Living polymers such as wormlike micelles have attracted considerable experimental and theoretical interest over the past three decades, but the differential-integral equations that describe the joint processes of reversible scission and stress relaxation were only recently developed and have not yet been solved. Here, we introduce a numerical method that is simple, stable, accurate, flexible, and fast compared to alternatives. After validating the method and its predictions, we provide a preliminary discussion on previously unquantified sources of uncertainty in a popular stochastic approach to modeling the same problem.
{"title":"A new numerical method for linear rheology of living polymers","authors":"Claire Love, Joseph D. Peterson","doi":"10.1122/8.0000875","DOIUrl":"https://doi.org/10.1122/8.0000875","url":null,"abstract":"Living polymers such as wormlike micelles have attracted considerable experimental and theoretical interest over the past three decades, but the differential-integral equations that describe the joint processes of reversible scission and stress relaxation were only recently developed and have not yet been solved. Here, we introduce a numerical method that is simple, stable, accurate, flexible, and fast compared to alternatives. After validating the method and its predictions, we provide a preliminary discussion on previously unquantified sources of uncertainty in a popular stochastic approach to modeling the same problem.","PeriodicalId":508264,"journal":{"name":"Journal of Rheology","volume":"5 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141921162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Milad Saadat, W. Hartt V, Norman J. Wagner, Safa Jamali
Predicting the response of complex fluids to different flow conditions has been the focal point of rheology and is generally done via constitutive relations. There are, nonetheless, scenarios in which not much is known from the material mathematically, while data collection from samples is elusive, resource-intensive, or both. In such cases, meta-modeling of observables using a parametric surrogate model called multi-fidelity neural networks (MFNNs) may obviate the constitutive equation development step by leveraging only a handful of high-fidelity (Hi-Fi) data collected from experiments (or high-resolution simulations) and an abundance of low-fidelity (Lo-Fi) data generated synthetically to compensate for Hi-Fi data scarcity. To this end, MFNNs are employed to meta-model the material responses of a thermo-viscoelastic (TVE) fluid, consumer product Johnson’s® Baby Shampoo, under four flow protocols: steady shear, step growth, oscillatory, and small/large amplitude oscillatory shear (S/LAOS). In addition, the time–temperature superposition (TTS) of the material response and MFNN predictions are explored. By applying simple linear regression (without induction of any constitutive equation) on log-spaced Hi-Fi data, a series of Lo-Fi data were generated and found sufficient to obtain accurate material response recovery in terms of either interpolation or extrapolation for all flow protocols except for S/LAOS. This insufficiency is resolved by informing the MFNN platform with a linear constitutive model (Maxwell viscoelastic) resulting in simultaneous interpolation and extrapolation capabilities in S/LAOS material response recovery. The roles of data volume, flow type, and deformation range are discussed in detail, providing a practical pathway to multifidelity meta-modeling of different complex fluids.
{"title":"Data-driven constitutive meta-modeling of nonlinear rheology via multifidelity neural networks","authors":"Milad Saadat, W. Hartt V, Norman J. Wagner, Safa Jamali","doi":"10.1122/8.0000831","DOIUrl":"https://doi.org/10.1122/8.0000831","url":null,"abstract":"Predicting the response of complex fluids to different flow conditions has been the focal point of rheology and is generally done via constitutive relations. There are, nonetheless, scenarios in which not much is known from the material mathematically, while data collection from samples is elusive, resource-intensive, or both. In such cases, meta-modeling of observables using a parametric surrogate model called multi-fidelity neural networks (MFNNs) may obviate the constitutive equation development step by leveraging only a handful of high-fidelity (Hi-Fi) data collected from experiments (or high-resolution simulations) and an abundance of low-fidelity (Lo-Fi) data generated synthetically to compensate for Hi-Fi data scarcity. To this end, MFNNs are employed to meta-model the material responses of a thermo-viscoelastic (TVE) fluid, consumer product Johnson’s® Baby Shampoo, under four flow protocols: steady shear, step growth, oscillatory, and small/large amplitude oscillatory shear (S/LAOS). In addition, the time–temperature superposition (TTS) of the material response and MFNN predictions are explored. By applying simple linear regression (without induction of any constitutive equation) on log-spaced Hi-Fi data, a series of Lo-Fi data were generated and found sufficient to obtain accurate material response recovery in terms of either interpolation or extrapolation for all flow protocols except for S/LAOS. This insufficiency is resolved by informing the MFNN platform with a linear constitutive model (Maxwell viscoelastic) resulting in simultaneous interpolation and extrapolation capabilities in S/LAOS material response recovery. The roles of data volume, flow type, and deformation range are discussed in detail, providing a practical pathway to multifidelity meta-modeling of different complex fluids.","PeriodicalId":508264,"journal":{"name":"Journal of Rheology","volume":"94 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141808126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose a torque rheometer coupled with an ultrasonic velocity profiler (UVP) for evaluating multiphase fluids as bulk rheology in oscillatory shear flows. The rheometer mainly consists of wide-gap coaxial cylinders, where the outer cylinder is sinusoidally oscillated and the inner cylinder is fixed to a torque sensor for measuring the wall shear stress. Based on Cauchy’s equation of motion, the spatiotemporal distribution of the shear stress is obtained from the velocity information and the wall shear stress as a boundary condition. This rheometer was applied to a carboxymethyl cellulose aqueous solution and compared with a standard torque-type rheometer. The results of the evaluated viscoelastic properties agreed well with each other, indicating the validity of the proposed rheometry. To further investigate the applicability of the rheometer to multiphase fluids, suspensions of solid spherical particles with a diameter of 220μm with volume fraction of 0.8–3.4% were measured, which are out of the applicable ranges of the standard rheometer. For volume fractions up to 3% where the UVP measurement is available, the relative viscosity agrees well with a theoretical formula. This indicates the applicability of the method to examine multiphase fluids.
{"title":"Coupling a torque rheometer with an ultrasonic velocity profiler for evaluating multiphase fluids in oscillatory shear flows","authors":"K. Ohie, Taiki Yoshida, Yuji Tasaka","doi":"10.1122/8.0000818","DOIUrl":"https://doi.org/10.1122/8.0000818","url":null,"abstract":"We propose a torque rheometer coupled with an ultrasonic velocity profiler (UVP) for evaluating multiphase fluids as bulk rheology in oscillatory shear flows. The rheometer mainly consists of wide-gap coaxial cylinders, where the outer cylinder is sinusoidally oscillated and the inner cylinder is fixed to a torque sensor for measuring the wall shear stress. Based on Cauchy’s equation of motion, the spatiotemporal distribution of the shear stress is obtained from the velocity information and the wall shear stress as a boundary condition. This rheometer was applied to a carboxymethyl cellulose aqueous solution and compared with a standard torque-type rheometer. The results of the evaluated viscoelastic properties agreed well with each other, indicating the validity of the proposed rheometry. To further investigate the applicability of the rheometer to multiphase fluids, suspensions of solid spherical particles with a diameter of 220μm with volume fraction of 0.8–3.4% were measured, which are out of the applicable ranges of the standard rheometer. For volume fractions up to 3% where the UVP measurement is available, the relative viscosity agrees well with a theoretical formula. This indicates the applicability of the method to examine multiphase fluids.","PeriodicalId":508264,"journal":{"name":"Journal of Rheology","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141815808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, the nonlinear rheological behavior of aqueous suspensions composed of two typical nanocellulose [rod-like cellulose nanocrystals (CNCs) and filamentous cellulose nanofibrils (CNFs)] was examined and compared by using various large-amplitude oscillatory shear (LAOS) analysis methods, such as Fourier-transform rheology, stress decomposition, Chebyshev polynomials, and the sequence of physical processes. From our analysis, the nonlinear rheological parameters of higher harmonics, dissipation ratio, strain hardening ratio, shear thickening ratio, transient modulus, and cage modulus were obtained and quantitatively analyzed. CNCs tend to assemble to form anisotropic structures in an aqueous medium while the CNFs are entangled to form gels. The CNF suspensions demonstrated a significant viscous modulus overshoot and had stronger yield stresses, but the yield of CNC suspensions was more ductile. In the case of low concentrations, the CNF suspensions demonstrated stronger intracycle shear thickening behavior in medium-amplitude oscillatory shear region and lower dissipation ratios at small strain amplitudes. Although both nanocellulose suspensions revealed the existence of four intracycle rheological transition processes (viscoplastic deformation, structural recovery, early-stage yielding, and late-stage yielding), the CNF suspensions exhibited a stronger structural recovery ability. Larger strain amplitudes did not invariably result in a broader range of intracycle rheological transitions, which are also affected by the excitation frequency. The application of the various LAOS analysis methods provided valuable intracycle nonlinear rheological insights into nanocellulose suspensions, which are of great importance for enhancing their industrial perspectives.
{"title":"Nonlinear oscillatory rheology of aqueous suspensions of cellulose nanocrystals and nanofibrils","authors":"Jiatong Xu, Pengguang Wang, Ziyu Zhou, Baihua Yuan, Hongbin Zhang","doi":"10.1122/8.0000808","DOIUrl":"https://doi.org/10.1122/8.0000808","url":null,"abstract":"In this work, the nonlinear rheological behavior of aqueous suspensions composed of two typical nanocellulose [rod-like cellulose nanocrystals (CNCs) and filamentous cellulose nanofibrils (CNFs)] was examined and compared by using various large-amplitude oscillatory shear (LAOS) analysis methods, such as Fourier-transform rheology, stress decomposition, Chebyshev polynomials, and the sequence of physical processes. From our analysis, the nonlinear rheological parameters of higher harmonics, dissipation ratio, strain hardening ratio, shear thickening ratio, transient modulus, and cage modulus were obtained and quantitatively analyzed. CNCs tend to assemble to form anisotropic structures in an aqueous medium while the CNFs are entangled to form gels. The CNF suspensions demonstrated a significant viscous modulus overshoot and had stronger yield stresses, but the yield of CNC suspensions was more ductile. In the case of low concentrations, the CNF suspensions demonstrated stronger intracycle shear thickening behavior in medium-amplitude oscillatory shear region and lower dissipation ratios at small strain amplitudes. Although both nanocellulose suspensions revealed the existence of four intracycle rheological transition processes (viscoplastic deformation, structural recovery, early-stage yielding, and late-stage yielding), the CNF suspensions exhibited a stronger structural recovery ability. Larger strain amplitudes did not invariably result in a broader range of intracycle rheological transitions, which are also affected by the excitation frequency. The application of the various LAOS analysis methods provided valuable intracycle nonlinear rheological insights into nanocellulose suspensions, which are of great importance for enhancing their industrial perspectives.","PeriodicalId":508264,"journal":{"name":"Journal of Rheology","volume":"47 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140970739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Seyed Mahmoud Arzideh, A. Córdoba, Jeffrey G. Ethier, J. Schieber, D. Venerus
Equibiaxial elongational deformations are omnipresent in polymer processing technologies. The challenge of generating well-controlled equibiaxial elongational deformations in the laboratory has, however, severely inhibited progress on understanding the rheology of polymeric liquids and other complex fluids in this flow. More recently, a novel technique known as continuous lubricated squeezing flow has been developed that allows for rheological measurements in equibiaxial elongational deformations. In the present study, we examine the rheological behavior of two entangled polyisobutylene (PIB) melts with different molecular weight distributions in constant strain rate equibiaxial elongation flows. These new data are compared with predictions from two molecular models for entangled polymer melts inspired by the idea that entanglements dominate the relaxation dynamics. One model is the discrete slip-link model (DSM), and the other is known as the Rolie Double Poly (RDP) model. For the PIB with a relatively narrow molecular weight distribution, the predictions of both models are in good agreement with experiments and the DSM gives nearly quantitative agreement. For the broad molecular weight distribution PIB, both the DSM and RDP model predict strain hardening, which is not observed in the experiments.
{"title":"Equibiaxial elongation of entangled polyisobutylene melts: Experiments and theoretical predictions","authors":"Seyed Mahmoud Arzideh, A. Córdoba, Jeffrey G. Ethier, J. Schieber, D. Venerus","doi":"10.1122/8.0000809","DOIUrl":"https://doi.org/10.1122/8.0000809","url":null,"abstract":"Equibiaxial elongational deformations are omnipresent in polymer processing technologies. The challenge of generating well-controlled equibiaxial elongational deformations in the laboratory has, however, severely inhibited progress on understanding the rheology of polymeric liquids and other complex fluids in this flow. More recently, a novel technique known as continuous lubricated squeezing flow has been developed that allows for rheological measurements in equibiaxial elongational deformations. In the present study, we examine the rheological behavior of two entangled polyisobutylene (PIB) melts with different molecular weight distributions in constant strain rate equibiaxial elongation flows. These new data are compared with predictions from two molecular models for entangled polymer melts inspired by the idea that entanglements dominate the relaxation dynamics. One model is the discrete slip-link model (DSM), and the other is known as the Rolie Double Poly (RDP) model. For the PIB with a relatively narrow molecular weight distribution, the predictions of both models are in good agreement with experiments and the DSM gives nearly quantitative agreement. For the broad molecular weight distribution PIB, both the DSM and RDP model predict strain hardening, which is not observed in the experiments.","PeriodicalId":508264,"journal":{"name":"Journal of Rheology","volume":"2 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140365715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
While it is known that the Rolie Poly model is not guaranteed to be thermodynamically consistent, definite examples of a thermodynamically inconsistent prediction have not yet been published. Additionally, the source of the problem (and its historical context) may not be widely known. This work provides additional background information and a definite example of negative entropy production in an experimentally relevant flow, including a discussion of the implications in terms of an experimentally measurable quantity like recoverable strain.
{"title":"Definite example of negative entropy production in the Rolie Poly model","authors":"Charles T. Drucker, Joseph D. Peterson","doi":"10.1122/8.0000815","DOIUrl":"https://doi.org/10.1122/8.0000815","url":null,"abstract":"While it is known that the Rolie Poly model is not guaranteed to be thermodynamically consistent, definite examples of a thermodynamically inconsistent prediction have not yet been published. Additionally, the source of the problem (and its historical context) may not be widely known. This work provides additional background information and a definite example of negative entropy production in an experimentally relevant flow, including a discussion of the implications in terms of an experimentally measurable quantity like recoverable strain.","PeriodicalId":508264,"journal":{"name":"Journal of Rheology","volume":"63 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study theoretically the elongational viscosity (or Trouton ratio, in dimensionless form) for steady viscoelastic flows in confined and symmetric hyperbolic tubes considering Navier-type slip along the wall(s). Both the planar and the cylindrical axisymmetric geometrical configurations are addressed. Under the classic lubrication approximation, and for a variety of constitutive models such as Phan-Thien and Tanner, Giesekus, and Finite Extensibility Nonlinear Elastic with the Peterlin approximation models, the same general analytical formula for the Trouton ratio is derived as for the Oldroyd-B model, in terms of the velocity at the midplane/axis of symmetry and the Deborah number only. Assuming that the velocity field is approximated by the Newtonian lubrication profile, based on our previous study in the absence of slip, we show that a constant extensional strain rate can be achieved in the limits of zero or infinite slip. For finite slip, a slight modification of the geometry is required to achieve a constant strain rate. In these cases, the formula for the steady state Trouton ratio reduces to that for transient homogeneous elongation. We also provide analytical formulae for the modification (decrease) for both the extensional strain rate and the Hencky strain achieved in the confined geometries because of introducing wall slip.
{"title":"On the elongational viscosity of viscoelastic slip flows in hyperbolic confined geometries","authors":"Kostas D. Housiadas, A. Beris","doi":"10.1122/8.0000822","DOIUrl":"https://doi.org/10.1122/8.0000822","url":null,"abstract":"We study theoretically the elongational viscosity (or Trouton ratio, in dimensionless form) for steady viscoelastic flows in confined and symmetric hyperbolic tubes considering Navier-type slip along the wall(s). Both the planar and the cylindrical axisymmetric geometrical configurations are addressed. Under the classic lubrication approximation, and for a variety of constitutive models such as Phan-Thien and Tanner, Giesekus, and Finite Extensibility Nonlinear Elastic with the Peterlin approximation models, the same general analytical formula for the Trouton ratio is derived as for the Oldroyd-B model, in terms of the velocity at the midplane/axis of symmetry and the Deborah number only. Assuming that the velocity field is approximated by the Newtonian lubrication profile, based on our previous study in the absence of slip, we show that a constant extensional strain rate can be achieved in the limits of zero or infinite slip. For finite slip, a slight modification of the geometry is required to achieve a constant strain rate. In these cases, the formula for the steady state Trouton ratio reduces to that for transient homogeneous elongation. We also provide analytical formulae for the modification (decrease) for both the extensional strain rate and the Hencky strain achieved in the confined geometries because of introducing wall slip.","PeriodicalId":508264,"journal":{"name":"Journal of Rheology","volume":"134 27","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140369695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
James J. Griebler, G. Donley, Victoria Wisniewski, Simon A. Rogers
Understanding the yielding of complex fluids is an important rheological challenge that affects our ability to engineer and process materials for a wide variety of applications. Common theoretical understandings of yield stress fluids follow the Oldroyd–Prager formalism in which the material behavior below the yield stress is treated as solidlike, and above the yield stress as liquidlike, with an instantaneous transition between the two states. This formalism was built on a quasi-static approach to the yield stress, while most applications, ranging from material processing to end user applications, involve a transient approach to yielding over a finite timescale. Using stress-controlled oscillatory shear experiments, we show that yield stress fluids flow below their yield stresses. This is quantified through measuring the strain shift, which is the value about which the strain oscillates during a stress-controlled test and is a function of only the unrecoverable strain. Measurements of the strain shift are, therefore, measurements of flow having taken place. These experimental results are compared to the Herschel–Bulkley form of the Saramito model, which utilizes the Oldroyd–Prager formalism, and the recently published Kamani–Donley–Rogers (KDR) model, in which one constitutive equation represents the entire range of material responses. Scaling relationships are derived, which allow us to show why yield stress fluids will flow across all stresses, above and below their yield stress. Finally, derivations are presented that show strain shift can be used to determine average metrics previously attainable only through recovery rheology, and these are experimentally verified.
{"title":"Strain shift measured from stress-controlled oscillatory shear: Evidence for a continuous yielding transition and new techniques to determine recovery rheology measures","authors":"James J. Griebler, G. Donley, Victoria Wisniewski, Simon A. Rogers","doi":"10.1122/8.0000756","DOIUrl":"https://doi.org/10.1122/8.0000756","url":null,"abstract":"Understanding the yielding of complex fluids is an important rheological challenge that affects our ability to engineer and process materials for a wide variety of applications. Common theoretical understandings of yield stress fluids follow the Oldroyd–Prager formalism in which the material behavior below the yield stress is treated as solidlike, and above the yield stress as liquidlike, with an instantaneous transition between the two states. This formalism was built on a quasi-static approach to the yield stress, while most applications, ranging from material processing to end user applications, involve a transient approach to yielding over a finite timescale. Using stress-controlled oscillatory shear experiments, we show that yield stress fluids flow below their yield stresses. This is quantified through measuring the strain shift, which is the value about which the strain oscillates during a stress-controlled test and is a function of only the unrecoverable strain. Measurements of the strain shift are, therefore, measurements of flow having taken place. These experimental results are compared to the Herschel–Bulkley form of the Saramito model, which utilizes the Oldroyd–Prager formalism, and the recently published Kamani–Donley–Rogers (KDR) model, in which one constitutive equation represents the entire range of material responses. Scaling relationships are derived, which allow us to show why yield stress fluids will flow across all stresses, above and below their yield stress. Finally, derivations are presented that show strain shift can be used to determine average metrics previously attainable only through recovery rheology, and these are experimentally verified.","PeriodicalId":508264,"journal":{"name":"Journal of Rheology","volume":"24 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140374190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper calculates for liquid mixtures of high and low molecular weight components, how many solute molecules flow on the average conjointly. The application of the approach to solutions of poly(dimethyl siloxane) in its pentamer, to suspensions of gibbsite (Al(OH)3) in dimethyl sulfoxide, and to human blood testifies that the approach is applicable without restrictions regarding the chemical nature of the high molecular weight compound. The shear thinning of the systems under investigation can be understood in terms of a reduction of the shear-overlap parameter Σ, where the generalized intrinsic viscosity {η} constitutes the central property governing the composition and shear rate dependence of the viscosities. Furthermore, the present analysis demonstrates that intrinsic viscosities can be determined for all solutes and that they decrease with rising shear rates according to a Boltzmann sigmoid for the systems DMS5/PDMS and blood. The comparison of the hydrodynamic specific volumes of the solutes (i.e., of [η]) with the corresponding specific volumes in the pure state leads to the conclusion that solutes that cannot interpenetrate carry a considerable amount of solvent piggyback with them when flowing. In addition to the pure description of the observations, the approach was able to point to new phenomena, e.g., the solidification of the gibbsite suspensions beyond a characteristic solute concentration, which shifts to higher values with increasing shear rates. Because of its general nature, the present approach should become helpful, above all in the areas of technology (reactions in flowing systems) and health (rheology of blood).
{"title":"A cluster approach to rationalize shear thinning: Application to polymer solutions and suspension fluids","authors":"Bernhard A. Wolf","doi":"10.1122/8.0000785","DOIUrl":"https://doi.org/10.1122/8.0000785","url":null,"abstract":"This paper calculates for liquid mixtures of high and low molecular weight components, how many solute molecules flow on the average conjointly. The application of the approach to solutions of poly(dimethyl siloxane) in its pentamer, to suspensions of gibbsite (Al(OH)3) in dimethyl sulfoxide, and to human blood testifies that the approach is applicable without restrictions regarding the chemical nature of the high molecular weight compound. The shear thinning of the systems under investigation can be understood in terms of a reduction of the shear-overlap parameter Σ, where the generalized intrinsic viscosity {η} constitutes the central property governing the composition and shear rate dependence of the viscosities. Furthermore, the present analysis demonstrates that intrinsic viscosities can be determined for all solutes and that they decrease with rising shear rates according to a Boltzmann sigmoid for the systems DMS5/PDMS and blood. The comparison of the hydrodynamic specific volumes of the solutes (i.e., of [η]) with the corresponding specific volumes in the pure state leads to the conclusion that solutes that cannot interpenetrate carry a considerable amount of solvent piggyback with them when flowing. In addition to the pure description of the observations, the approach was able to point to new phenomena, e.g., the solidification of the gibbsite suspensions beyond a characteristic solute concentration, which shifts to higher values with increasing shear rates. Because of its general nature, the present approach should become helpful, above all in the areas of technology (reactions in flowing systems) and health (rheology of blood).","PeriodicalId":508264,"journal":{"name":"Journal of Rheology","volume":"10 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140377250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wouter Peerbooms, Tim Nadorp, Antoine van der Heijden, W. Breugem
In the literature, two different frameworks exist for describing the rheology of solid/liquid suspensions: (1) the “viscous” framework in terms of the relative suspension viscosity, ηr, as a function of the reduced solid volume fraction, ϕ/ϕm, with ϕm the maximum flowable packing fraction, and (2) the “frictional” framework in terms of a macroscopic friction coefficient, μ, as a function of the viscous number, Iv, defined as the ratio of the viscous shear to the wall-normal particle stress. Our goal is to compare the two different frameworks, focusing on the effect of friction between particles. We have conducted a particle-resolved direct numerical simulation study of a dense non-Brownian suspension of neutrally buoyant spheres in slow plane Couette flow. We varied the bulk solid volume fraction from ϕb=0.1 to 0.6 and considered three different Coulomb friction coefficients: μc=0, 0.2, and 0.39. We find that ηr scales well with ϕ/ϕm, with ϕm obtained from fitting the Maron–Pierce correlation. We also find that μ scales well with Iv. Furthermore, we find a monotonic relation between ϕ/ϕm and Iv, which depends only weakly on μc. Since ηr=μ/Iv, we thus find that the two frameworks are largely equivalent and that both account implicitly for Coulomb friction. However, we find that the normal particle stress differences, N1 and N2, when normalized with the total shear stress and plotted against either ϕ/ϕm or Iv, remain explicitly dependent on μc in a manner that is not yet fully understood.
在文献中，有两种不同的框架用于描述固/液悬浮液的流变性：(1) "粘性 "框架，以相对悬浮粘度 ηr 作为还原固体体积分数 ϕ/ϕm 的函数，其中 ϕm 为最大可流动堆积分数；(2) "摩擦 "框架，以宏观摩擦系数 μ 作为粘性数 Iv 的函数，粘性数 Iv 定义为粘性剪切力与颗粒壁面法向应力之比。我们的目标是比较这两种不同的框架，重点关注颗粒间摩擦的影响。我们对中性浮力球体在慢平面库特流中的致密非布朗悬浮液进行了粒子分辨直接数值模拟研究。我们将固体体积分数从 ϕb=0.1 变为 0.6，并考虑了三种不同的库仑摩擦系数：μc=0、0.2 和 0.39。我们发现 ηr 与 ϕ/ϕm 的比例关系很好，其中 ϕm 是通过拟合马龙-皮尔斯相关性得到的。我们还发现，μ 与 Iv 的关系也很好。此外，我们还发现 ϕ/ϕm 与 Iv 之间存在单调关系，而 Iv 只微弱地依赖于 μc。由于ηr=μ/Iv，我们发现这两个框架在很大程度上是等价的，而且都隐含地考虑了库仑摩擦。然而，我们发现，当将法向颗粒应力差 N1 和 N2 与总剪切应力进行归一化并绘制成 ϕ/ϕm 或 Iv 图时，它们仍然以一种尚未完全理解的方式明确依赖于 μc。
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