July 26, 2017
7:00 – 8:20
Registration
8:20 – 8:30
Welcome
FLOW INSTABILITIES
(Chairman: Yong Woo Inn)
8:30 – 9:00
The Extrudate Swell of HDPE: Rheological Effects
Autors:
Vinod Kumar Konaganti 1), Mahmoud Ansari 1), Evan Mitsoulis 2) and Savvas G. Hatzikiriakos 1, a)
Affiliations:
1) Department of Chemical and Biological Engineering, The University of British Columbia, Vancouver, BC, Canada.
2) School of Mining Engineering and Metallurgy, National Technical University of Athens, 157 80, Athens, Greece.
Contact:
a) Corresponding author:
Abstract:
The extrudate swell of an industrial grade high molecular weight high-density polyethylene (HDPE) in capillary dies is studied experimentally and numerically using the integral K-BKZ constitutive model. The non-linear viscoelastic flow properties of the polymer resin are studied for a broad range of large step shear strains and high shear rates using the cone partitioned plate (CPP) geometry of the stress/strain controlled rotational rheometer. This allowed the determination of the rheological parameters accurately, in particular the damping function, which is proven to be the most important in simulating transient flows such as extrudate swell. A series of simulations performed using the integral K-BKZ Wagner model with different values of the Wagner exponent n, ranging from n=0.15 to 0.5, demonstrates that the extrudate swell predictions are extremely sensitive to the Wagner damping function exponent. Using the correct n-value resulted in extrudate swell predictions that are in excellent agreement with experimental measurements.
Savvas George Hatzikiriakos | The University of British Columbia | Canada
9:00 – 9:30
Slip and Frictional Heating of Extruded Polyethylene Melts
Autors:
José Pérez-González 1, a), Benjamín M. Marín-Santibáñez 2), Héctor S. Zamora-López 2) and Francisco Rodríguez-González 3)
Affiliations:
1) Laboratorio de Reología y Física de la Materia Blanda, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, U. P. Adolfo López Mateos Edif. 9, C. P. 07738, Ciudad de México, México.
2) Escuela Superior de Ingeniería Química e Industrias Extractivas, Instituto Politécnico Nacional, U. P. Adolfo López Mateos Edif. 8, 3er piso, C. P. 07738, Ciudad de México, México.
3) Departamento de Biotecnología, Centro de Desarrollo de Productos Bióticos, Instituto Politécnico Nacional, Col. San Isidro, C.P. 62731. Yautepec, Morelos, México.
Contact:
a) Corresponding author:
Abstract:
Extrusion of polymer melts with slip at the die generates frictional heating. The relationship between slip flow and frictional heating during the continuous extrusion of a non-slipping linear low-density (LLDPE) and a slipping high-density polyethylene (HDPE), respectively, both pure as well as blended with a fluoropolymer processing aid (PA), was investigated in this work by Rheo-particle image velocimetry and thermal imaging. Significant rises in temperature were measured under slip and no slip conditions, being these much higher than the values predicted by the adiabatic flow assumption. Clear difference was made between viscous and frictional heating before the stick-slip regime for the LLDPE, even though they could not be distinguished from one another at higher stresses. Such a difference, however, could not be made for the slipping HDPE, since overall in the presence of slip, frictional and viscous heating act synergistically to increase the melt temperature.
José Pérez-González | Instituto Politécnico Nacional | Mexico
9:30 – 10:00
Cofee break & Exhibition
APPLIED RHEOLOGY
(Chairman: George Hatzikiriakos)
10:00 – 10:30
Polymer Melt Rheology and Flow Simulations Applied to Cast Film Extrusion Die Design: An Industrial Perspective
Autor:
Olivier Catherine
Affiliation:
Cloeren Incorporated, 401 16th Street – Orange Texas 77630, United States of America.
Contact:
Corresponding author:
Abstract:
This article is an overview of the techniques used today in the area of rheology and flow simulation, on the industrial level, for cast film extrusion die design. This industry has made significant progress over the past three decades and die and feedblock design and optimization certainly have been instrumental in the overall improvement. Dies and coextrusion feedblocks are a critical aspect of the process due to the layering and forming function, which drive the final product economics and properties. Polymer melt rheology is a key aspect to consider when optimizing the flow patterns in the extrusion equipment. Not only is rheology critical for the flow channel design when aiming at obtaining a uniform flow distribution at the die exit, but also it is playing a major role in the thermal aspect of the flow due to the strong mechanical and thermal coupling. This coupling comes, on one hand, from the occurrence of viscous dissipation in the flow and on the other hand from the significant temperature dependency of melt viscosity. Viscous dissipation is due to relatively high melt viscosities and strain rates, especially with today’s processes which involve formidable extrusion speeds. The third aspect discussed in this paper is the complexity of residence time distribution in modern flow channels, which is evaluated with advanced three-dimensional flow simulation and particle tracking.
Olivier Catherine | Cloeren Incorporated | USA
10:30 – 11:00
Rheological Characterization and Thermal Modeling of Polyolefins for Process Design and Tailored Interfaces
Autors:
Alex M. Jordan 1), Kyungtae Kim 1), Frank S. Bates 1), Christopher W. Macosko 1, a), Shaffiq Jaffer 2) and Olivier Lhost 2)
Affiliations:
1) Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, MN 55455, USA.
2) Total, S.A., Tour Coupole – 2, place Jean Millier 92078 Paris La Défense Cedex, France.
Contact:
a) Corresponding author:
Abstract:
While chemically similar, it has long been known that polyethylene (PE) and polypropylene (PP) are immiscible and suffer poor interfacial adhesion when processed as layered films or blends. In this paper we present an examination of the effect that processing conditions, such as extrusion residence time and post-extrusion take-up, have on the interfacial adhesion between PE and PP. We show that transient heat transfer analysis and rheological measurement can be used to determine processing conditions, which maximize adhesion between immiscible polymer pairs.
Christopher W. Macosko | University of Minnesota | USA
11:00 – 11:30
Applied Rheology for Understanding Flow Instabilities in Polymer Processing
Autor:
Martin Zatloukal
Affiliation:
Polymer Centre, Faculty of Technology, Tomas Bata University in Zlín, Vavrečkova 275, 760 01, Zlín, Czech Republic.
Contact:
Corresponding author:
Abstract:
Due to the fact that polymer melts behaves as nonNewtonian viscoelastic fluids, their flow behavior is rather complex and leads to number of flow phenomena which have negative impact on their processing and final product properties. The polymer melt elasticity, high shear viscosity, extensional viscosity and its tendency to slip at the solid surfaces causes the flow destabilization. Typical flow instabilities occurring during polymer processing are die drool, neck-in, dog-bone effect, draw resonance, interfacial instabilities in coextrusion as well as number of instabilities occurring in film blowing and melt blowing technologies such as snaking, freezeline height instability, bubble breathing and flutter, heavy-bubble instability, whipping, extrudate breakup, flies, shots, jam and melt spraying. In this work, it is demonstrated how the polymer melt rheology and modeling of polymer processing can be used to understand and minimize some the above mentioned flow instabilities.
Martin Zatloukal | Tomas Bata University in Zlin | Czech Republic
11:30 – 12:00
Worm Melt Fracture and Fast Die Build-up at High Shear Rates in Extrusion Blow Molding of Large Drums
Autors:
Yong Woo Inn a) and Ashish M. Sukhadia
Affiliation:
Chevron Phillips Chemical Company LP Bartlesville Research and Technology Center Bartlesville, OK 74004-0001, USA.
Contact:
a) Corresponding author:
Abstract:
In the extrusion blow molding process of high density polyethylene (HDPE) for making of large size drums, string-like defects, which are referred to as worm melt fracture in the industry, are often observed on the extrudate surface. Such string-like defects in various shapes and sizes are observed in capillary extrusion at very high shear rates after the slip-stick transition. The HDPE resin with broader molecular weight distribution (MWD) exhibits a greater degree of worm melt fracture while the narrow MWD PE resin, which has higher slip velocity and a uniform slip layer, shows a lesser degree of worm melt fracture. It is hypothesized that the worm melt fracture is related to fast die build-up and cohesive slip layer, a failure within the polymer melts at an internal surface. If the cohesive slip layer at an internal surface emerges out from the die, it can be attached on the surface of extrudate as string-like defects, the worm melt fracture. The resin having more small chains and lower plateau modulus can be easier to have such an internal failure and consequently exhibit more “worm” defects.
Yong Woo Inn | Chevron Phillips Chemical Company LP | USA
12:00 – 13:30
Lunch & Exhibition
ELONGATIONAL RHEOLOGY
(Chairman: Helmut Münstedt)
13:30 – 14:00
Long Chain Branching of PLA
Autors:
Liangliang Gu 1), Yuewen Xu 2, 3), Grant Fahnhorst 3) and Christopher W. Macosko 1, a)
Affiliations:
1) Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA.
2) present address: Void Technologies, Neenah, WI 54956, USA.
3) Department of Chemistry, University of Minnesota, 07 Pleasant St SE, Minneapolis, MN 55455, USA.
Contact:
a) Corresponding author:
Abstract:
A trifunctional aziridine linker, trimethylolpropane tris(2-methyl-1-aziridinepropionate) (TTMAP), was melt blended with linear polylactic acid (PLA) to make star branched PLA. Adding pyromellitic dianhydride (PMDA) led to long chain branched (LCB) PLA. Mixing torque evolution during melt processing revealed high reactivity of aziridine with the carboxyl end group on PLA and an incomplete reaction of PMDA with the hydroxyl end group. Star-shaped PLA exhibited higher viscosity but no strain hardening in extensional flow while LCB PLA showed significant extensional hardening. Excess TTMAP in the branching reaction resulted in gel formation, which led to failure at low strain in extension. PMDA conversion was estimated based on gelation theory. The strain rate dependence of extensional hardening indicated that the LCB PLA had a low concentration of long chain branched molecules with an H-shaped topology. Unlike current methods used to branch PLA, free radical chemistry or use of an epoxy functional oligomers, our branching strategy produced strain hardening with less increase in shear viscosity. This study provides guidelines for design of polymers with low shear viscosity, which reduces pressure drop in extrusion, combined with strong extensional hardening, which enhances performance in processes that involve melt stretching.
Christopher W. Macosko | University of Minnesota | USA
14:00 – 14:30
Shear and Elongational Rheology of Photo-oxidative Degraded HDPE and LLDPE
Autors:
Manfred Hermann Wagner a), Wang Zheng b), Peng Wang c), Sebastián Ramos Talamante d) and Esmaeil Narimissa e)
Affiliation:
Polymer Engineering/Polymer Physics, Berlin Institute of Technology (TU Berlin), Fasanenstrasse 90, 10623 Berlin, Germany.
Contacts:
a) Corresponding author:
b)
c)
d)
e)
Abstract:
The effect of photo-oxidative degradation of high-density polyethylene (HDPE) and linear low-density polyethylene (LLDPE) was investigated by linear and non-linear rheological measurements. The linear-viscoelastic rheological measurements were performed at different temperatures, while the elongational viscosity was measured at 170°C and at different strain rates. The rheological data are indicative of structural changes caused by photo-oxidative degradation including formation of long-chain branches (LCB), cross-linking, and chain scission, and they revealed a cyclic and continuing competition between chain scission and LCB/gel formation. These findings are supported by additional FTIR measurements and direct measurements of the gel content of the degraded samples.
Manfred Hermann Wagner | Berlin Institute of Technology (TU Berlin) | Germany
14:30 – 15:00
Cofee break & Exhibition
NOVEL RHEOLOGICAL TECHNIQUES
(Chairman: Christopher W. Macosko)
15:00 – 15:30
The Intrinsic Mechanical Nonlinearity 3Q0(ω) of Linear Homopolymer Melts
Autors:
Miriam Angela Cziep b), Mahdi Abbasi c) and Manfred Wilhelm a)
Affiliation:
Institute of Chemical Technology and Polymer Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
Contacts:
a) Corresponding author:
b)
c)
Abstract:
Medium amplitude oscillatory shear (MAOS) in combination with Fourier Transformation of the mechanical stress signal (FT rheology) was utilized to investigate the influence of molecular weight, molecular weight distribution and the monomer on the intrinsic nonlinearity 3Q0(ω). Nonlinear master curves of 3Q0(ω) have been created, applying the time-temperature superposition (TTS) principle. These master curves showed a characteristic shape with an increasing slope at small frequencies, a maximum 3Q0, max and a decreasing slope at high frequencies. 3Q0(De) master curves of monodisperse polymers were evaluated and quantified with the help of a semi-empiric equation, derived from predictions from the pom-pom and molecular stress function (MSF) models. This resulted in a monomer independent description of the nonlinear mechanical behavior of linear, monodisperse homopolymer melts, where 3Q0(ω,Z) is only a function of the frequency ω and the number of entanglements Z. For polydisperse samples, 3Q0(ω) showed a high sensitivity within the experimental window towards an increasing PDI. At small frequencies, the slope of 3Q0(ω) decreases until approximately zero as a plateau value is reached, starting at a PDI around 2 and higher.
Manfred Wilhelm | Karlsruhe Institute of Technology (KIT), Institute for Chemical Technology and Polymer Chemistry | Germany
15:30 – 16:00
Shear Rheology and 1H TD-NMR Combined to Low-Field RheoNMR: Set-Up and Application to Quiescent and Flow-Induced Crystallization of Polymers
Autors:
Volker Räntzsch 1), Mürüvvet Begüm Özen 1), Karl-Friedrich Ratzsch 1, 2), Gisela Guthausen 1) and Manfred Wilhelm 1, a)
Affiliations:
1) Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.
2) University of Freiburg, Freiburg Materials Research Center (FMF), Freiburg, Germany.
Contact:
a) Corresponding author:
Abstract:
Rheology provides access to the flow properties of soft matter, while 1H TD-NMR is a useful technique for the characterization of molecular dynamics. To achieve greater insight into the interplay of these domains, especially under flow, it is desirable to combine these two methods in one set-up. We present a low-field RheoNMR set-up based on a portable 30 MHz 1H NMR unit that was integrated into a commercial strain-controlled shear rheometer. This unique combination can simultaneously conduct a full rheological characterization (G’, G”, |η*|, FT-Rheology: I3/1, Q0) while monitoring molecular dynamics in-situ via 1H TD-NMR for temperatures from -15 to +210 °C. Possible applications include the quantitative measurement of the composition in multiphase systems (fats, polymers, etc.) and soft matter during the application of flow, e.g. measurements on the flow-induced crystallization of polymers.
Manfred Wilhelm | Karlsruhe Institute of Technology (KIT), Institute for Chemical Technology and Polymer Chemistry | Germany
18:30
Conference dinner
July 27, 2017
RHEOLOGY OF POLYMER BLENDS AND COMPOSITES
(Chairman: José Pérez-González)
8:00 – 8:30
Droplet Size in Flow: Theoretical Model and Application to Polymer Blends
Autors:
Ivan Fortelný a) and Josef Jůza b)
Affiliation:
Institute of Macromolecular Chemistry, Czech Academy of Sciences, Heyrovského nám. 2, 162 06 Prague 6, Czech Republic.
Contacts:
a) Corresponding author:
b)
Abstract:
The paper is focused on prediction of the average droplet radius, R, in flowing polymer blends where the droplet size is determined by dynamic equilibrium between the droplet breakup and coalescence. Expressions for the droplet breakup frequency in systems with low and high contents of the dispersed phase are derived using available theoretical and experimental results for model blends. Dependences of the coalescence probability, Pc, on system parameters, following from recent theories, is considered and approximate equation for Pc in a system with a low polydispersity in the droplet size is proposed. Equations for R in systems with low and high contents of the dispersed phase are derived. Combination of these equations predicts realistic dependence of R on the volume fraction of dispersed droplets, φ. Theoretical prediction of the ratio of R to the critical droplet radius at breakup agrees fairly well with experimental values for steadily mixed polymer blends.
Ivan Fortelný | Institute of Macromolecular Chemistry ASCR | Czech Republic
8:30 – 9:00
Rheological Properties of Conductive Polymer Composites around the Electrical Percolation Threshold
Autors:
Zdeněk Starý 1, a) and Helmut Münstedt 2, b)
Affiliations:
1) Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Heyrovsky Sq. 2, 162 06 Prague 6, Czech Republic.
2) Institute of Polymer Materials, Friedrich-Alexander University Erlangen-Nürnberg, Martensstrasse 7, D-91058 Erlangen, Germany.
Contacts:
a) Corresponding author:
b)
Abstract:
The electrical conductivity of polymeric materials containing conductive particles shows a typical percolation behavior. Besides this effect adding the particles to a polymer matrix affects the rheological properties considerably. In the literature one can find some studies relating the electrical percolation to a comparable change of rheological quantities. The term “rheological percolation” is introduced; however, its definition is not consistent in the literature. In this contribution some literature data obtained from dynamic-mechanical measurements are discussed and confronted with own data from oscillatory and creep-recovery measurements. From a critical evaluation of the data it follows that rheological properties change continuously with the filler content in the range of the electrical percolation threshold. A simple model is proposed to explain the differences between the electrical and rheological behavior of polymer composites.
Zdeněk Starý | Institute of Macromolecular Chemistry ASCR | Czech Republic
9:00 – 10:30
Cofee break & Poster section & Exhibition
An Examination of the Differential Constitutive Models under Large Amplitude Oscillatory Shear Flow
Autors:
Radek Pivokonsky a), Petr Filip, Jana Zelenkova and Blanka Ledvinkova
Affiliation:
Institute of Hydrodynamics, Acad. Sci. Czech Rep., Pod Patankou 5, 166 12 Prague, Czech Republic.
Contact:
a) Corresponding author:
Abstract:
The exponential Phan-Tien and Tanner, Giesekus, Leonov, and modified eXtended Pom-Pom models are examined under large amplitude oscillatory shear flows using poly(ethylene oxide) solution. Optimization of the nonlinear adjustable parameters of the individual models is based on Fourier transform coefficients of the largest amplitude oscillatory shear characteristics where both magnitude and phase are taken into account. An efficiency of the individual models is shown for large amplitude oscillatory shear characteristics as well as for steady shear characteristics.
Radek Pivokonsky | Institute of Hydrodynamics ASCR | Czech Republic
Viscoelastic Rate Type Fluids with Temperature Dependent Material Parameters – Stability of the Rest State
Autors:
Judith Stein 1, a) and Vít Průša 2, b)
Affiliations:
1) Institute of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Heidelberg University, Im Neuenheimer Feld 205, Heidelberg, DE 69120, Germany.
2) Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 8 – Karlín, CZ 186 75, Czech Republic.
Contacts:
a)
b) Corresponding author:
Abstract:
We study the dynamics of small perturbations to the rest state of a viscoelastic rate type fluid with temperature dependent material parameters. We show that if the material parameters are chosen appropriately, then the quiescent state of the fluid filling an isolated (mechanically, thermally) vessel is a stable state. The outlined analysis explicitly documents the importance of thermodynamic analysis in the development of advanced models for complex fluids.
Vít Průša | Charles University in Prague | Czech Republic
Investigation of Flow Behavior for Linear Melt Blown Polypropylenes with Different Molecular Weights in Very Wide Shear Rate Range
Autors:
Jiri Drabek 1, a), Martin Zatloukal 1, b) and Mike Martyn 2, c)
Affiliations:
1) Polymer Centre, Faculty of Technology, Tomas Bata University in Zlín, Vavrečkova 275, 760 01 Zlín, Czech Republic.
2) IRC in Polymer Engineering, School of Engineering, Design & Technology, University of Bradford, Bradford BD7 1DP, UK.
Contacts:
a)
b) Corresponding author:
c)
Abstract:
In this work, three different linear polypropylenes, with melt flow rate between 450-1200 g.10min-1, have been characterized by using rotational and twin bore capillary rheometer equipped by novel inert orifice die design as well as by the instrumented injection molding machine. The measured data, that shows first as well as second Newtonian plateau, were consequently fitted by four conventional models (Cross, Carreau, Generalized Quemada and Carreau-Yasuda models) as well as by two novel viscosity models (modified Quemada and Carreau models) suggested here for the first time. It has been found that modified 5-parametric Carreau model has the highest capability to describe the measured shear viscosity data for given polymer melts.
Jiri Drabek | Tomas Bata University in Zlin | Czech Republic
Effect of Second to First Normal Stress Difference Ratio at the Die Exit on Neck-in Phenomenon in Polymeric Flat Film Production
Autors:
Tomas Barborik a) and Martin Zatloukal b)
Affiliation:
Polymer Centre, Faculty of Technology, Tomas Bata University in Zlín, Vavreckova 275, 760 01 Zlin, Czech Republic.
Contacts:
a)
b) Corresponding author:
Abstract:
In this study, viscoelastic modeling of the extrusion film casting process, based on the 1D membrane model and modified Leonov constitutive equation, was conducted and the effect of the viscoelastic stress state at the die exit (captured here via second to first normal stress difference ratio) on the unwanted neck-in phenomenon has been analyzed for wide range of Deborah numbers and materials having different level of uniaxial and planar extensional strain hardening. Relevant experimental data for LDPE and theoretical predictions based on multimode eXtended Pom-Pom model acquired from the open literature were used for the validation purposes. It was found that firstly, the predicting capabilities of both constitutive equations for given material and processing conditions are comparable even if the single mode modified Leonov model was used and secondly, the agreement between theoretical and experimental data on neck-in is fairly good. Results of the theoretical study revealed that the viscoelastic stress state at the die exit (i.e. –N2/N1 ratio) increases the level of neck-in if uniaxial extensional strain hardening, planar to uniaxial extensional viscosity ratio and Deborah number increases. It has also been revealed that there exists threshold value for Deborah number and extensional strain hardening below which the neck-in becomes independent on the die exit stress state.
Tomas Barborik | Tomas Bata University in Zlin | Czech Republic
Entry Flow Vortices in Polymer Melt Extrusion: A Review
Autors:
Jan Musil a) and Martin Zatloukal b)
Affiliation:
Polymer Centre, Faculty of Technology, Tomas Bata University in Zlín, Vavrečkova 275, 760 01, Zlín, Czech Republic.
Contacts:
a)
a) Corresponding author:
Abstract:
Although, circular or planar abrupt entry flows are geometrically very simple hydrodynamic problem highly viscoelastic polymer melts makes it very complex with extreme differences in velocities and stresses across the geometry. Despite these flows are very common in polymer melt extrusion industry their strongly non-viscometric and transient nature represents exceedingly challenging task for experimental as well as theoretical investigation and consequently complicates their fully understanding. Polymer melts flowing through abrupt entry contractions exhibit several unique features of which the vortices are one of them. Occurrence of infinitesimal stress singularity in the salient corner leads to presence of weak concave Newtonian viscous vortex. Moreover, polymer melts with increasing extensional to shear viscosity (Trouton) ratio as a function of flow rate exhibit strong convex elastic vortex caused by complete reorientation of stress field near the re-entrant corner (infinite stress singularity point) as a result of momentum balance in the flow direction. This leads to separation of the flow into the primary “funnel-shaped” flow around the centre line/plane on which the secondary recirculation flow(s) in the corner(s) (vortices) are superimposed. Polymer melt captured in the vortex very slowly rotates in the direction opposite to the main flow direction (2D simplification) or takes a helical path moving also in the third direction (real 3D flow). Since the first visual experimental observation performed by Tordella as well as preliminary theoretical prediction made by Langlois and Rivlin at the end of the 1950s this phenomenon represents one of the most fundamental rheological problem ever. In this review paper, the most important experimental as well as theoretical papers focused on entry flow vortices are reviewed and discussed.
Jan Musil | Tomas Bata University in Zlin | Czech Republic
Rheological Properties of Polymer Melts with High Elasticity
Autors:
Jozef Feranc 1, a), Martina Matvejová 1), Pavol Alexy 1), Jozef Preťo 2) and Ján Hronkovič 2)
Affiliations:
1) Institute of Natural and Synthetic Polymers, Slovak University of Technology, Radlinského 9, 812 37 Bratislava, Slovakia.
2) Vipo, a. s, Generála Slobodu 1069/4, 968 01 Partizánske, Slovakia.
Contact:
a) Corresponding author:
Abstract:
In the recent years efforts to complex description of the rheological characteristic increase even in the case of polymeric blends with high part of elastic deformation. However, unlike the most thermoplastic these blends have a certain specific features. Besides the already mentioned the higher part of elastic deformation it is especially higher viscosity, which are shown mainly for the measurement in the range of high shear rates. For this reason, the presented work is focused on the description of measurement methodology for blends with high part of elastic deformation using capillary rheometer. The measurements were carried out on a commercial polymer blend with trade name A517 based on rubbery polymer. Capillary rheometer Gӧttfert RG 75 was used, with diameter of chamber 15 mm. Measurements were performed using capillaries with different ratio of length/diameter at temperature 100°C. Because of existence elastic part of deformation, it is not possible to achieve a steady state pressure using measurements at constant volumetric flow at high shear rates. Therefore we decided to measure the flow characteristic using isobaric mode.
Pavol Alexy | Slovak University of Technology | Slovak Republic
Flow of Bovine Collagen in Rectangular Slit
Autors:
Jan Skočilas 1, a), Rudolf Žitný 1), Jaromír Štancl 1), Stanislav Solnař 1), Aleš Landfeld 2) and Milan Houška 2, b)
Affiliations:
1) Faculty of Mechanical Engineering, Technická 4, 166 29 Prague 6, Czech Republic.
2) Food Research Institute Prague, Radiová 7, 102 00 Prague 10, Czech Republic.
Contacts:
a) Corresponding author:
b)
Abstract:
This contribution deals with the investigation of the bovine collagen flow in the rectangular slit. The slightly compressible collagen liquid (9.5% mass fraction of native bovine collagen in water) was extruded by capillary rheometer of given geometry. A piston pushed the collagen sample from a container to the rectangular capillary. The extrusion rheometer is equipped by pressure sensors mounted at wall of capillary and manually adjusted hydraulic drive enables continuous variation of the piston velocity. The pressure profiles are measured in five places along the capillary simultaneously with increasing shear rate within the range from 1500 to 5000 s-1. It is possible to identify non-elastic shear flow characteristic and the compressibility of collagen matter.
Jan Skočilas | Czech Technical University in Prague | Czech Republic
Analysis of LDPE-ZnO-Clay Nanocomposites using Novel Cumulative Rheological Parameters
Autor:
Milan Kracalik
Affiliation:
Johannes Kepler University Linz, Institute of Polymer Science, Altenberger Str. 69, 4040 Linz, Austria.
Contact:
Corresponding author:
Abstract:
Polymer nanocomposites exhibit complex rheological behaviour due to physical and also possibly chemical interactions between individual phases. Up to now, rheology of dispersive polymer systems has been usually described by evaluation of viscosity curve (shear thinning phenomenon), storage modulus curve (formation of secondary plateau) or plotting information about dumping behaviour (e.g. Van Gurp-Palmen-plot, comparison of loss factor tan δ). On the contrary to evaluation of damping behaviour, values of cot δ were calculated and called as „storage factor“, analogically to loss factor. Then values of storage factor were integrated over specific frequency range and called as “cumulative storage factor”. In this contribution, LDPE-ZnO-clay nanocomposites with different dispersion grades (physical networks) have been prepared and characterized by both conventional as well as novel analysis approach. Next to cumulative storage factor, further cumulative rheological parameters like cumulative complex viscosity, cumulative complex modulus or cumulative storage modulus have been introduced.
Milan Kracalik | Johannes Kepler University Linz | Austria
Protein-Polymer Conjugates Hydrogels: Synthesis and Characterization
Autors:
Andreia Araújo 1, a), Bradley D. Olsen 2, b) and Ana Vera Machado 1, c)
Affiliations:
1) Institute for Polymers and Composites/I3N, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal.
2) Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.
Contacts:
a)
b)
c) Corresponding author:
Abstract:
Efforts to mimic Nature’s structures and functions in the design of new materials and active assemblies have encouraged engineers to look to proteins as a source of building blocks for the next generation of polymeric materials [2]. The integration of structural and functional properties of peptides or proteins with the versatility of synthetic polymers has gained major importance in materials design and application. The peptide segments can endow these materials with unique self-assembly properties, induce the formation of hierarchically organized nanoscale structures, both in solution and in the solid state, with a much higher level of complexity as compared to ordinary block copolymers. In several instances, these hybrid materials can be sensitive to environmental parameters such as temperature, pH, or ion strength. In this work, recombinant protein engineering techniques were firstly applied to make high yielding proteins with thermo-responsive properties. These proteins reacted with synthetic polymeric soft blocks by macromolecular coupling. The resulting materials were processed in the form of hydrogels and rheological measurements were performed to characterize the structural properties. The results shown that the gelation process was similar to the polypeptides alone and stiff gels were formed upon heating.
Ana Vera Machado | University of Minho | Portugal
The Dynamic Magnetoviscoelastic Properties of Biomineralized (Fe3O4) PVP-CMC Hydrogel
Autors:
Ayan Ray a), Nabanita Saha b) and Petr Saha c)
Affiliation:
Centre of Polymer Systems, Tomas Bata University in Zlin, Trida Tomase Bati 5678, 760 01 Zlín, Czech Republic.
Contacts:
a)
b) Corresponding author:
c)
Abstract:
The Polyvinylpyrrolidone (PVP) and carboxymethylcellulose (CMC) based polymer matrix was used as a template for the preparation of magnetic hydrogel. This freshly prepared PVP-CMC hydrogel template was successfully mineralized by in situ synthesis of magnetic nanoparticles (Fe3O4) via chemical co-precipitation reaction using liquid diffusion method. The present study emphasizes on the rheological behavior of non-mineralized and mineralized PVP-CMC hydrogels. Scanning Electron Microscopy (SEM), transmission electron microscopy (TEM), X-ray Diffraction (XRD) pattern, Fourier transform infrared spectroscopy (FT-IR), Vibrating sample magnetometer (VSM) and dynamic magneto rheometer were used to study the morphological, physical, chemical and magnetic properties of nanoparticle (Fe3O4) filled PVP-CMC hydrogel respectively in order to monitor how Fe3O4 magnetic nanoparticles affects the mechanical properties of the hydrogel network. The storage (G’) and loss (G”) moduli with a complex viscosity of the system was measured using a parallel plate rheometer. Frequency and amplitude sweep with temperature variation was performed to determine the frequency and amplitude dependent magneto viscoelastic moduli for both hydrogel samples. A strong shear thinning effect was observed in both (non-mineralized and mineralized) PVP-CMC hydrogels, which confirm that Fe3O4 filled magnetic hydrogels, are pseudoplastic in nature. This Fe3O4 filled PVP-CMC hydrogel can be considered as stimuli-responsive soft matter that may be used as an actuator in medical devices.
Ayan Ray | Tomas Bata University in Zlin | Czech Republic
Rheological Performance of Bacterial Cellulose based Nonmineralized and Mineralized Hydrogel Scaffolds
Autors:
Probal Basu a), Nabanita Saha b), Smarak Bandyopadhyay c) and Petr Saha d)
Affiliation:
Centre of Polymer Systems, University Institute, Tomas Bata University in Zlin, Trida Tomase Bati 5678, 760 01 Zlín, The Czech Republic.
Contacts:
a)
b) Corresponding author:
c)
d)
Abstract:
Bacterial cellulose (BC) based hydrogels (BC-PVP and BC-CMC) are modified with β-tri-calcium phosphate (β-TCP) and hydroxyapatite (HA) to improve the structural and functional properties of the existing hydrogel scaffolds. The modified hydrogels are then biomineralized with CaCO3 following liquid diffusion technique, where salt solutions of Na2CO3 (5.25 g/100 mL) and CaCl2 (7.35 g/100 mL) were involved. The BC-PVP and BC-CMC are being compared with the non-mineralized (BC-PVP-β-TCP/HA and BC-CMC-β-TCP/HA) and biomineralized (BC-PVP-β-TCP/HA-CaCO3 and BC-CMC- β-TCP/HA-CaCO3) hydrogels on the basis of their structural and rheological properties. The Fourier Transform Infrared (FTIR) spectral analysis demonstrated the presence of BC, CMC, PVP, β-TCP, HA in the non-mineralized and BC, CMC, PVP, β-TCP, HA and CaCO3 in the biomineralized samples. Interestingly, the morphological property of non-mineralized and biomineralized, hydrogels are different than that of BC-PVP and BC-CMC based novel biomaterials. The Scanning Electron Microscopic (SEM) images of the before mentioned samples reveal the denser structures than BC-PVP and BC-CMC, which exhibits the changes in their pore sizes. Concerning rheological analysis point of view, all the non-mineralized and biomineralized hydrogel scaffolds have shown significant elastic property. Additionally, the complex viscosity (η*) values have also found in decreasing order with the increase of angular frequency (ω) 0.1 rad.sec-1 to 100 rad.sec-1. All these BC based hydrogel scaffolds are elastic in nature, can be recommended for their application as an implant for bone tissue engineering.
Probal Basu | Tomas Bata University in Zlin | Czech Republic
Viscoelastic Behavior of Mineralized (CaCO3) Chitin Based PVP-CMC Hydrogel Scaffolds
Autors:
Vida Čadež 1, a), Nabanita Saha 2, b), Maja Dutour Sikirić 1, c) and Petr Saha 2, d)
Affiliations:
1) Division of Physical Chemistry, Ruđer Bošković Institute, Bijenička cesta 54, 10000 Zagreb, Croatia.
2) Centre of Polymer Systems, University Institute, Tomas Bata University in Zlin, tř. Tomáše Bati 5678, 760 01 Zlín, Czech Republic.
Contacts:
a)
b) Corresponding author:
c)
d)
Abstract:
Enhancement of the mechanical as well as functional properties of the perspective mineralized PVP-CMC-CaCO3 hydrogel scaffold applicable for bone tissue engineering is quite essential. Therefore, the incorporation feasibility of chitin, a bioactive, antibacterial and biodegradable material, was examined in order to test its ability to enchance mechanical properties of the PVP-CMC-CaCO3 hydrogel scaffold. Chitin based PVP-CMC hydrogels were prepared and characterized both as non-mineralized and mineralized (CaCO3) form of hydrogel scaffolds. Both α-chitin (commercially bought) and β-chitin (isolated from the cuttlebone) were individually tested. It was observed that at 1% strain all hydrogel scaffolds have linear trend, with highly pronounced elastic properties in comparison to viscous ones. The complex viscosity has directly proportional behavior with negative slope against angular frequency within the range of ω = 0.1 – 100 rad.s-1. Incorporation of β-chitin increased storage modulus of all mineralized samples, making it interesting for further research.
Petr Saha | Tomas Bata University in Zlin | Czech Republic
Quality of Nanofibrous Mats in Relation to Rheological Characterization of PVB and PVB/Silica Solutions
Autors:
Petra Peer a) and Petr Filip
Affiliation:
Institute of Hydrodynamics, Academy of Sciences of the Czech Republic, Pod Patankou 5, 166 12 Prague 6, Czech Republic.
Contact:
a) Corresponding author:
Abstract:
Rheological properties are influenced by many factors ranging from the characteristics of the carrier fluid (poly(vinyl butyral)), solvent (methanol) and a filler (fumed silica nanoparticles) to the flowing conditions. There is compared rheological characterization of the neat PVB solution with the PVB/silica suspension. This characterization is confronted with quality of the corresponding nanofibrous mats and a role of elasticity is discussed. It is shown that in this case a role of elasticity is rather limited.
Petra Peer | Institute of Hydrodynamics ASCR | Czech Republic
Some Aspects of Applying Nanostructured Materials in Air Filtration, Water Filtration and Electrical Engineering
Autors:
Dusan Kimmer 1, a), Ivo Vincent 1, b), Lenka Lovecka 1, c), Tomas Kazda 2, d), Adam Giurg 3, e) and Ondrej Skorvan 4, f)
Affiliations:
1) SPUR a.s., trida Tomase Bati 299, Louky, 763 02 Zlin, Czech Republic.
2) The Faculty of Electrical Engineering and Communication Brno University of Technology, Brno, Czech Republic.
3) Department of Inorganic Technology, University of Chemistry and Technology, Prague, Praha, Czech Republic.
4) ASIO spol. s r.o., Kširova 552/45, 619 00 Brno, Czech Republic, Czech Republic.
Contacts:
a) Corresponding author:
b)
c)
d)
e)
f)
Abstract:
Nanostructures prepared from nanofibres and nanostructured composites prepared from nanofibres and fillers are gradually becoming increasingly demanded materials for applications in various industrial branches connected with catalysis, environment protection (air filtration, waste water treatment, sound absorption), in biological engineering, electronics (battery separators, electrode materials), etc. Selected applications of these materials prepared in the company SPUR a.s. are summed up in the following presentation.
Dušan Kimmer | SPUR a.s. | Czech Republic
On the Relation between Sensory Attributes and Rheological Characterization of Cosmetic Products
Autors:
Petr Filip a) and Tereza Moravkova
Affiliation:
Institute of Hydrodynamics, Academy of Sciences of the Czech Republic, Pod Patankou 5, 166 12 Prague 6, Czech Republic.
Contact:
a) Corresponding author:
Abstract:
Sensory attributes occupy irreplaceable position in offering the cosmetic and food products in the market. However, their evaluation is expensive and time-consuming. One of the possibilities how to eliminate at least partially these shortcomings is represented by an application of instrumental analysis. The aim of this contribution is to present rheological modelling using four eye creams and twelve body lotions. The parameters of the proposed models are coupled with selected sensory attributes. It enables a priori prediction of these attributes in a relatively cheap and fast way.
Petr Filip | Institute of Hydrodynamics ASCR | Czech Republic
INTRODUCTION OF NOVEL RHEOLOGICAL TOOLS
(Chairman: Donggang Yao)
10:30 – 11:00
Sophisticated Rheometric Tools for Polymer Characterization
Autors:
Andre Braun a), Gunther Arnold and Jörg Läuger
Affiliation:
Anton Paar Germany GmbH, Hellmuth-Hirth-Straße 6, 73760, Ostfildern, Germany.
Contact:
a) Corresponding author:
Abstract:
Though rheology offer a broad spectrum of tests to characterize polymeric material, those methods are permanently further developed to overcome experimental limitations or to have access to parameters which have not been considered so far. The aim of this contribution is to highlight several tools which can be of interest for advanced rheological testing and which can broaden the possibilities to get profound knowledge of polymer properties. A limitation for rheological characterization of polymer melts and concentrated solutions at high shear rates and large deformation are edge fractures. By using a cone-partitioned-plate geometry in a two motor rheometer with a separate motor transducer configuration can be used to measure towards larger strains and shear rates as compared with standard cone-and-plate geometries. Combining classical rheology with optical methods is of great interest to investigate changes of the macroscopic behaviour along with the dynamics of its microstructure simultaneously. Newly developed rheometers with two drive units working in counter rotation have the advantage to create a stagnation plane in which the microstructure can be visualized. This allows e.g. observing the dynamics of emulsion droplets exposed to shear flow using microscopic devices. Another optical method is to use polarized light imaging to observe flow induced crystallization processes of polymers as well as to characterize the orientation of polymer chains in polymer solutions or melts under shear flow. The presentation will show different examples where the combination of rheological testing and microstructural analysis can help to understand the behavior of the material in shear flow. Ambient conditions have a great impact on rheological properties of a material and need therefore be controlled. Where Temperature has always been in focus, humidity was less taken into account. A special accessory was therefore developed to control the temperature and relative humidity separately during rheological testing. This presentation will highlight some examples where setting temperature and humidity enables to a better understanding on the material properties at processing and storage conditions.
Andre Braun | Anton Paar Germany GmbH | Germany
11:00 – 11:30
Large Amplitude Oscillatory Shear Measurements of Polymer Melts: Comparison of Different Geometries
Autors:
Lukas Schwab 1, a) and Aloyse Franck 2, b)
Affiliations:
1) Waters GmbH, UB TA Instruments, Helfmann-Park 10, 65760 Eschborn, Germany.
2) TA Instruments, 159 Lukens Drive, New Castle, DE, USA.
Contacts:
a)
b)
Abstract:
As application and processing conditions for polymer melts often involve high shear rates, measuring their mechanical properties in the linear viscoelastic regime is often not sufficient. Hence measurements in the non-linear regime, i.e. under large amplitude oscillatory shear (LAOS), are an important field of research. Measuring polymers at large deformation amplitudes is often accompanied by material edge fracture or slip, which deteriorate the quality of the collected data. The selection of the geometry is thus an important factor for the measurement as this can improve fracture or slip issues. In this work two geometries designed for large deformation amplitudes, the cone-partitioned plate (CPP) and a biconical, closed cavity system with grooved surfaces, are compared to a standard cone-plate geometry system in terms of reproducibility and quality of both linear and nonlinear measurements on polymer melts. For interpreting the data in the nonlinear viscoelastic region, different methods are used, including Lissajou figures and the intensities of higher harmonic contributions. Due to advances in instrument software and hardware, discrete Fourier transform analysis is readily available for calculating the harmonic spectrum. Alternatively, the intensity of the fundamental and the additional harmonics up to the ninth can be calculated by direct correlation.
Lukas Schwab | Waters GmbH, UB TA Instruments | Germany
11:30 – 12:00
Following Phase Transitions with Rheometry and Simultaneous Raman-Spectroscopy
Autor:
Jan Philip Plog
Affiliation:
Thermo Fisher Scientific, Karlsruhe, Germany.
Contact:
Corresponding author:
Abstract:
The use of a coupled rheometer and Raman spectrometer for obtaining comprehensive insight into a materials behavior is presented. Rheology is the analytical method of choice to correlate the absolute flow and deformation characteristics of a given material with its behavior towards a certain processing or application step. However, Rheology as an integral method only yields answers on the bulk of the investigated sample. It does not give any insights into what is actually happening on the molecular level when rheological changes are observed. Raman spectroscopy has shown its ability as a powerful, effective and non-invasive method for chemical analysis. Coupling a rheometer with a Raman spectrometer provides direct information about the molecular reaction kinetics and the mechanical properties. This is extremely useful for studying phase transition behavior like i.e. the crystallization behavior of polymer melts during processing. It can also provide insight for in-situ characterization and monitoring which can be challenging when working with on-line techniques as only relative flow fields are characterized. Finally, the coupling gives the researcher the advantage of maximizing and synchronizing the information gathered from a single measurement as well as enabling transient information on their materials during fast processing conditions. In this contribution we present results obtained with the new combination of a Thermo Scientific HAAKE MARS rheometer with a Thermo Scientific Raman spectrometer. Details of this unique set-up as well as selected results will be presented.
Jan Philip Plog | Thermo Fisher Scientific| Germany
12:00 – 13:30
Lunch & Exhibition
CONSTITUTIVE EQUATIONS
(Chairman: Manfred Hermann Wagner)
13:30 – 14:00
Dynamics and Rheology of Finitely Extensible Polymer Coils: An Overview
Autor:
Donggang Yao
Affiliation:
School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.
Contact:
Corresponding author:
Abstract:
One contemporary research issue in non-Newtonian fluid mechanics is to accurately and effectively model viscoelastic polymer flow of practical relevance. In the past several years, we have been working on the formulation of a finitely extensible coil model for polymer flow, particularly including these elements: (1) decoupled equations for kinematical and dynamical variables, (2) logarithmic relaxation at large deformation, (3) rotational retardation, (4) controllable straining, and (5) finite stretch. In this paper, we provide a constructive overview of this nonlinear coil formulation focusing on integration of these elements in a single, unified constitutive model with a minimal number of model parameters that are linked with corresponding physical processes. We also use this opportunity to share the rationale and thought process in the model development. In one particular implement of the general formulation, three parameters are used to tackle with the principal dynamics of a deforming polymer coil: one for finite stretch dictated by a ceiling stretch of the coil, the second one for rotational recovery/retardation, and the third one for adjusting stretch hardening of the rubbery coil. The new model, even in a single mode, is able to simultaneously predict practical material functions in simple shear and coaxial extension and to fit well to representative experimental data. Particularly in the steady-state (or quasi-steady state) flow case, a nearly closed-form stress to velocity gradient relationship can be derived with which shear thinning and elongational thickening can be simultaneously considered while computational advantages of a classical GNF model is retained. The model also fits reasonably well to representative experimental transient data for both shear and extension.
Donggang Yao | School of Materials Science & Engineering, Georgia Institute of Technology | USA
14:00 – 14:30
Strain Sweeps from Oldroyd 8-Constant Framework
Autors:
Chaimongkol Saengow 1, 3, b) and Alan Jeffrey Giacomin 1, 2 a)
Affiliations:
1) Polymers Research Group, Chemical Engineering Department, Queen’s University, Kingston, ON, CANADA K7L 3N6.
2) Mechanical and Materials Engineering Department, Queen’s University, Kingston, ON, CANADA K7L 3N6.
3) College of Integrated Science and Technology Rajamangala University of Technology Lanna Doisaket, Chiangmai, THAILAND 50220.
Contacts:
a) Corresponding author:
b)
Abstract:
Large-amplitude oscillatory shear flow is a popular experiment for studying the nonlinear physics of complex fluids. Specifically, the strain sweep is used routinely to identify when a complex fluid begins to exhibit nonlinear behavior. In this paper, we give the exact shear stress expression for the Oldroyd 8-constant framework evaluated for large-amplitude oscillatory shear flow (LAOS). We choose the Oldroyd 8-constant framework for its rich diversity of popular special cases (we list 14 of these cases). From our shear stress expression, we get exact expressions for the real and imaginary parts of the complex viscosity as functions of both the test frequency, and the shear rate amplitude. We then demonstrate the use of our results for our favorite special case of the Oldroyd 8-constant framework, the corotational Jeffreys model. In our Worked Example, we use this case to explore the influence of η∞ on the strain sweep response. We find that increasing η∞ raises the real part of the complex viscosity, and decreases its imaginary part.
Alan Jeffrey Giacomin | Queen’s University | Canada
14:30 – 15:00
Refreshment & Exhibition
FLOW MODELING
(Chairman: Alan Jeffrey Giacomin)
15:00 – 15:30
Computer Aided Die Design: a New Open-Source Methodology
Autors:
Olga Sousa Carneiro 1, a), Ananth Rajkumar 1, b), Luís Lima Ferrás 1, c), Célio Fernandes 1, d), Alberto Sacramento 2, e) and João Miguel Nóbrega 1, f)
Affiliations:
1) IPC/i3N – Institute Polymers and Composites, Department of Polymer Engineering University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal.
2) Soprefa – Componentes Industriais SA. Mosteirô, Portugal.
Contacts:
a) Corresponding author:
b)
c)
d)
e)
f)
Abstract:
In this work we present a detailed description of how to use open source based computer codes to aid the design of complex profile extrusion dies, aiming to improve its flow distribution. The work encompasses the description of the overall open-source die design methodology, the implementation of the energy conservation equation in an existing OpenFOAM® solver, which will be then capable of simulating the steady non-isothermal flow of an incompressible generalized Newtonian fluid, and two case studies to illustrate the capabilities and practical usefulness of the developed methodology. The results obtained with these case studies, used to solve real industrial problems, demonstrate that the computational design aid is an excellent alternative, from economical and technical points of view, to the experimental trial-and-error procedure commonly used in industry.
Olga Sousa Carneiro | University of Minho | Portugal
15:30 – 16:00
A Primer on Experimental and Computational Rheology with Fractional Viscoelastic Constitutive Models
Autors:
Luís Lima Ferrás 1, 2, a), Neville John Ford 2, b), Maria Luísa Morgado 3, c), Magda Rebelo 4, d), Gareth Huw McKinley 5, e) and João Miguel Nóbrega 1, f)
Affiliations:
1) IPC/i3N – Institute Polymers and Composites, Department of Polymer Engineering, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal.
2) Department of Mathematics, University of Chester, CH1 4BJ, UK.
3) Centro de Matemática, Polo CMAT-UTAD, Departamento de Matemática, Universidade de Trás-os-Montes e Alto Douro, UTAD, Quinta de Prados 5001-801, Vila Real, Portugal.
4) Centro de Matemática e Aplicações (CMA) and Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal.
5) Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA.
Contacts:
a) Corresponding author:
b)
c)
d)
e)
f)
Abstract:
This work presents a brief introduction to fractional calculus and its application to some problems in rheology. We present two different viscoelastic models based on fractional derivatives (the Fractional Maxwell Model – FMM and the Fractional Viscoelastic Fluid – FVF) and discuss their reduction to the classical Newtonian and Maxwell fluids. A third model is also studied (an extension of the FMM to an invariant form), being given by a combination of the K-BKZ integral model with a fractional memory function which we denote the Fractional K-BKZ model. We discuss and illustrate the ability of these models to fit experimental data, and present numerical results for simple stress relaxation following step strain and steady shearing.
João Miguel Nóbrega | University of Minho | Portugal
16:00
End of the conference