatmicrostructural processes relatively similar to the ones proposed here may characterizeyielding in our depletion gels. Could then the stronger in-cycle yielding observed for thissystem be in part associated with the larger softness of the nanoemulsion investigatedhere? This effect of the particle softness has been recently pointed out in a manuscript byKoumakis et al. (2012).VC 2014 by The Society of Rheology, Inc.J. Rheol. 58(5), 1391-1394 September/October (2014) 0148-6055/2014/58(5)/1391/4/$30.00 1391Author Response: This is certainly a possibility, although we note that even the“hard” PMMA particle system studied in the work by Koumakis and coworkers alsoexhibits a significant stress overshoot (but it is exaggerated for softer particles). For refer-ence, one might wish to compare the relative “softness” of the particles between ourwork and that of Koumakis and coworkers. The effective elastic modulus of our droplets(estimated to be equal to the Laplace pressure, c/a) is approximately 0.5 MPa. This isobviously much softer than PMMA (2–3 GPa) but is still two orders of magnitudestiffer than the elastic modulus of PNIPAM microgel particles (5–10 kPa) measured byHashmi and Dufresne (2009).It is thus unclear a priori how much deformation of the nanodroplets one would expectduring yielding. To estimate the potential amount of deformation, we calculate the capil-lary number, characterizing the magnitude of viscoelastic stress relative to the Laplacepressure, at the local stress maximum, Ca ¼ rca/c, where c is the interfacial tension ofthe two fluids. In our measurements, Ca is vanishingly small, O(107), due to the nano-scopic size of the droplets. In this limit, simple theories for droplet deformation in vis-cous flows [Maffetone and Minale (1998)] would predict for this capillary number andthe viscosities of the two liquids a relative deformation of the droplets less than 0.0001%,much smaller than the accumulated strain on the material at the yield point. Indeed, wesee no observable anisotropy in the 2D rheo-SANS patterns at high q-values that wouldindicate droplet deformation, even at the highest strain amplitudes studied. We thereforeconclude that there is no significant deformation of the droplets under conditions relevantto the initial yielding of these gels.Question: Ralph Colby: Since Fig. 1a shows an acute change in response whenchanging temperature by 1 K, can you tell us how much does the temperature of the sam-ple rise during LAOS?Author Response: For the LAOS experiments, the temperature was maintained at50.060.15 C using a circulating bath connected to the lower plate. The temperaturestability during measurement shows a small initial increase of small initial increase of0.05 C during a typical dynamic strain sweep due to the small remaining transientduring heating. We first note that this temperature is relatively deep in the gel region(Tgel  44 C for this sample), where the linear moduli are not so acutely dependent ontemperature. Using these same conditions, we found that the nonlinear viscoelasticityof the sample was highly reproducible despite any temperature fluctuations. As such,we do not believe small temperature fluctuations due to the precision of the tempera-ture control will produce significant changes in the measured rheology for theseconditions.Nevertheless, it is possible that the sample experiences temperature excursions due toviscous heating not measured by the rheometer, since the temperature is measured insidethe lower plate. To estimate the magnitude of these effects, we calculate the Brinkmannumber, which for oscillatory shear in a cone-plate geometry can be defined asBr ¼ g _c0ð ÞH2 _c20k Tw  Tfð Þ ;where _c0 is the shear rate amplitude (xc0), H is the gap height at the cone edge, k is thethermal conductivity of the fluid (assumed here to be approximately that of water), andTw and Tf are the temperatures of the wall and bulk fluid, respectively. As a worst case,we assume the thermal driving force for heat transfer, Tw – Tf, to be on the order of the1392 KIM et al.precision of the temperature control, 0.15 C. For these conditions and the ranges of shearrate amplitude and viscosity we measure, we calculate Br  O(104–102). Therefore,we assume any temperature excursions due to viscous heating are negligible.Question: Ralph Colby: You correctly point out that the slope of 1 in Fig. 8(c) indi-cates a shear stress independent of shear rate (a yield stress) but what does the steeperslope at lower shear rates in Fig. 8(c) mean?Author Response: To remind the reader, the instantaneous viscosity plotted in Fig.8(c) is not the steady shear viscosity, but rather an apparent viscosity, gL, defined at thepoint of maximum instantaneous shear rate, xc(t), in the Lissajous curve. The steeperslope at strain rate amplitudes near the onset of region II is due to the influence of thelocation of the stress overshoot relative to the point of maximum instantaneous shear rate(i.e., zero instantaneous strain) at which the instantaneous viscosity is defined. As shownin Fig. 5(c) for such strain amplitudes (dark blue curve), the instantaneous stress isactually decreasing at the point of maximum instantaneous shear rate. This is what causesthe slope in Fig. 8(c) to be greater than 1 for this portion of region II. As such, the par-ticular definition of gL we choose is ill-posed in this regime, as the gel is not yet in thefully flowing portion of the intracycle response. Therefore, gL values for strain ampli-tudes near the onset of region II should not be interpreted as “true” viscosities in the strictsense, but rather simply a relative measure of the viscous response in the process immedi-ately preceding flow.A better definition of gL would perhaps be at the instantaneous shear rate correspond-ing to the local stress minimum, which is not observed at strain amplitudes close to theonset of region II. We note that these two definitions produce approximately identicalresults for strain amplitudes deeper into region II, since the local stress minimum (onceestablished) falls nearly at the point of maximum shear rate. However, since the presentdefinition has some precedent [Ewoldt et al. (2008)], we use it so that it is comparablewith previously reported literature.Dimitris Vlassopoulos: The yielding studies in colloidal glasses and gels clearlyshow the gradual nature of the yielding process, as stated by the authors also supportedby recent simulation studies. In this respect, two-step yielding can be viewed as a genericterm pointing to more than one relevant length scales in the system. The present resultappears to fit in this framework and so one wonders to what degree the “three-stage” issystem specific or not. In other words, the gel yields gradually (starting from the largerlength scales) as shown in colloid-polymer systems.Author Response: Indeed, our results are consistent with the framework that multi-stage yielding arises in materials with hierarchical structures and dynamic processes. Inparticular, we believe our results should be general to gels and glasses with significantarrested structural heterogeneity, which in this case is homogenized before the eventualtransition to flow. However, there are still some features of the mechanical response,such as the local maximum during intracycle yielding as well as the frequency-dependence of various nonlinear measures, which may depend on the particular featuresof the system.We also emphasize that the complex rheological signatures accompanying thesehierarchical processes under LAOS deformation are best elucidated through intra-cycle analysis of the full nonlinear response, which shows distinct transitionsbetween different stages of yielding, as opposed to intercycle analysis of linearized1393DISCUSSION OF 010405JORmoduli, in which these transitions appear more gradual due to averaging of the intra-cycle response.Dimitris Vlassopoulos: In addition, one wonders whether the “sequence of physicalprocesses” methodology (which was proposed in the context of dense nearly nonthixo-tropic systems) is valid for systems such as the present gel, which is thixotropic andhence often the structural time scale exceeds the period of a cycle. In that case, the con-cept of the above sequence is violated.Author Response: There is certainly thixotropy in the system. However, as we dis-cuss in Sec. III C, the thixotropy observed in the Lissajous curves occurs over time scalesfar longer than a single cycle (as is evident in Fig. 4). Therefore, our LAOS measure-ments can be approximated as probing a quasistatic state of the system at the beginningof the thixotropic response. As such, we believe that the SPP approach (i.e., the calcula-tion and interpretation of the instantaneous moduli R0 and R00 and nonlinear measures cal-culated there from) is valid in the sense that the processes so identified are fast processesthat relax within one cycle and are much faster than the underlying thixotropy.We do caution, however, that the analogy between the intracycle response in LAOSand steady shear responses that held for other systems, such as reported by Rogers et al.(2011b), is certainly violated in the present system for exactly the reasons you point out.A more comprehensive characterization of the thixotropic would thus require detailedmeasurements under startup of steady shear, which we leave for future studies.ReferencesEwoldt, R. H., A. E. Hosoi, and G. H. McKinley, “New measures for characterizing nonlinear viscoelasticity inlarge amplitude oscillatory shear,” J. Rheol. 52, 1427–1458 (2008).Hashmi, S. M., and E. R. Dufresne, “Mechanical properties of individual microgel particles through the deswel-ling transition,” Soft Matter 5, 3682–3688 (2009).Hsiao, L. C., R. S. Newman, S. C. Glotzer, and M. J. Solomon, ‘‘Role of isostaticity and load-bearing micro-structure in the elasticity of yielded colloidal gels,’’ PNAS 109(40), 16029–16034 (2012).Koumakis, N., and G. Petekidis, “Two step yielding in attractive colloids: transition from gels to attractiveglasses,” Soft Matter 7(6), 2456–2470 (2011).Koumakis, N., A. Pamvouxoglou, A. S. Poulos, and G. Petekidis, “Direct comparison of the rheology of modelhard and soft particle glasses,” Soft Matter 8, 4271–4284 (2012).Maffetone, P. L., and M. Minale, “Equation of change for ellipsoidal drops in viscous flow,” J. Non-NewtonianFluid Mech. 78, 227–241 (1998).Rogers, S. A., B. M. Erwin, D. Vlassopoulos, and M. Cloitre, “A sequence of physical processes determinedand quantified in LAOS: Application to a yield stress fluid,” J. Rheol. 55, 435–458 (2011).1394 KIM et al.

Discussion of 010405JOR by J. Kim et al

https://flore.unifi.it/bitstream/2158/1175608/1/JOR_Discussion_1.4892817.pdf

Discussion of 010405JOR by J. Kim et al

Abstract

Similar works

Full text

Available Versions

Florence Research