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Konstantinou PC, Stephanou PS. Predicting High-Density Polyethylene Melt Rheology Using a Multimode Tube Model Derived Using Non-Equilibrium Thermodynamics. Polymers (Basel) 2023; 15:3322. [PMID: 37571216 PMCID: PMC10422373 DOI: 10.3390/polym15153322] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Revised: 07/31/2023] [Accepted: 08/03/2023] [Indexed: 08/13/2023] Open
Abstract
Based on the Generalized bracket, or Beris-Edwards, formalism of non-equilibrium thermodynamics, we recently proposed a new differential constitutive model for the rheological study of entangled polymer melts and solutions. It amended the shortcomings of a previous model that was too strict regarding the values of the convective constraint release parameter for the model not to violate the second law of thermodynamics, and it has been shown capable of predicting a transient stress undershoot (following the overshoot) at high shear rates. In this study, we wish to further examine this model's capability to predict the rheological response of industrial polymer systems by extending it to its multiple-mode version. The comparison with industrial rheological data (High-Density Polyethylene resins), which was based on comparison with experimental data available in (a) Small Amplitude Oscillatory shear, (b) start-up shear, and (c) start-up uniaxial elongation, was noted to be good.
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Affiliation(s)
| | - Pavlos S. Stephanou
- Department of Chemical Engineering, Cyprus University of Technology, P.O. Box 50329, 3603 Limassol, Cyprus;
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2
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Stephanou PS. Elucidating the rheological implications of adding particles in blood. RHEOLOGICA ACTA 2021; 60:603-616. [PMID: 34334825 PMCID: PMC8313244 DOI: 10.1007/s00397-021-01289-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Revised: 06/29/2021] [Accepted: 06/30/2021] [Indexed: 06/13/2023]
Abstract
UNLABELLED In the past few decades, nanotechnology has been employed to provide breakthroughs in the diagnosis and treatment of several diseases using drug-carrying particles (DCPs). In such an endeavor, the optimal design of DCPs is paramount, which necessitates the use of an accurate and trustworthy constitutive model in computational fluid dynamics (CFD) simulators. We herein introduce a continuum model for elaborating on the rheological implications of adding particles in blood. The model is developed using non-equilibrium thermodynamics to guarantee thermodynamic admissibility. Red blood cells are modeled as deformed droplets with a constant volume that are able to aggregate, whereas particles are considered rigid spheroids. The model predictions are compared favorably against rheological data for both spherical and non-spherical particles immersed in non-aggregating blood. It is expected that the use of this model will allow for the testing of DCPs in virtual patients and for their tailor-design in treating various diseases. SUPPLEMENTARY INFORMATION The online version contains supplementary material available at 10.1007/s00397-021-01289-x.
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Affiliation(s)
- Pavlos S. Stephanou
- Department of Chemical Engineering, Cyprus University of Technology, PO Box 50329, 3603 Limassol, Cyprus
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Stephanou PS, Tsimouri IC. A constitutive hemorheological model addressing the deformability of red blood cells in Ringer solutions. SOFT MATTER 2020; 16:7585-7597. [PMID: 32812628 DOI: 10.1039/d0sm00974a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Red blood cells (RBCs) can deform substantially, a feature that allows them to pass through capillaries that are narrower than the largest dimension of an undeformed RBC. Clearly, to understand how they transport through our microcirculation, we need a constitutive model able of accurately predicting the deformability of RBCs, which seems currently unavailable. To address this void, we herein propose a new model that accounts for the deformability of RBCs by modeling them as deformed droplets with a constant volume. To make sure the model is by construction thermodynamically admissible we employ non-equilibrium thermodynamics as our tool. Since RBCs are merely droplets with the inner fluid exhibiting a higher viscosity than that of the outer one, RBCs are described by a conformation tensor constrained to have a constant determinant (volume). The model predicts the second normal stress coefficient in steady-state simple shear flow to first shear thicken and then shear thin, which is an unexpected behavior; however, we cannot judge whether such a prediction is aphysical or not due to unavailable experimental rheological data in the literature. We show that the new model is capable of addressing the deformability of isolated (very low hematocrit) RBCs in simple shear and the shear viscosity of non-aggregating blood. As derived the model addresses only non-aggregating blood, but can very easily be generalized to account for aggregating blood.
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Affiliation(s)
- Pavlos S Stephanou
- Department of Chemical Engineering, Cyprus University of Technology, PO Box 50329, 3603 Limassol, Cyprus.
| | - Ioanna Ch Tsimouri
- Department of Materials, Polymer Physics, ETH Zürich, CH-8093 Zürich, Switzerland
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Simple, Accurate and User-Friendly Differential Constitutive Model for the Rheology of Entangled Polymer Melts and Solutions from Nonequilibrium Thermodynamics. MATERIALS 2020; 13:ma13122867. [PMID: 32604858 PMCID: PMC7345944 DOI: 10.3390/ma13122867] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Revised: 06/18/2020] [Accepted: 06/22/2020] [Indexed: 11/23/2022]
Abstract
In a recent reformulation of the Marrucci-Ianniruberto constitutive equation for the rheology of entangled polymer melts in the context of nonequilibrium thermodynamics, rather large values of the convective constraint release parameter βccr had to be used in order for the model not to violate the second law of thermodynamics. In this work, we present an appropriate modification of the model, which avoids the splitting of the evolution equation for the conformation tensor into an orientation and a stretching part. Then, thermodynamic admissibility simply dictates that βccr ≥ 0, thus allowing for more realistic values of βccr to be chosen. Moreover, and in view of recent experimental evidence for a transient stress undershoot (following the overshoot) at high shear rates, whose origin may be traced back to molecular tumbling, we have incorporated additional terms into the model accounting, at least in an approximate way, for non-affine deformation through a slip parameter ξ. Use of the new model to describe available experimental data for the transient and steady-state shear and elongational rheology of entangled polystyrene melts and concentrated solutions shows close agreement. Overall, the modified model proposed here combines simplicity with accuracy, which renders it an excellent choice for managing complex viscoelastic fluid flows in large-scale numerical calculations.
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Stephanou PS, Kröger M. Assessment of the Tumbling-Snake Model against Linear and Nonlinear Rheological Data of Bidisperse Polymer Blends. Polymers (Basel) 2019; 11:E376. [PMID: 30960360 PMCID: PMC6419188 DOI: 10.3390/polym11020376] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Revised: 02/12/2019] [Accepted: 02/16/2019] [Indexed: 11/16/2022] Open
Abstract
We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the academic case of a monodisperse sample. Here, we extend these studies and provide the stationary solutions of the tumbling-snake model both analytically, for small shear rates, and via Brownian dynamics simulations, for a bidisperse sample over a wide range of shear rates and model parameters. We further show that the tumbling-snake model bears the necessary capacity to compare well with available linear and non-linear rheological data for bidisperse systems. This capacity is added to the already documented ability of the model to accurately predict the shear rheology of monodisperse systems.
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Affiliation(s)
- Pavlos S Stephanou
- Modeling Department, Novamechanics Ltd., P.O. Box 26014, 1666 Nicosia, Cyprus.
- Department of Environmental Science and Technology, Cyprus University of Technology, PO Box 50329, 3603 Limassol, Cyprus.
| | - Martin Kröger
- Polymer Physics, Department of Materials, ETH Zurich, CH⁻8093 Zurich, Switzerland.
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Stephanou PS, Georgiou GG. A nonequilibrium thermodynamics perspective of thixotropy. J Chem Phys 2019; 149:244902. [PMID: 30599698 DOI: 10.1063/1.5049397] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a new description of elasto-viscoplastic fluids by relating the notion of thixotropy directly to internal viscoelasticity and network structures through a general, thermodynamically consistent approach. By means of non-equilibrium thermodynamics, a thermodynamically admissible elasto-viscoplastic model is derived which introduces self-consistently and effortlessly thixotropic effects and reproduces at both low and high shear rates experimental data usually fitted with empirical constitutive equations, such as the Bingham and Herschel-Bulkley models. The predictions of the new model are in very good agreement with available steady-state shear rheological data for soft colloidal pastes and blood, i.e., systems exhibiting a yield stress, and with time-dependent rheological data for blood, i.e., during a triangular time-dependent change in the shear rate, exhibiting a hysteresis. The proposed approach is expected to provide the means to improve our understanding of thixotropic fluids.
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Affiliation(s)
- Pavlos S Stephanou
- Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
| | - Georgios G Georgiou
- Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
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Tang X, Yang J, Tian F, Xu T, Xie C, Chen W, Li L. Flow-induced density fluctuation assisted nucleation in polyethylene. J Chem Phys 2018; 149:224901. [PMID: 30553254 DOI: 10.1063/1.5054273] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Xiaoliang Tang
- National Synchrotron Radiation Lab and CAS Key Laboratory of Soft Matter Chemistry, Anhui Provincial Engineering Laboratory of Advanced Functional Polymer Film, University of Science and Technology of China, Hefei, China
| | - Junsheng Yang
- National Synchrotron Radiation Lab and CAS Key Laboratory of Soft Matter Chemistry, Anhui Provincial Engineering Laboratory of Advanced Functional Polymer Film, University of Science and Technology of China, Hefei, China
- Computational Physics Key Laboratory of Sichuan Province, Yibin University, Yibin, China
| | - Fucheng Tian
- National Synchrotron Radiation Lab and CAS Key Laboratory of Soft Matter Chemistry, Anhui Provincial Engineering Laboratory of Advanced Functional Polymer Film, University of Science and Technology of China, Hefei, China
| | - Tingyu Xu
- National Synchrotron Radiation Lab and CAS Key Laboratory of Soft Matter Chemistry, Anhui Provincial Engineering Laboratory of Advanced Functional Polymer Film, University of Science and Technology of China, Hefei, China
| | - Chun Xie
- National Synchrotron Radiation Lab and CAS Key Laboratory of Soft Matter Chemistry, Anhui Provincial Engineering Laboratory of Advanced Functional Polymer Film, University of Science and Technology of China, Hefei, China
| | - Wei Chen
- National Synchrotron Radiation Lab and CAS Key Laboratory of Soft Matter Chemistry, Anhui Provincial Engineering Laboratory of Advanced Functional Polymer Film, University of Science and Technology of China, Hefei, China
| | - Liangbin Li
- National Synchrotron Radiation Lab and CAS Key Laboratory of Soft Matter Chemistry, Anhui Provincial Engineering Laboratory of Advanced Functional Polymer Film, University of Science and Technology of China, Hefei, China
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Stephanou PS, Kröger M. From intermediate anisotropic to isotropic friction at large strain rates to account for viscosity thickening in polymer solutions. J Chem Phys 2018; 148:184903. [PMID: 29764144 DOI: 10.1063/1.5019337] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The steady-state extensional viscosity of dense polymeric liquids in elongational flows is known to be peculiar in the sense that for entangled polymer melts it monotonically decreases-whereas for concentrated polymer solutions it increases-with increasing strain rate beyond the inverse Rouse time. To shed light on this issue, we solve the kinetic theory model for concentrated polymer solutions and entangled melts proposed by Curtiss and Bird, also known as the tumbling-snake model, supplemented by a variable link tension coefficient that we relate to the uniaxial nematic order parameter of the polymer. As a result, the friction tensor is increasingly becoming isotropic at large strain rates as the polymer concentration decreases, and the model is seen to capture the experimentally observed behavior. Additional refinements may supplement the present model to capture very strong flows. We furthermore derive analytic expressions for small rates and the linear viscoelastic behavior. This work builds upon our earlier work on the use of the tumbling-snake model under shear and demonstrates its capacity to improve our microscopic understanding of the rheology of entangled polymer melts and concentrated polymer solutions.
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Affiliation(s)
- Pavlos S Stephanou
- Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
| | - Martin Kröger
- Department of Materials, Polymer Physics, ETH Zürich, CH-8093 Zürich, Switzerland
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Stephanou PS, Kröger M. Tumbling-Snake Model for Polymeric Liquids Subjected to Biaxial Elongational Flows with a Focus on Planar Elongation. Polymers (Basel) 2018; 10:E329. [PMID: 30966364 PMCID: PMC6415193 DOI: 10.3390/polym10030329] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2018] [Revised: 03/14/2018] [Accepted: 03/14/2018] [Indexed: 02/02/2023] Open
Abstract
We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate.
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Affiliation(s)
- Pavlos S Stephanou
- Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, Nicosia 1678, Cyprus.
| | - Martin Kröger
- Polymer Physics, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland.
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Stephanou PS, Kröger M. Non-constant link tension coefficient in the tumbling-snake model subjected to simple shear. J Chem Phys 2017; 147:174903. [DOI: 10.1063/1.4991935] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pavlos S. Stephanou
- Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
| | - Martin Kröger
- Department of Materials, Polymer Physics, ETH Zürich, CH-8093 Zürich, Switzerland
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11
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Sgouros AP, Megariotis G, Theodorou DN. Slip-Spring Model for the Linear and Nonlinear Viscoelastic Properties of Molten Polyethylene Derived from Atomistic Simulations. Macromolecules 2017. [DOI: 10.1021/acs.macromol.7b00694] [Citation(s) in RCA: 41] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- A. P. Sgouros
- School of Chemical Engineering, National Technical University of Athens (NTUA),GR-15780 Athens, Greece
| | - G. Megariotis
- School of Chemical Engineering, National Technical University of Athens (NTUA),GR-15780 Athens, Greece
| | - D. N. Theodorou
- School of Chemical Engineering, National Technical University of Athens (NTUA),GR-15780 Athens, Greece
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