Rheology and the Thermo-Mechanics of Non-Newtonian Fluids

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: closed (29 February 2016) | Viewed by 39175

Special Issue Editor


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Guest Editor
1. Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA
2. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA
Interests: multi-component flows; non-newtonian fluids; granular materials; heat transfer; mathematical modelling

Special Issue Information

Dear Colleagues,

Understanding the thermo-mechanics of complex (non-linear) fluids, commonly known as non-Newtonian fluids, is important because these fluids are not only encountered in nature (for example, in mud slides and avalanches), but also in many chemical, biological, food, pharmaceutical, and personal care processing industries. These fluids include the traditional non-Newtonian fluid models, electro- or magneto-rheological fluids, granular materials, slurries, drilling fluids, polymers, blood and other biofluids, mixtures of fluids and particles, etc. This Special Issue of Fluids is dedicated to the recent advances in the mathematical and physical modeling of those fluids with industrial applications, especially those concerned with CFD studies.

Prof. Dr. Mehrdad Massoudi
Guest Editor

 

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Keywords

  • Polymers
  • Suspensions
  • Slurries
  • Viscoelasticity
  • Biofluids
  • Electro-rheology
  • Magneto-rheology
  • CFD applications

Published Papers (8 papers)

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Research

238 KiB  
Article
On Thermomechanics of a Nonlinear Heat Conducting Suspension
by Mehrdad Massoudi and A. D. Kirwan
Fluids 2016, 1(2), 19; https://doi.org/10.3390/fluids1020019 - 18 Jun 2016
Cited by 6 | Viewed by 3874
Abstract
In this short paper, we discuss and provide constitutive relations for the stress tensor and the heat flux vector for a nonlinear density-gradient dependent (Korteweg-type) fluid. Specifically, we attempt to present a unified thermo-mechanical approach to the two models given in papers of [...] Read more.
In this short paper, we discuss and provide constitutive relations for the stress tensor and the heat flux vector for a nonlinear density-gradient dependent (Korteweg-type) fluid. Specifically, we attempt to present a unified thermo-mechanical approach to the two models given in papers of Massoudi (International Journal of Non-Linear Mechanics, 2001, 36(1), pp. 25–37.) and Massoudi (Mathematical Methods in the Applied Sciences, 2006, 29(13), pp. 1599–1613.) where the entropy law is used and restrictions are also obtained on the constitutive parameters. In most thermomechanical studies of nonlinear fluids using the entropy law, the stress tensor is assumed to be nonlinear and the heat flux vector still has the form of the Fourier type, i.e., it is proportional to the temperature gradient. In this paper, we use a generalized (nonlinear) form for the heat flux vector. When our model is linearized we obtain constraints, due to the entropy inequality, which are in agreement with the earlier results. Full article
(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)
2926 KiB  
Article
Modeling the Viscoelastic Behavior of Amorphous Shape Memory Polymers at an Elevated Temperature
by Fangda Cui, Swapnil Moon and I. Joga Rao
Fluids 2016, 1(2), 15; https://doi.org/10.3390/fluids1020015 - 13 May 2016
Cited by 8 | Viewed by 5085
Abstract
Shape memory polymers (SMPs) are soft active materials, their special property is the ability to hold a temporary shape and when exposed to a suitable trigger, they come back to their original shape. These external stimuli can be temperature, light or electro-magnetic fields. [...] Read more.
Shape memory polymers (SMPs) are soft active materials, their special property is the ability to hold a temporary shape and when exposed to a suitable trigger, they come back to their original shape. These external stimuli can be temperature, light or electro-magnetic fields. Amorphous SMPs are a class of thermally-activated SMPs that rely on glass transition to retain their temporary shape. Above the glass transition temperature (T > Tg), (amorphous SMPs exhibit finite deformation and viscoelastic behavior. In this work we develop a model to capture the viscoelastic behavior of the amorphous SMPs at elevated temperatures. The model uses an approach that was initially developed to study non-Newtonian viscoelastic fluids. We accomplish this by developing a multi-branch model based on the theory of multiple natural configurations using the maximization of the rate dissipation to determine the evolution of the natural configurations. We apply our model to study several different deformations at an elevated temperature T = 130 °C and show that this approach is able to capture the viscoelastic behavior of these polymers. The predictions of the theory are then compared with experimental results. Full article
(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)
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1211 KiB  
Article
Natural Drag-Reducing Polymers: Discovery, Characterization and Potential Clinical Applications
by Joie N. Marhefka and Marina V. Kameneva
Fluids 2016, 1(2), 6; https://doi.org/10.3390/fluids1020006 - 6 May 2016
Cited by 9 | Viewed by 4860
Abstract
About seven decades ago, it was discovered that special long-chain soluble polymers added to fluid at nanomolar concentrations significantly reduce resistance to turbulent flow (Toms effect). These so-called drag-reducing polymers (DRPs) do not affect resistance to laminar flow. While the flow parameters associated [...] Read more.
About seven decades ago, it was discovered that special long-chain soluble polymers added to fluid at nanomolar concentrations significantly reduce resistance to turbulent flow (Toms effect). These so-called drag-reducing polymers (DRPs) do not affect resistance to laminar flow. While the flow parameters associated with the Toms effect do not occur in the cardiovascular system, many later studies demonstrated that intravenous injections of DRPs given to experimental animals produced significant hemodynamic effects, such as increasing tissue perfusion, suggesting potential clinical use of these polymers. Moreover, it was found that the specific viscoelastic properties of these polymers make them capable of modifying traffic of blood cells in microvessels and beneficially redistributing them in the blood capillary system—a phenomenon related to rheological properties of DRPs and not related to their specific chemistry. The domain of drag reducing polymers includes many organic and water-soluble, synthetic and natural long-chain molecules. The study presented here employed chemical and rheological methods, as well as macro and microfluidic tests, to characterize the DRP that we discovered in the Aloe vera plant, which was found to be a more powerful drag reducer and less fragile than many synthetic DRPs. The drag-reducing component of aloe gel was purified and chemically identified, which helped to standardize preparation and made this polymer a strong candidate for clinical use. Examples of successful testing of the aloe-derived DRP in animal models are described. Full article
(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)
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3783 KiB  
Article
Splash Dynamics of Paint on Dry, Wet, and Cooled Surfaces
by David Baron, Haiyan Su and Ashwin Vaidya
Fluids 2016, 1(2), 12; https://doi.org/10.3390/fluids1020012 - 14 Apr 2016
Cited by 1 | Viewed by 5725
Abstract
In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington’s experiments has now [...] Read more.
In his classic study in 1908, A.M. Worthington gave a thorough account of splashes and their formation through visualization experiments. In more recent times, there has been renewed interest in this subject, and much of the underlying physics behind Worthington’s experiments has now been clarified. One specific set of such recent studies, which motivates this paper, concerns the fluid dynamics behind Jackson Pollock’s drip paintings. The physical processes and the mathematical structures hidden in his works have received serious attention and made the scientific pursuit of art a compelling area of exploration. Our current work explores the interaction of watercolors with watercolor paper. Specifically, we conduct experiments to analyze the settling patterns of droplets of watercolor paint on wet and frozen paper. Variations in paint viscosity, paper roughness, paper temperature, and the height of a released droplet are examined from time of impact, through its transient stages, until its final, dry state. Observable phenomena such as paint splashing, spreading, fingering, branching, rheological deposition, and fractal patterns are studied in detail and classified in terms of the control parameters. Full article
(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)
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1363 KiB  
Article
On the Flows of Fluids Defined through Implicit Constitutive Relations between the Stress and the Symmetric Part of the Velocity Gradient
by Kumbakonam R. Rajagopal
Fluids 2016, 1(2), 5; https://doi.org/10.3390/fluids1020005 - 24 Mar 2016
Cited by 3 | Viewed by 4014
Abstract
Though implicit constitutive relations have been in place for a long time, wherein the stress, the strain (or the symmetric part of the velocity gradient), and their time derivatives have been used to describe the response of viscoelastic and inelastic bodies, it is [...] Read more.
Though implicit constitutive relations have been in place for a long time, wherein the stress, the strain (or the symmetric part of the velocity gradient), and their time derivatives have been used to describe the response of viscoelastic and inelastic bodies, it is only recently purely algebraic relationships between the stress and the displacement gradient (or the velocity gradient) have been introduced to describe the response of non-linear fluids and solids. Such models can describe phenomena that the classical theory, wherein the stress is expressed explicitly in terms of kinematical variables, is incapable of describing, and they also present a sensible way to approach important practical problems, such as the flows of colloids and suspensions and the turbulent flows of fluids, and that of the fracture of solids. In this paper we review this new class of algebraic implicit constitutive relations that can be used to describe the response of fluids. Full article
(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)
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10049 KiB  
Article
Heat Transfer and Dissipation Effects in the Flow of a Drilling Fluid
by Wei-Tao Wu and Mehrdad Massoudi
Fluids 2016, 1(1), 4; https://doi.org/10.3390/fluids1010004 - 18 Mar 2016
Cited by 17 | Viewed by 4360
Abstract
In this paper we study the effects of dissipation in the Couette flow and heat transfer in a drilling fluid, and explore the effects of concentration and the shear-rate and temperature-dependent viscosity, along with a variable thermal conductivity. A brief discussion on the [...] Read more.
In this paper we study the effects of dissipation in the Couette flow and heat transfer in a drilling fluid, and explore the effects of concentration and the shear-rate and temperature-dependent viscosity, along with a variable thermal conductivity. A brief discussion on the constitutive relations for the stress tensor, the diffusive particle flux vector, and the heat flux vector is presented. The one-dimensional forms of the governing equations are solved numerically and the results are presented through a parametric study by varying the dimensionless numbers. Full article
(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)
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270 KiB  
Article
On Objectivity, Irreversibility and Non-Newtonian Fluids
by A. D. Kirwan
Fluids 2016, 1(1), 3; https://doi.org/10.3390/fluids1010003 - 1 Mar 2016
Cited by 8 | Viewed by 4133
Abstract
Early progress in non-Newtonian fluid mechanics was facilitated by the emergence of two fundamental and complementary principles: objective constitutive characterizations and unambiguous identification of irreversible processes. Motivated by practical and economic concerns in recent years, this line of fluid research has expanded to [...] Read more.
Early progress in non-Newtonian fluid mechanics was facilitated by the emergence of two fundamental and complementary principles: objective constitutive characterizations and unambiguous identification of irreversible processes. Motivated by practical and economic concerns in recent years, this line of fluid research has expanded to include debris flows, slurries, biofluids and fluid-solid mixtures; i.e., complex nonlinear fluids with disparate flow properties. Phenomenological descriptions of these fluids now necessarily include strong nonlinear coupling between the fluxes of mass, energy and momentum. Here, I review these principles, illustrate how they constrain the constitutive equations for non-Newtonian fluids and demonstrate how they have impacted other areas of fluid research. Full article
(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)
736 KiB  
Article
Simulation of Individual Polymer Chains and Polymer Solutions with Smoothed Dissipative Particle Dynamics
by Sergey Litvinov, Qingguang Xie, Xiangyu Hu, Nikolaus Adams and Marco Ellero
Fluids 2016, 1(1), 7; https://doi.org/10.3390/fluids1010007 - 6 Feb 2016
Cited by 21 | Viewed by 6334
Abstract
In an earlier work (Litvinov et al., Phys.Rev.E 77, 066703 (2008)), a model for a polymer molecule in solution based on the smoothed dissipative particle dynamics method (SDPD) has been presented. In the present paper, we show that the model can be extended [...] Read more.
In an earlier work (Litvinov et al., Phys.Rev.E 77, 066703 (2008)), a model for a polymer molecule in solution based on the smoothed dissipative particle dynamics method (SDPD) has been presented. In the present paper, we show that the model can be extended to three-dimensional situations and simulate effectively diluted and concentrated polymer solutions. For an isolated suspended polymer, calculated static and dynamic properties agree well with previous numerical studies and theoretical predictions based on the Zimm model. This implies that hydrodynamic interactions are fully developed and correctly reproduced under the current simulated conditions. Simulations of polymer solutions and melts are also performed using a reverse Poiseuille flow setup. The resulting steady rheological properties (viscosity, normal stress coefficients) are extracted from the simulations and the results are compared with the previous numerical studies, showing good results. Full article
(This article belongs to the Special Issue Rheology and the Thermo-Mechanics of Non-Newtonian Fluids)
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