Rebecca E. Hudson-Kershaw , Mohua Das , Gareth H. McKinley , Daniel J. Curtis
{"title":"σOWCh: Optimally Windowed Chirp rheometry using combined motor transducer/single head rheometers","authors":"Rebecca E. Hudson-Kershaw , Mohua Das , Gareth H. McKinley , Daniel J. Curtis","doi":"10.1016/j.jnnfm.2024.105307","DOIUrl":"10.1016/j.jnnfm.2024.105307","url":null,"abstract":"<div><p>Recent advances in rheometry exploiting frequency-modulated (chirp) waveforms have dramatically reduced the time required to perform linear viscoelastic characterisation of complex materials. However, the technique was optimised for ‘separate motor transducer’ instruments, in which the drive motor imposing the strain deformation is decoupled from the torque transducer. Whilst the use of optimised windowed chirps (OWCh) using other rheometers has been recently reported in the literature, no systematic study concerning the use of ‘combined motor transducer’ instruments (in which the motor and transducer subsystems are integrated into a single ‘head’) has been undertaken. In the present study, we demonstrate the use of OWCh rheometry using combined motor transducer/single-head rheometers using a stress-controlled operating principle, thus avoiding the reliance on complicated and instrument-specific feedback control systems that would be required to perform strain-controlled experiments. The use of stress-controlled chirps requires a modification to the established OWCh analysis protocol such that the complex viscosity <span><math><mrow><msup><mrow><mi>η</mi></mrow><mrow><mo>∗</mo></mrow></msup><mrow><mo>(</mo><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> is used as an intermediate proxy function for ultimately computing the complex modulus <span><math><mrow><msup><mrow><mi>G</mi></mrow><mrow><mo>∗</mo></mrow></msup><mrow><mo>(</mo><mi>ω</mi><mo>)</mo></mrow></mrow></math></span>. This approach negates the effect of the strain offset that is inherent to stress-controlled oscillatory rheometry. Secondly, a correction algorithm and operational criteria for identifying inertial artefacts is established before we consider the impact of chirp digitisation on data acquisition. The use of stress-controlled OWCh rheometry (which we term Stress-OWCh, i.e. <span><math><mi>σ</mi></math></span>OWCh) is demonstrated for a diverse range of material classes including, Newtonian calibration fluids (silicone oil), polymer solutions (polyethylene oxide in water), an entangled polymer melt (polydimethylsiloxane), worm-like micellar systems (cetylpyridinium chloride/sodium salicylate), time-evolving critical gels (gelatin) and aging elastoviscoplastic materials (Laponite®). This novel implementation of chirp waveforms using a single-head rheometer will facilitate the wider adoption of OWCh rheometry and allow the benefits of frequency-modulation techniques to be exploited where separate motor transducer instruments are unavailable/unsuitable.</p></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"333 ","pages":"Article 105307"},"PeriodicalIF":2.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S037702572400123X/pdfft?md5=8699673a8af80917a3a3c894395db0a9&pid=1-s2.0-S037702572400123X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Oscillatory one-roll and two-roll solutions in laminar viscoelastic Rayleigh-Bénard convection in a square cavity","authors":"Govind Maurya, Suneet Singh, Lalit Kumar","doi":"10.1016/j.jnnfm.2024.105308","DOIUrl":"10.1016/j.jnnfm.2024.105308","url":null,"abstract":"<div><p>Rayleigh-Bénard convection in square closed cavities filled with Oldroyd-B fluid was studied using OpenFOAM-based RheoTool. For the RBC in Newtonian fluids, the transition always occurs from conduction to steady state convection with increasing Rayleigh number (<em>Ra</em>). On the other hand, the viscoelastic fluids may also show the transition from conduction to oscillatory convection. Further increase in <em>Ra</em> may result in a steady state convective solutions. It is further noted that the behavior is similar to Newtonian fluids for larger values of viscosity ratio (<em>B</em>). Considering the abovementioned different flow behavior at different values of the parameters, it is noted that there are five different types of solutions possible for the viscoelastic fluids viz. pure conduction (PC), one roll periodic oscillations (ORPO), one roll steady state (ORSS) convection, two roll periodic oscillations (TRPO), simultaneous one and two roll steady state convection. Therefore, a bifurcation diagram in the parametric space of <em>Ra</em> and <em>B</em> is presented, depicting these five regions corresponding to each type of solution. The boundaries of these regions have been identified by numerical simulation. Note that all these regions exist in the laminar flow regime, and the transition to turbulence is not considered here. Interestingly, at low values of <em>B</em>, as one increases <em>Ra</em>, it is seen that the ORSS region is sandwiched between ORPO and TRPO. The likely reason for this interesting behavior is explained. Moreover, representative solutions in each region in terms of isotherms, streamlines, and vector plots have been included to demonstrate the dynamics of each delineated region.</p></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"332 ","pages":"Article 105308"},"PeriodicalIF":2.7,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wenming Yang , Yifan Li , Jiantuo Ren , Xiaolong Yang
{"title":"Non-Newtonian behaviors of ferrofluid Couette–Poiseuille flows in time-varying magnetic fields","authors":"Wenming Yang , Yifan Li , Jiantuo Ren , Xiaolong Yang","doi":"10.1016/j.jnnfm.2024.105306","DOIUrl":"10.1016/j.jnnfm.2024.105306","url":null,"abstract":"<div><p>We analyze the fully developed Couette–Poiseuille flows of ferrofluids between two parallel flat walls subject to three types of time-varying magnetic fields. In these scenarios, ferrofluids exhibit diverse non-Newtonian characteristics such as distinct flow velocity distribution, apparent viscosity and shear stress compared to ordinary Couette–Poiseuille flows. The influence of spin viscosity is explored first through the solution of the governing equations with zero and non-zero spin viscosities. It shows that although the value of the spin viscosity is very small, its inviscid limit would have great influence over the velocity and spin velocity distributions. The assumption of zero spin viscosity leads to an exaggerated non-Newtonian behavior induced by time-varying magnetic fields in the ferrofluid Couette–Poiseuille flows. Then the solutions of equations with non-zero spin viscosity are utilized to delve into non-Newtonian behaviors of ferrofluid Couette–Poiseuille flow under the application of the three time-varying magnetic fields. The results indicate that negative rotational viscosity will occur if the dimensionless frequency lies in the range 1–10, which is a distinguishing feature compared with Newtonian flows. At this point, non-Newtonian flow induced by magnetic field arises, although this effect is very tiny. Within the same frequency range, reversed tangential stress appears in strong uniform alternating magnetic fields. The minimum negative rotational viscosity may arrive at up to 20 % of the intrinsic viscosity in the rotating magnetic field when the magnetization relaxation time is 4 ms.</p></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"332 ","pages":"Article 105306"},"PeriodicalIF":2.7,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142095341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Preface to Special Visual Issue: E Mitsoulis","authors":"Yannis E. Dimakopoulos , Georgios C. Georgiou","doi":"10.1016/j.jnnfm.2024.105297","DOIUrl":"10.1016/j.jnnfm.2024.105297","url":null,"abstract":"","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"331 ","pages":"Article 105297"},"PeriodicalIF":2.7,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141993115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Victor C. Ibezim , David J.C. Dennis , Robert J. Poole
{"title":"Micro-PIV of viscoelastic fluid flow in microporous media","authors":"Victor C. Ibezim , David J.C. Dennis , Robert J. Poole","doi":"10.1016/j.jnnfm.2024.105295","DOIUrl":"10.1016/j.jnnfm.2024.105295","url":null,"abstract":"<div><p>The present experimental investigation combines the bulk flow properties of polymer solutions and measurable rheological parameters as they flow through a distinctive micro-porous structure, with micro-PIV (micro-particle image velocimetry) to measure the velocity distribution and velocity fluctuations within individual pores of a novel porous glass structure. To investigate the effects of fluid elasticity at pore scale, aqueous solutions of a polyacrylamide (PAA) & polyethylene oxide (PEO) in the concentration range of 50–200 ppm, which were characterized in both shear and extensional flows using shear and capillary break-up extensional rheometers (CaBER) respectively, were used as working fluids. The velocity field measurement includes the velocity magnitude and fluctuation intensity in several different pores within the porous material across a Weissenberg number <span><math><mrow><mi>W</mi><mi>i</mi></mrow></math></span> range of approximately 0.01 to 1 for each of the test fluids. The global averaged fluctuation intensity increases with <span><math><mrow><mi>W</mi><mi>i</mi></mrow></math></span> but the critical value, which indicates the onset of significant unsteadiness (i.e. well above noise floor/Newtonian baseline) within the flow at pore scale gives an approximately constant value of <span><math><mrow><mi>W</mi><mi>i</mi><mo>≈</mo></mrow></math></span>0.4, which is almost 40 times higher than the value that is observed in the pressure-drop measurements for the data to rise above the Newtonian base line. We therefore postulate that the enhanced pressure-drop behaviour of the bulk flow may not be due to local velocity fluctuations within the pores but due to mean flow effects, at least over a significant portion of the data (up to <span><math><mrow><mi>W</mi><mi>i</mi><mo>≈</mo></mrow></math></span>0.4).</p></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"332 ","pages":"Article 105295"},"PeriodicalIF":2.7,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0377025724001113/pdfft?md5=a43a620daf8334c96025b7999426f7b0&pid=1-s2.0-S0377025724001113-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141990463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mónica S.N. Oliveira , Konstantinos Zografos , Marco Ellero , Patrick D. Anderson , Robert J. Poole
{"title":"Editorial for XXI International Workshop on Numerical Methods for non-Newtonian Flows 2023","authors":"Mónica S.N. Oliveira , Konstantinos Zografos , Marco Ellero , Patrick D. Anderson , Robert J. Poole","doi":"10.1016/j.jnnfm.2024.105296","DOIUrl":"10.1016/j.jnnfm.2024.105296","url":null,"abstract":"","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"332 ","pages":"Article 105296"},"PeriodicalIF":2.7,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142171858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The life and work of Ken Walters FRS (1934-2022)","authors":"","doi":"10.1016/j.jnnfm.2024.105258","DOIUrl":"10.1016/j.jnnfm.2024.105258","url":null,"abstract":"<div><p>Ken Walters was one of the most prominent rheologists of recent times. He brought his mathematical training to rheology and pioneered analysis of many common test procedures. In order to do this he contributed to the formation of nonlinear constitutive equations for viscoelastic fluids and he was an early exponent of computational studies in rheology. He also applied his skills in fruitful collaborations with industry - notably the oil and china clay industries. He was born in Swansea, South Wales, in 1934 and he remained a devoted Welshman despite travelling widely. His academic studies in Swansea with James Oldroyd led to the PhD degree in 1959. In 1960, after a stint in the U.S.A., he was appointed as a Lecturer at Aberystwyth, and he remained there until his death in 2022. He built a very strong research team at Aberystwyth which became a dominant factor in the rheological scene in the United Kingdom.</p><p>He was a keen promoter of rheology and he assisted in the organisation of many conferences and meetings. He was the founding Editor of the Journal of Non-Newtonian Fluid Mechanics (JNNFM). He authored or co-authored four well-known books on rheology plus several tracts of a religious nature - Ken was always a devoted Christian. He was also a very able sportsman especially at cricket and golf. He is survived by his wife Mary, three children and seven grandchildren.</p></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"330 ","pages":"Article 105258"},"PeriodicalIF":2.7,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141024695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jianyi Du , Hiroko Ohtani , Kevin Ellwood , Gareth H. McKinley
{"title":"Capillarity-driven thinning and breakup of weakly rate-thickening fluids","authors":"Jianyi Du , Hiroko Ohtani , Kevin Ellwood , Gareth H. McKinley","doi":"10.1016/j.jnnfm.2024.105294","DOIUrl":"10.1016/j.jnnfm.2024.105294","url":null,"abstract":"<div><p>A number of commercial fluids, including synthetic automotive oils, food and consumer products containing polymer additives exhibit weakly rate-thickening responses in the final stages of capillarity-driven thinning, where a large accumulated strain and high extensional strain rate alter the thinning dynamics of the slender liquid filament. Consequently, measurements of capillarity-driven thinning dynamics typically feature two distinct regions at the early and late stages of the filament breakup process, each dominated by distinct mechanisms. These features have been incorporated in a simple Inelastic Rate-Thickening (IRT) model with linear and quadratic contributions to the constitutive stress–strain rate relationship, in which the apparent extensional viscosity slowly thickens at high strain rates. We numerically compute the thinning dynamics of the IRT model assuming an axially-slender axisymmetric filament and no fluid inertia. The computational results motivate a similarity transformation and we obtain a new self-similar solution in which the second-order stress is balanced by capillarity. The new asymptotic solution leads to a self-similar filament shape that is more slender than the Newtonian counterpart and, close to singularity, results in a quadratic dependence of the mid-point radius of the filament with time to breakup. A new and distinct asymptotic geometric correction factor, <span><math><mrow><mi>X</mi><mo>≈</mo><mn>0</mn><mo>.</mo><mn>5827</mn></mrow></math></span> is derived and we show that a more accurate value of the true extensional viscosity in a rate-thickening fluid can be recovered from an interpolated time-varying geometric correction factor based on the magnitudes of different stress components. Finally, we propose a statistically data-driven protocol to select the best-fit constitutive model using a parameter-free information criterion. This enables us to more accurately quantify the extensional rheological behavior of complex rate-thickening viscoelastic fluids using capillarity-driven thinning dynamics.</p></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"331 ","pages":"Article 105294"},"PeriodicalIF":2.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141865149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rafael A. Figueiredo , Cassio M. Oishi , Fernando T. Pinho , Roney L. Thompson
{"title":"On more insightful dimensionless numbers for computational viscoelastic rheology","authors":"Rafael A. Figueiredo , Cassio M. Oishi , Fernando T. Pinho , Roney L. Thompson","doi":"10.1016/j.jnnfm.2024.105282","DOIUrl":"10.1016/j.jnnfm.2024.105282","url":null,"abstract":"<div><p>Abrupt contraction flows involving viscoelastic fluids represent a longstanding computational challenge within the field of non-Newtonian fluid mechanics. Despite the apparent simplicity of the geometry, these flows have given rise to intricate discussions in the study of viscoelastic phenomena. This study aims to re-examine the numerical solutions for flows through abrupt contractions, offering a fresh interpretation through the lens of reformulated dimensionless numbers. These numbers are designed to consider the characteristic shear rate of the problem, providing a more comprehensive understanding of the underlying dynamics.</p><p>When investigating models with intermediate levels of complexity, such as the Giesekus and Phan-Thien-Tanner constitutive equations, the usual comparison with the corresponding Oldroyd-B model becomes inadequate because it tends to rely on the nominal relaxation time (<span><math><mi>λ</mi></math></span>) and the nominal total viscosity (<span><math><mi>η</mi></math></span>) instead of their effective counterparts when defining the Reynolds number (<span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span>), the Weissenberg number (<span><math><mrow><mi>W</mi><mi>i</mi></mrow></math></span>) and the ratio of solvent to total viscosities (<span><math><mi>β</mi></math></span>) (<span><math><mi>β</mi></math></span> plays a role only in rheological models involving a solvent contribution). If these dimensionless numbers are tailored to account for the characteristic shear rate specific to the problem under investigation, the choice of the corresponding Oldroyd-B flow, at the adequate values of <span><math><mrow><mi>R</mi><mi>e</mi></mrow></math></span>, <span><math><mrow><mi>W</mi><mi>i</mi></mrow></math></span>, and <span><math><mi>β</mi></math></span> allows for significantly better quantification of the correct effects of nonlinear viscoelasticity of the original model.</p><p>We show the conventional approach tends to overemphasize the role of the nonlinear parameter in nonlinear constitutive equations, like the Giesekus and PTT models, when examining standard abrupt contraction flow outputs such as the Couette correction and vortex size. This overestimation occurs because the conventional method does not allow the Reynolds and Weissenberg numbers (and possibly <span><math><mi>β</mi></math></span>) to carry the portion of the nonlinear effect that can potentially be captured by the linear Oldroyd-B model through the use of characteristic shear rate-based values. We believe the present approach provides a better perspective of the role played by the nonlinear parameter and its extension to more general flows is also discussed.</p></div>","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"331 ","pages":"Article 105282"},"PeriodicalIF":2.7,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141852465","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Moisés Romero-Ureña , Luis Medina-Torres , Octavio Manero , J. Esteban López-Aguilar
{"title":"Rheo-optics of giant micelles: SALS patterns of cetyltrimethylammonium tosylate solutions in presence of sodium bromide","authors":"Moisés Romero-Ureña , Luis Medina-Torres , Octavio Manero , J. Esteban López-Aguilar","doi":"10.1016/j.jnnfm.2024.105286","DOIUrl":"10.1016/j.jnnfm.2024.105286","url":null,"abstract":"<div><p>In this work, we present a systematic study based on Small-Angle Light Scattering (SALS) patterns of the simple shear flow response of semi-diluted solutions of cetyltrimethylammonium tosylate (CTAT; 5.5 <span><math><mrow><mi>w</mi><mi>t</mi><mo>.</mo><mtext>%</mtext></mrow></math></span> - 0.12 M) in the presence of sodium bromide (NaBr) at different <span><math><mrow><mrow><mo>[</mo><mi>N</mi><mi>a</mi><mi>B</mi><mi>r</mi><mo>]</mo></mrow><mo>=</mo><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>12</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>19</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo>}</mo></mrow></mrow></math></span> M concentrations. We evidence a relationship between rheological and light scattering data that reveals a transition into a fast-breaking regime in the dynamics of wormlike micelles formed by the CTAT/NaBr system (Macías et al., 2011; Fierro et al., 2021). This transition into a micellar fast-breaking regime with salt addition (<span><math><mrow><mrow><mo>[</mo><mi>N</mi><mi>a</mi><mi>B</mi><mi>r</mi><mo>]</mo></mrow><mo>≥</mo><mn>0</mn></mrow></math></span>) appears marked by the following features: (i) a decrease in the relaxation time of the material <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, accompanied by (ii) a decrease of the viscosity level at low shear rates <span><math><msub><mrow><mi>η</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> (Macías et al., 2011; Fierro et al., 2021; Schubert et al., 2003; Alkschbirs et al., 2015; Bandyopadhyay et al., 2003). With these, (iii) the formation of butterfly-like patterns is recorded originating from concentration fluctuations, evolution that is accompanied by: (iv) shear banding in the form of non-monotonic flow curves and (v) slow oscillatory transient responses in start-up flow tests captured theoretically with the Bautista–Manero–Puig (BMP) model. In addition, the Cox–Merz rule is fulfilled at molar salt-to-surfactant ratios of <span><math><mrow><mi>R</mi><mo>≥</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></math></span>. This results in shorter structure-recovery time-scales than the characteristic-time of the flow (Macías et al., 2011; Fierro et al., 2021; Manero et al., 2002). In the case of the elastic modulus <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, the variation was small, which suggests a transition from an entangled to a multiconnected network, as suggested by Kadoma & van Egmond (1997), Kadoma et al. (1997) and Fierro et al. (2021). <em>From a theoretical perspective</em>, we provide predictions for the shear–stress and the first normal-stress growth coefficients in transient start-up simple shear flow using the BMP model. Here, banding <span><math><mi>R</mi></math></span>=1.5 solutions display overshot responses at relatively high shear rates (<span><math><mrow><mover><mrow><mi>γ</mi></mrow><mrow><mo>̇</mo></mrow","PeriodicalId":54782,"journal":{"name":"Journal of Non-Newtonian Fluid Mechanics","volume":"331 ","pages":"Article 105286"},"PeriodicalIF":2.7,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}