We examine the impact of confinement on the structure, dynamics, and rheology of spherically confined macromolecular suspensions, with a focus on the role played by entropic forces, by comparing the limits of strong hydrodynamics and no hydrodynamics. We present novel measurements of the osmotic pressure, intrinsic viscosity, and long-time self-diffusivity in spherical confinement and find confinement induces strong structural correlations and restrictions on configurational entropy that drive up osmotic pressure and viscosity and drive down self-diffusion. Even in the absence of hydrodynamics, confinement produces distinct short-time and long-time self-diffusion regimes. This finding revises the previous understanding that short-time self-diffusion is a purely hydrodynamic quantity. The entropic short-time self-diffusion is proportional to an entropic mobility, a direct analog to the hydrodynamic mobility. A caging plateau following the short-time regime is stronger and more durable without hydrodynamics, and entropic drift—a gradient in volume fraction—drives particles out of their cages. The distinct long-time regime emerges when an entropic mobility gradient arising from heterogeneous distribution of particle volume drives particles out of local cages. We conclude that entropic mobility gradients produce a distinct long-time dynamical regime in confinement and that hydrodynamic interactions weaken this effect. From a statistical physics perspective, confinement restricts configurational entropy, driving up confined osmotic pressure, viscosity, and (inverse) long-time dynamics as confinement tightens. We support this claim by rescaling the volume fraction as the distance from confinement-dependent maximum packing, which collapses the data for each rheological measure onto a single curve.
{"title":"Confined Brownian suspensions: Equilibrium diffusion, thermodynamics, and rheology","authors":"A. M. Sunol, R. Zia","doi":"10.1122/8.0000520","DOIUrl":"https://doi.org/10.1122/8.0000520","url":null,"abstract":"We examine the impact of confinement on the structure, dynamics, and rheology of spherically confined macromolecular suspensions, with a focus on the role played by entropic forces, by comparing the limits of strong hydrodynamics and no hydrodynamics. We present novel measurements of the osmotic pressure, intrinsic viscosity, and long-time self-diffusivity in spherical confinement and find confinement induces strong structural correlations and restrictions on configurational entropy that drive up osmotic pressure and viscosity and drive down self-diffusion. Even in the absence of hydrodynamics, confinement produces distinct short-time and long-time self-diffusion regimes. This finding revises the previous understanding that short-time self-diffusion is a purely hydrodynamic quantity. The entropic short-time self-diffusion is proportional to an entropic mobility, a direct analog to the hydrodynamic mobility. A caging plateau following the short-time regime is stronger and more durable without hydrodynamics, and entropic drift—a gradient in volume fraction—drives particles out of their cages. The distinct long-time regime emerges when an entropic mobility gradient arising from heterogeneous distribution of particle volume drives particles out of local cages. We conclude that entropic mobility gradients produce a distinct long-time dynamical regime in confinement and that hydrodynamic interactions weaken this effect. From a statistical physics perspective, confinement restricts configurational entropy, driving up confined osmotic pressure, viscosity, and (inverse) long-time dynamics as confinement tightens. We support this claim by rescaling the volume fraction as the distance from confinement-dependent maximum packing, which collapses the data for each rheological measure onto a single curve.","PeriodicalId":16991,"journal":{"name":"Journal of Rheology","volume":" ","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44544353","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}
The shear rheology of particle suspensions in shear-thinning polymeric fluids is studied experimentally using parallel plate measurements and numerically using fully resolved, 3D finite volume simulations with the Giesekus fluid model. We show in our experiments that the steady shear viscosity and first normal stress difference coefficient of the suspension evolve from shear-thickening to substantially shear-thinning as the degree of shear-thinning of the suspending fluid increases. Moreover, in highly shear-thinning fluids, the suspension exhibits greater shear-thinning of the viscosity than the suspending fluid itself. Our dilute body-fitted simulations show that in the absence of hydrodynamic interactions, shear-thinning can arise from the particle-induced fluid stress (PIFS), which ceases to grow with increasing shear rate at low values of [Formula: see text] (solvent viscosity ratio) and finite values of [Formula: see text] (the Giesekus drag coefficient). In a Giesekus suspending fluid, the polymers surrounding the suspended particle are unable to stretch sufficiently at high Weissenberg numbers (Wi) and the reduced polymer stress results in a lower PIFS. When coupled with the shear-thinning stresslet, this effect creates an overall shear-thinning of the viscosity. We then explore the effects of particle-particle interactions on the suspension rheology using immersed boundary simulations. We show that multiparticle simulations are necessary to obtain the shear-thinning behavior of the per-particle viscosity of suspensions in shear-thinning fluids at moderate values of [Formula: see text]. Particle-particle interactions lead to a substantial decrease in the PIFS and an enhancement of the shear-thinning of the stresslet compared to the single particle simulations. This combination leads to the shear-thinning of the per-particle viscosity seen in experiments. We also find that very low values of [Formula: see text] and finite values of [Formula: see text] have opposing effects on the per-particle viscosity that can lead to a nonmonotonic per-particle viscosity versus shear rate in a highly shear-thinning fluid. Overall, the addition of rigid particles to highly shear-thinning fluids, such as joint synovial fluid, leads to increased viscosity and also increased shear-thinning at high shear rates.
{"title":"Rheology of non-Brownian particle suspensions in viscoelastic solutions. Part II: Effect of a shear thinning suspending fluid","authors":"Anni Zhang, E. Shaqfeh","doi":"10.1122/8.0000541","DOIUrl":"https://doi.org/10.1122/8.0000541","url":null,"abstract":"The shear rheology of particle suspensions in shear-thinning polymeric fluids is studied experimentally using parallel plate measurements and numerically using fully resolved, 3D finite volume simulations with the Giesekus fluid model. We show in our experiments that the steady shear viscosity and first normal stress difference coefficient of the suspension evolve from shear-thickening to substantially shear-thinning as the degree of shear-thinning of the suspending fluid increases. Moreover, in highly shear-thinning fluids, the suspension exhibits greater shear-thinning of the viscosity than the suspending fluid itself. Our dilute body-fitted simulations show that in the absence of hydrodynamic interactions, shear-thinning can arise from the particle-induced fluid stress (PIFS), which ceases to grow with increasing shear rate at low values of [Formula: see text] (solvent viscosity ratio) and finite values of [Formula: see text] (the Giesekus drag coefficient). In a Giesekus suspending fluid, the polymers surrounding the suspended particle are unable to stretch sufficiently at high Weissenberg numbers (Wi) and the reduced polymer stress results in a lower PIFS. When coupled with the shear-thinning stresslet, this effect creates an overall shear-thinning of the viscosity. We then explore the effects of particle-particle interactions on the suspension rheology using immersed boundary simulations. We show that multiparticle simulations are necessary to obtain the shear-thinning behavior of the per-particle viscosity of suspensions in shear-thinning fluids at moderate values of [Formula: see text]. Particle-particle interactions lead to a substantial decrease in the PIFS and an enhancement of the shear-thinning of the stresslet compared to the single particle simulations. This combination leads to the shear-thinning of the per-particle viscosity seen in experiments. We also find that very low values of [Formula: see text] and finite values of [Formula: see text] have opposing effects on the per-particle viscosity that can lead to a nonmonotonic per-particle viscosity versus shear rate in a highly shear-thinning fluid. Overall, the addition of rigid particles to highly shear-thinning fluids, such as joint synovial fluid, leads to increased viscosity and also increased shear-thinning at high shear rates.","PeriodicalId":16991,"journal":{"name":"Journal of Rheology","volume":" ","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47681844","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}
A. Geffrault, H. Bessaies-Bey, N. Roussel, P. Coussot
We analyze different flow regimes of a filament formed by extrusion of a material through a cylindrical die. We deduce that the elongational yield stress of a simple yield stress fluid (i.e., with negligible thixotropy effects) can be determined from the mass of the droplet after filament breakage and an estimation of the critical radius at pinch-off at the solid-liquid regime transition. We demonstrate that such a simple characterization is relevant in a relatively wide range of extrusion velocities, i.e., this velocity slightly affects the drop mass in this range. For the simple yield stress fluids used, Carbopol gel, clay-water paste at different concentrations, and emulsion, covering a large range of yield stress values (50–1000 Pa), the elongational yield stress appears to be equal to the simple shear yield stress times a factor equal to about [Formula: see text]. As a consequence, this simple test may be used to obtain, almost instantaneously and without sophisticated apparatus (a syringe and a balance are sufficient), a good estimate of the shear yield stress of simple yield stress fluids. In that case, the main source of uncertainty (up to about 20%) is the value of the critical radius at the solid-liquid transition. Finally, we review the operating conditions (material properties and extrusion characteristics) for which we can expect this approach to be valid.
{"title":"Instant yield stress measurement from falling drop size: The “syringe test”","authors":"A. Geffrault, H. Bessaies-Bey, N. Roussel, P. Coussot","doi":"10.1122/8.0000557","DOIUrl":"https://doi.org/10.1122/8.0000557","url":null,"abstract":"We analyze different flow regimes of a filament formed by extrusion of a material through a cylindrical die. We deduce that the elongational yield stress of a simple yield stress fluid (i.e., with negligible thixotropy effects) can be determined from the mass of the droplet after filament breakage and an estimation of the critical radius at pinch-off at the solid-liquid regime transition. We demonstrate that such a simple characterization is relevant in a relatively wide range of extrusion velocities, i.e., this velocity slightly affects the drop mass in this range. For the simple yield stress fluids used, Carbopol gel, clay-water paste at different concentrations, and emulsion, covering a large range of yield stress values (50–1000 Pa), the elongational yield stress appears to be equal to the simple shear yield stress times a factor equal to about [Formula: see text]. As a consequence, this simple test may be used to obtain, almost instantaneously and without sophisticated apparatus (a syringe and a balance are sufficient), a good estimate of the shear yield stress of simple yield stress fluids. In that case, the main source of uncertainty (up to about 20%) is the value of the critical radius at the solid-liquid transition. Finally, we review the operating conditions (material properties and extrusion characteristics) for which we can expect this approach to be valid.","PeriodicalId":16991,"journal":{"name":"Journal of Rheology","volume":" ","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47379901","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}
The shear and elongational rheology of linear and pom-pom shaped polystyrene (PS) blends was investigated experimentally and modeled using constitutive models such as the Doi–Edwards and the molecular stress function (MSF) model. The pom-pom molecule is the simplest topology to combine shear thinning with strain hardening in elongational flow. A PS pom-pom with a self-entangled backbone (Mw,bb = 280 kg mol−1) and 22 entangled sidearms (Mw,a = 22 kg mol−1) at each star was blended with two linear PS with weight average molecular weights of Mw = 43 and 90 kg mol−1 and low polydispersities (Ð < 1.05). A semilogarithmic relationship between the weight content of the pom-pom, ϕpom-pom, and the zero-shear viscosity was found. Whereas the pure pom-pom has in uniaxial elongational flow at T = 160 °C strain hardening factors (SHFs) of SHF ≈100, similar values can be found in blends with up to ϕpom-pom = 50 wt. % in linear PS43k and PS90k. By blending only 2 wt. % pom-pom with linear PS43k, SHF = 10 can still be observed. Furthermore, above ϕpom-pom = 5–10 wt. %, the uniaxial extensional behavior can be well-described with the MSF model with a single parameter set for each linear PS matrix. The results show that the relationship between shear and elongational melt behavior, i.e., zero-shear viscosity and SHF, can be uncoupled and customized tuned by blending linear and pom-pom shaped polymers and very straightforwardly predicted theoretically. This underlines also the possible application of well-designed branched polymers as additives in recycling.
{"title":"Complex polymer topologies in blends: Shear and elongational rheology of linear/pom-pom polystyrene blends","authors":"V. Hirschberg, S. Lyu, M. G. Schußmann","doi":"10.1122/8.0000544","DOIUrl":"https://doi.org/10.1122/8.0000544","url":null,"abstract":"The shear and elongational rheology of linear and pom-pom shaped polystyrene (PS) blends was investigated experimentally and modeled using constitutive models such as the Doi–Edwards and the molecular stress function (MSF) model. The pom-pom molecule is the simplest topology to combine shear thinning with strain hardening in elongational flow. A PS pom-pom with a self-entangled backbone (Mw,bb = 280 kg mol−1) and 22 entangled sidearms (Mw,a = 22 kg mol−1) at each star was blended with two linear PS with weight average molecular weights of Mw = 43 and 90 kg mol−1 and low polydispersities (Ð < 1.05). A semilogarithmic relationship between the weight content of the pom-pom, ϕpom-pom, and the zero-shear viscosity was found. Whereas the pure pom-pom has in uniaxial elongational flow at T = 160 °C strain hardening factors (SHFs) of SHF ≈100, similar values can be found in blends with up to ϕpom-pom = 50 wt. % in linear PS43k and PS90k. By blending only 2 wt. % pom-pom with linear PS43k, SHF = 10 can still be observed. Furthermore, above ϕpom-pom = 5–10 wt. %, the uniaxial extensional behavior can be well-described with the MSF model with a single parameter set for each linear PS matrix. The results show that the relationship between shear and elongational melt behavior, i.e., zero-shear viscosity and SHF, can be uncoupled and customized tuned by blending linear and pom-pom shaped polymers and very straightforwardly predicted theoretically. This underlines also the possible application of well-designed branched polymers as additives in recycling.","PeriodicalId":16991,"journal":{"name":"Journal of Rheology","volume":" ","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45454866","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}
Oscillatory rheometric techniques such as small amplitude oscillatory shear (SAOS) and, more recently, medium amplitude oscillatory shear and large amplitude oscillatory shear (LAOS) are widely used for rheological characterization of the viscoelastic properties of complex fluids. However, in a time-evolving or mutating material, the build-up or breakdown of microstructure is commonly both time- and shear-rate (or shear-stress) dependent, and thixotropic phenomena are observed in many complex fluids including drilling fluids, biopolymer gels, and many food products. Conventional applications of Fourier transforms for analyzing oscillatory data assume the signals are time-translation invariant, which constrains the mutation number of the material to be extremely small. This constraint makes it difficult to accurately study shear-induced microstructural changes in thixotropic and gelling materials, and it is becoming increasingly important to develop more advanced signal processing techniques capable of robustly extracting time-resolved frequency information from oscillatory data. In this work, we explore applications of the Gabor transform (a short-time Fourier transform combined with a Gaussian window), for providing optimal joint time-frequency resolution of a mutating material’s viscoelastic properties. First, we show using simple analytic models and measurements on a bentonite clay that the Gabor transform enables us to accurately measure rapid changes in both the storage and/or loss modulus with time as well as extract a characteristic thixotropic/aging time scale for the material. Second, using the Gabor transform we demonstrate the extraction of useful viscoelastic data from the initial transient response following the inception of oscillatory flow. Finally, we consider extension of the Gabor transform to nonlinear oscillatory deformations using an amplitude-modulated input strain signal, in order to track the evolution of the Fourier–Tschebyshev coefficients of thixotropic fluids at a specified deformation frequency. We refer to the resulting test protocol as Gaborheometry (Gabor-transformed oscillatory shear rheometry). This unconventional, but easily implemented, rheometric approach facilitates both SAOS and LAOS studies of time-evolving materials, reducing the number of required experiments and the data postprocessing time significantly.
{"title":"Gaborheometry: Applications of the discrete Gabor transform for time resolved oscillatory rheometry","authors":"Joshua David John Rathinaraj, G. McKinley","doi":"10.1122/8.0000549","DOIUrl":"https://doi.org/10.1122/8.0000549","url":null,"abstract":"Oscillatory rheometric techniques such as small amplitude oscillatory shear (SAOS) and, more recently, medium amplitude oscillatory shear and large amplitude oscillatory shear (LAOS) are widely used for rheological characterization of the viscoelastic properties of complex fluids. However, in a time-evolving or mutating material, the build-up or breakdown of microstructure is commonly both time- and shear-rate (or shear-stress) dependent, and thixotropic phenomena are observed in many complex fluids including drilling fluids, biopolymer gels, and many food products. Conventional applications of Fourier transforms for analyzing oscillatory data assume the signals are time-translation invariant, which constrains the mutation number of the material to be extremely small. This constraint makes it difficult to accurately study shear-induced microstructural changes in thixotropic and gelling materials, and it is becoming increasingly important to develop more advanced signal processing techniques capable of robustly extracting time-resolved frequency information from oscillatory data. In this work, we explore applications of the Gabor transform (a short-time Fourier transform combined with a Gaussian window), for providing optimal joint time-frequency resolution of a mutating material’s viscoelastic properties. First, we show using simple analytic models and measurements on a bentonite clay that the Gabor transform enables us to accurately measure rapid changes in both the storage and/or loss modulus with time as well as extract a characteristic thixotropic/aging time scale for the material. Second, using the Gabor transform we demonstrate the extraction of useful viscoelastic data from the initial transient response following the inception of oscillatory flow. Finally, we consider extension of the Gabor transform to nonlinear oscillatory deformations using an amplitude-modulated input strain signal, in order to track the evolution of the Fourier–Tschebyshev coefficients of thixotropic fluids at a specified deformation frequency. We refer to the resulting test protocol as Gaborheometry (Gabor-transformed oscillatory shear rheometry). This unconventional, but easily implemented, rheometric approach facilitates both SAOS and LAOS studies of time-evolving materials, reducing the number of required experiments and the data postprocessing time significantly.","PeriodicalId":16991,"journal":{"name":"Journal of Rheology","volume":" ","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48462572","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}
Krutarth M. Kamani, G. Donley, R. Rao, Anne M. Grillet, C. Roberts, A. Shetty, S. Rogers
A full understanding of the sequence of processes exhibited by yield stress fluids under large amplitude oscillatory shearing is developed using multiple experimental and analytical approaches. A novel component rate Lissajous curve, where the rates at which strain is acquired unrecoverably and recoverably are plotted against each other, is introduced and its utility is demonstrated by application to the analytical responses of four simple viscoelastic models. Using the component rate space, yielding and unyielding are identified by changes in the way strain is acquired, from recoverably to unrecoverably and back again. The behaviors are investigated by comparing the experimental results with predictions from the elastic Bingham model that is constructed using the Oldroyd–Prager formalism and the recently proposed continuous model by Kamani, Donley, and Rogers in which yielding is enhanced by rapid acquisition of elastic strain. The physical interpretation gained from the transient large amplitude oscillatory shear (LAOS) data is compared to the results from the analytical sequence of physical processes framework and a novel time-resolved Pipkin space. The component rate figures, therefore, provide an independent test of the interpretations of the sequence of physical processes analysis that can also be applied to other LAOS analysis frameworks. Each of these methods, the component rates, the sequence of physical processes analysis, and the time-resolved Pipkin diagrams, unambigiously identifies the same material physics, showing that yield stress fluids go through a sequence of physical processes that includes elastic deformation, gradual yielding, plastic flow, and gradual unyielding.
{"title":"Understanding the transient large amplitude oscillatory shear behavior of yield stress fluids","authors":"Krutarth M. Kamani, G. Donley, R. Rao, Anne M. Grillet, C. Roberts, A. Shetty, S. Rogers","doi":"10.1122/8.0000583","DOIUrl":"https://doi.org/10.1122/8.0000583","url":null,"abstract":"A full understanding of the sequence of processes exhibited by yield stress fluids under large amplitude oscillatory shearing is developed using multiple experimental and analytical approaches. A novel component rate Lissajous curve, where the rates at which strain is acquired unrecoverably and recoverably are plotted against each other, is introduced and its utility is demonstrated by application to the analytical responses of four simple viscoelastic models. Using the component rate space, yielding and unyielding are identified by changes in the way strain is acquired, from recoverably to unrecoverably and back again. The behaviors are investigated by comparing the experimental results with predictions from the elastic Bingham model that is constructed using the Oldroyd–Prager formalism and the recently proposed continuous model by Kamani, Donley, and Rogers in which yielding is enhanced by rapid acquisition of elastic strain. The physical interpretation gained from the transient large amplitude oscillatory shear (LAOS) data is compared to the results from the analytical sequence of physical processes framework and a novel time-resolved Pipkin space. The component rate figures, therefore, provide an independent test of the interpretations of the sequence of physical processes analysis that can also be applied to other LAOS analysis frameworks. Each of these methods, the component rates, the sequence of physical processes analysis, and the time-resolved Pipkin diagrams, unambigiously identifies the same material physics, showing that yield stress fluids go through a sequence of physical processes that includes elastic deformation, gradual yielding, plastic flow, and gradual unyielding.","PeriodicalId":16991,"journal":{"name":"Journal of Rheology","volume":" ","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43560756","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}
S. Haward, S. Varchanis, G. McKinley, M. A. Alves, A. Shen
Part I of this paper [Haward et al., J. Rheol. 67, 995–1009 (2023)] presents a three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. Here, in Part II, the OUBER device is employed to examine the uniaxial and biaxial extensional rheology of model dilute polymer solutions, compared with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [OSCER, Haward et al. Phys. Rev. Lett. 109, 128301 (2012)]. In each case, micro-particle image velocimetry is used to measure the extension rate as a function of the imposed flow conditions, and excess pressure drop measurements enable estimation of the tensile stress difference generated in the fluid via a new analysis based on the macroscopic power balance for flow through each device. Based on this analysis, for the most dilute polymer sample tested, which is “ultradilute”, the extensional viscosity is well described by Peterlin’s finitely extensible nonlinear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, although the fluids remain dilute, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as the polymer chains unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, thereby limiting the utility of this flow type for extensional viscosity measurement.
{"title":"Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar, and biaxial extensional rheology of dilute polymer solutions using numerically optimized stagnation point microfluidic devices","authors":"S. Haward, S. Varchanis, G. McKinley, M. A. Alves, A. Shen","doi":"10.1122/8.0000660","DOIUrl":"https://doi.org/10.1122/8.0000660","url":null,"abstract":"Part I of this paper [Haward et al., J. Rheol. 67, 995–1009 (2023)] presents a three-dimensional microfluidic device (the optimized uniaxial and biaxial extensional rheometer, OUBER) for generating near-homogeneous uniaxial and biaxial elongational flows. Here, in Part II, the OUBER device is employed to examine the uniaxial and biaxial extensional rheology of model dilute polymer solutions, compared with measurements made under planar extension in the optimized-shape cross-slot extensional rheometer [OSCER, Haward et al. Phys. Rev. Lett. 109, 128301 (2012)]. In each case, micro-particle image velocimetry is used to measure the extension rate as a function of the imposed flow conditions, and excess pressure drop measurements enable estimation of the tensile stress difference generated in the fluid via a new analysis based on the macroscopic power balance for flow through each device. Based on this analysis, for the most dilute polymer sample tested, which is “ultradilute”, the extensional viscosity is well described by Peterlin’s finitely extensible nonlinear elastic dumbbell model. In this limit, the biaxial extensional viscosity at high Weissenberg numbers (Wi) is half that of the uniaxial and planar extensional viscosities. At higher polymer concentrations, although the fluids remain dilute, the experimental measurements deviate from the model predictions, which is attributed to the onset of intermolecular interactions as the polymer chains unravel in the extensional flows. Of practical significance (and fundamental interest), elastic instability occurs at a significantly lower Wi in uniaxial extensional flow than in either biaxial or planar extensional flow, thereby limiting the utility of this flow type for extensional viscosity measurement.","PeriodicalId":16991,"journal":{"name":"Journal of Rheology","volume":" ","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49054403","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}
S. Haward, F. Pimenta, S. Varchanis, Daniel W. Carlson, Kazumi Toda-Peters, M. A. Alves, A. Shen
Numerical optimization of a “six-arm cross-slot” device yields several three-dimensional shapes of fluidic channels that impose close approximations to an ideal uniaxial (biaxial) stagnation point extensional flow under the constraints of having four inlets and two outlets (two inlets and four outlets) and for Newtonian creeping flow. One of the numerically designed geometries is considered suitable for fabrication at the microscale, and numerical simulations with the Oldroyd-B and Phan-Thien and Tanner models confirm that the optimal flow fields are observed in the geometry for both constant viscosity and shear thinning viscoelastic fluids. The geometry, named the optimized uniaxial and biaxial extensional rheometer (OUBER), is microfabricated with high precision by selective laser-induced etching of a fused-silica substrate. Employing a refractive index-matched viscous Newtonian fluid, microtomographic-particle image velocimetry enables the measurement of the flow field in a substantial volume around the stagnation point. The flow velocimetry, performed at low Reynolds number (<0.1), confirms the accurate imposition of the desired and predicted flows, with a pure extensional flow at an essentially uniform deformation rate being applied over a wide region around the stagnation point. In Part II of this paper [Haward et al., J. Rheol. 67, 1011–1030 (2023)], pressure drop measurements in the OUBER geometry are used to assess the uniaxial and biaxial extensional rheometry of dilute polymeric solutions, in comparison to measurements made in planar extension using an optimized-shape cross-slot extensional rheometer [OSCER, Haward et al., Phys. Rev. Lett. 109, 128301 (2012)].
“六臂交叉槽”装置的数值优化产生了几个三维形状的流体通道，这些通道在具有四个入口和两个出口(两个入口和四个出口)的约束下近似于理想的单轴(双轴)驻点扩展流和牛顿蠕动流。采用Oldroyd-B模型和Phan-Thien模型和Tanner模型进行的数值模拟证实，在恒定粘度和剪切稀化粘弹性流体的几何结构中都观察到最佳流场。该几何结构被命名为优化的单轴和双轴拉伸流变仪(OUBER)，通过选择性激光诱导蚀刻熔融二氧化硅衬底实现高精度微加工。采用折射率匹配的粘性牛顿流体，微层析-颗粒图像测速技术可以测量停滞点周围大量体积内的流场。在低雷诺数(<0.1)下进行的流速测量证实了期望和预测流动的准确施加，在停滞点周围的广泛区域内，以基本均匀的变形率施加纯拉伸流动。在本文的第二部分[Haward et al.， J. Rheol. 67, 1011-1030(2023)]中，使用OUBER几何形状的压降测量来评估稀释聚合物溶液的单轴和双轴拉伸流变，并与使用优化形状的交叉槽拉伸流变仪在平面拉伸中进行的测量进行比较[OSCER, Haward et al.， Phys]。科学通报，2009(1):1 - 3。
{"title":"Extensional rheometry of mobile fluids. Part I: OUBER, an optimized uniaxial and biaxial extensional rheometer","authors":"S. Haward, F. Pimenta, S. Varchanis, Daniel W. Carlson, Kazumi Toda-Peters, M. A. Alves, A. Shen","doi":"10.1122/8.0000659","DOIUrl":"https://doi.org/10.1122/8.0000659","url":null,"abstract":"Numerical optimization of a “six-arm cross-slot” device yields several three-dimensional shapes of fluidic channels that impose close approximations to an ideal uniaxial (biaxial) stagnation point extensional flow under the constraints of having four inlets and two outlets (two inlets and four outlets) and for Newtonian creeping flow. One of the numerically designed geometries is considered suitable for fabrication at the microscale, and numerical simulations with the Oldroyd-B and Phan-Thien and Tanner models confirm that the optimal flow fields are observed in the geometry for both constant viscosity and shear thinning viscoelastic fluids. The geometry, named the optimized uniaxial and biaxial extensional rheometer (OUBER), is microfabricated with high precision by selective laser-induced etching of a fused-silica substrate. Employing a refractive index-matched viscous Newtonian fluid, microtomographic-particle image velocimetry enables the measurement of the flow field in a substantial volume around the stagnation point. The flow velocimetry, performed at low Reynolds number (<0.1), confirms the accurate imposition of the desired and predicted flows, with a pure extensional flow at an essentially uniform deformation rate being applied over a wide region around the stagnation point. In Part II of this paper [Haward et al., J. Rheol. 67, 1011–1030 (2023)], pressure drop measurements in the OUBER geometry are used to assess the uniaxial and biaxial extensional rheometry of dilute polymeric solutions, in comparison to measurements made in planar extension using an optimized-shape cross-slot extensional rheometer [OSCER, Haward et al., Phys. Rev. Lett. 109, 128301 (2012)].","PeriodicalId":16991,"journal":{"name":"Journal of Rheology","volume":" ","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46907182","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}
Milad Hadaeghnia, S. Ahmadi, I. Ghasemi, P. Wood-Adams
We investigate the effect of minor phase rheological properties and compatibilizer on the phase morphology and graphene 3D structure in polyamide-6 (PA6)/polyolefin elastomer (POE) blends. It is revealed that in blends containing low viscosity (LV) POE, graphene is better dispersed facilitating its localization at the interface. In the blend containing high viscosity (HV) POE with poor graphene dispersion, large graphene aggregates are observed inside the POE phase with less interfacial coverage. Interestingly, graphene induces a co-continuous morphology and electrical and rheological percolation in both systems, although at a lower graphene content for the LV system. The LV system exhibits a more interconnected morphology, while in the HV system we observe a compact fractal-like POE structure with a lower degree of interconnectivity. Our morphological observation suggests that co-continuous morphology in the LV system is dominated by sheet formation, while in the HV system it is dominated by coalescence between moderately elongated domains. Fractal analysis of the graphene 3D network (based on the rheological characterization) is correlated with the higher degree of connectivity of the graphene 3D structure in the LV system. The 2D fractal dimension of the POE phase (host phase for graphene) is in line with the fractal dimension of the graphene flocs, indicating that the graphene flocs influence the blend morphology. The addition of compatibilizer to the HV system did not result in improved electrical properties.
{"title":"Fractal structures of PA6/POE blend nanocomposites and their dynamic properties","authors":"Milad Hadaeghnia, S. Ahmadi, I. Ghasemi, P. Wood-Adams","doi":"10.1122/8.0000501","DOIUrl":"https://doi.org/10.1122/8.0000501","url":null,"abstract":"We investigate the effect of minor phase rheological properties and compatibilizer on the phase morphology and graphene 3D structure in polyamide-6 (PA6)/polyolefin elastomer (POE) blends. It is revealed that in blends containing low viscosity (LV) POE, graphene is better dispersed facilitating its localization at the interface. In the blend containing high viscosity (HV) POE with poor graphene dispersion, large graphene aggregates are observed inside the POE phase with less interfacial coverage. Interestingly, graphene induces a co-continuous morphology and electrical and rheological percolation in both systems, although at a lower graphene content for the LV system. The LV system exhibits a more interconnected morphology, while in the HV system we observe a compact fractal-like POE structure with a lower degree of interconnectivity. Our morphological observation suggests that co-continuous morphology in the LV system is dominated by sheet formation, while in the HV system it is dominated by coalescence between moderately elongated domains. Fractal analysis of the graphene 3D network (based on the rheological characterization) is correlated with the higher degree of connectivity of the graphene 3D structure in the LV system. The 2D fractal dimension of the POE phase (host phase for graphene) is in line with the fractal dimension of the graphene flocs, indicating that the graphene flocs influence the blend morphology. The addition of compatibilizer to the HV system did not result in improved electrical properties.","PeriodicalId":16991,"journal":{"name":"Journal of Rheology","volume":" ","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48366867","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}
Constitutive models for the dynamics of polymer solutions traditionally rely on closure relations for the extra stress or related microstructural variables (e.g., conformation tensor) linking them to flow history. In this work, we study the eigendynamics of the conformation tensor within the GENERIC framework in mesoscopic computer simulations of polymer solutions to separate the effects of nonaffine motion from other sources of non-Newtonian behavior. We observe that nonaffine motion or slip increases with both the polymer concentration and the polymer chain length. Our analysis allows to uniquely calibrate a mixed derivative of the Gordon–Schowalter type in macroscopic models based on a micro-macromapping of the dynamics of the polymeric system. The presented approach paves the way for better polymer constitutive modeling in multiscale simulations of polymer solutions, where different sources of non-Newtonian behavior are modelled independently.
{"title":"Non-affine motion and selection of slip coefficient in constitutive modeling of polymeric solutions using a mixed derivative","authors":"D. Nieto Simavilla, P. Español, M. Ellero","doi":"10.1122/8.0000527","DOIUrl":"https://doi.org/10.1122/8.0000527","url":null,"abstract":"Constitutive models for the dynamics of polymer solutions traditionally rely on closure relations for the extra stress or related microstructural variables (e.g., conformation tensor) linking them to flow history. In this work, we study the eigendynamics of the conformation tensor within the GENERIC framework in mesoscopic computer simulations of polymer solutions to separate the effects of nonaffine motion from other sources of non-Newtonian behavior. We observe that nonaffine motion or slip increases with both the polymer concentration and the polymer chain length. Our analysis allows to uniquely calibrate a mixed derivative of the Gordon–Schowalter type in macroscopic models based on a micro-macromapping of the dynamics of the polymeric system. The presented approach paves the way for better polymer constitutive modeling in multiscale simulations of polymer solutions, where different sources of non-Newtonian behavior are modelled independently.","PeriodicalId":16991,"journal":{"name":"Journal of Rheology","volume":" ","pages":""},"PeriodicalIF":3.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44202894","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}
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