Recent Advances in Mechanics of Non-Newtonian Fluids

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

Deadline for manuscript submissions: closed (30 September 2019) | Viewed by 57454

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School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Interests: computational heat transfer; thermal control; machine learning
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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,

Non-Newtonian (non-Linear) fluids are common in nature, for example, mud, honey, but also in many chemical, biological, food, pharmaceutical, and personal care processing industries. This Special Issue of Fluids is dedicated to the recent advances in the mathematical and physical modeling of Non-linear fluids with industrial applications, especially those concerned with CFD studies. 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.

Prof. Wei-Tao Wu
Prof. Mehrdad Massoudi
Guest Editors

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Keywords

  • polymers
  • suspensions
  • slurries
  • viscoelasticity
  • biofluids
  • electro-rheology
  • magneto-rheology
  • CFD applications

Published Papers (15 papers)

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Editorial

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4 pages, 175 KiB  
Editorial
Recent Advances in Mechanics of Non-Newtonian Fluids
by Wei-Tao Wu and Mehrdad Massoudi
Fluids 2020, 5(1), 10; https://doi.org/10.3390/fluids5010010 - 8 Jan 2020
Cited by 19 | Viewed by 4877
Abstract
Flow of non-Newtonian (non-linear) fluids occurs not only in nature, for example, mud slides and avalanches, but also in many industrial processes involving chemicals (polymers), biological materials (blood), food (honey, ketchup, yogurt), pharmaceutical and personal care items (shampoo, creams), etc [...] Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)

Research

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15 pages, 5320 KiB  
Article
Natural Convection in a Non-Newtonian Fluid: Effects of Particle Concentration
by Chengcheng Tao, Wei-Tao Wu and Mehrdad Massoudi
Fluids 2019, 4(4), 192; https://doi.org/10.3390/fluids4040192 - 1 Nov 2019
Cited by 8 | Viewed by 3166
Abstract
In this paper we study the buoyancy driven flow of a particulate suspension between two inclined walls. The suspension is modeled as a non-linear fluid, where the (shear) viscosity depends on the concentration (volume fraction of particles) and the shear rate. The motion [...] Read more.
In this paper we study the buoyancy driven flow of a particulate suspension between two inclined walls. The suspension is modeled as a non-linear fluid, where the (shear) viscosity depends on the concentration (volume fraction of particles) and the shear rate. The motion of the particles is determined by a convection-diffusion equation. The equations are made dimensionless and the boundary value problem is solved numerically. A parametric study is performed, and velocity, concentration and temperature profiles are obtained for various values of the dimensionless numbers. The numerical results indicate that due to the non-uniform shear rate, the particles tend to concentrate near the centerline; however, for a small Lewis number (Le) related to the size of the particles, a uniform concentration distribution can be achieved. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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20 pages, 4662 KiB  
Article
Slug Translational Velocity for Highly Viscous Oil and Gas Flows in Horizontal Pipes
by Yahaya D. Baba, Archibong Archibong-Eso, Aliyu M. Aliyu, Olawale T. Fajemidupe, Joseph X. F. Ribeiro, Liyun Lao and Hoi Yeung
Fluids 2019, 4(3), 170; https://doi.org/10.3390/fluids4030170 - 12 Sep 2019
Cited by 10 | Viewed by 4432
Abstract
Slug translational velocity, described as the velocity of slug units, is the summation of the maximum mixture velocity in the slug body and the drift velocity. Existing prediction models in literature were developed based on observation from low viscosity liquids, neglecting the effects [...] Read more.
Slug translational velocity, described as the velocity of slug units, is the summation of the maximum mixture velocity in the slug body and the drift velocity. Existing prediction models in literature were developed based on observation from low viscosity liquids, neglecting the effects of fluid properties (i.e., viscosity). However, slug translational velocity is expected to be affected by the fluid viscosity. Here, we investigate the influence of high liquid viscosity on slug translational velocity in a horizontal pipeline of 76.2-mm internal diameter. Air and mineral oil with viscosities within the range of 1.0–5.5 Pa·s were used in this investigation. Measurement was by means of a pair of gamma densitometer with fast sampling frequencies (up to 250 Hz). The results obtained show that slug translational velocity increases with increase in liquid viscosity. Existing slug translational velocity prediction models in literature were assessed based on the present high viscosity data for which statistical analysis revealed discrepancies. In view of this, a new empirical correlation for the calculation of slug translational velocity in highly viscous two-phase flow is proposed. A comparison study and validation of the new correlation showed an improved prediction performance. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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14 pages, 561 KiB  
Article
The Influence of Bubbles on Foamed Cement Viscosity Using an Extended Stokesian Dynamics Approach
by Eilis Rosenbaum, Mehrdad Massoudi and Kaushik Dayal
Fluids 2019, 4(3), 166; https://doi.org/10.3390/fluids4030166 - 6 Sep 2019
Cited by 4 | Viewed by 3538
Abstract
We want to study the influence of bubbles on the viscosity of suspensions with a computational approach that also accounts for the arrangement of the bubbles due to shearing flow. This requires a large number of bubbles to properly simulate and requires a [...] Read more.
We want to study the influence of bubbles on the viscosity of suspensions with a computational approach that also accounts for the arrangement of the bubbles due to shearing flow. This requires a large number of bubbles to properly simulate and requires a large amount of computational resources. Here we develop a set of equations to define the viscosity ratio from the simulation results to show the influence of the bubbles on the viscosity as a function of the volume fraction. One application of this work has been used to study a specific type of cement that has bubbles injected into the slurry while it is still fluid. The bubbles are added to reduce the density but they also improve the properties of the cement with the increase in viscosity. We show that the computed results match the few experimental results that have been reported. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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17 pages, 1189 KiB  
Article
Investigation of Hydrodynamically Dominated Membrane Rupture, Using Smoothed Particle Hydrodynamics–Finite Element Method
by Hossein Asadi, Mohammad Taeibi-Rahni, Amir Mahdi Akbarzadeh, Khodayar Javadi and Goodarz Ahmadi
Fluids 2019, 4(3), 149; https://doi.org/10.3390/fluids4030149 - 3 Aug 2019
Cited by 4 | Viewed by 3590
Abstract
The rupturing process of a membrane, located between two fluids at the center of a three-dimensional channel, is numerically investigated. The smoothed particle hydrodynamics (SPH) and the finite element method (FEM) are used, respectively, for modeling the fluid and solid phases. A range [...] Read more.
The rupturing process of a membrane, located between two fluids at the center of a three-dimensional channel, is numerically investigated. The smoothed particle hydrodynamics (SPH) and the finite element method (FEM) are used, respectively, for modeling the fluid and solid phases. A range of pressure differences and membrane thicknesses are studied and two different rupturing processes are identified. These processes differ in the time scale of the rupture, the location of the rupture initiation, the level of destruction and the driving mechanism. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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17 pages, 2235 KiB  
Article
A New Model for Thermodynamic Characterization of Hemoglobin
by Francesco Farsaci, Ester Tellone, Antonio Galtieri and Silvana Ficarra
Fluids 2019, 4(3), 135; https://doi.org/10.3390/fluids4030135 - 17 Jul 2019
Cited by 9 | Viewed by 2642
Abstract
In this paper, we formulate a thermodynamic model of hemoglobin that describes, by a physical point of view, phenomena favoring the binding of oxygen to the protein. Our study is based on theoretical methods extrapolated by experimental data. After some remarks on the [...] Read more.
In this paper, we formulate a thermodynamic model of hemoglobin that describes, by a physical point of view, phenomena favoring the binding of oxygen to the protein. Our study is based on theoretical methods extrapolated by experimental data. After some remarks on the non-equilibrium thermodynamic theory with internal variables, some thermodynamic functions are determined by the value of the complex dielectric constant. In previous papers, we determined the explicit expression of a dielectric constant as a function of a complex dielectric modulus and frequency. The knowledge of these functions allows a new characterization of the material and leads to the study of new phenomena that has yet to be studied. In detail, we introduce the concept of “hemoglobe”, a model that considers the hemoglobin molecule as a plane capacitor, the dielectric of which is almost entirely constituted by the quaternary structure of the protein. This model is suggested by considering a phenomenological coefficient of the non-equilibrium thermodynamic theory related to the displacement polarization current. The comparison of the capacity determined by the mean of this coefficient, and determined by geometrical considerations, gives similar results; although more thermodynamic information is derived by the capacity determined considering the aforementioned coefficient. This was applied to the normal human hemoglobin, homozygous sickle hemoglobin, and sickle cell hemoglobin C disease. Moreover, the energy of the capacitor of the three hemoglobin was determined. Through the identification of displacement currents, the introduction of this model presents new perspectives and helps to explain hemoglobin functionality through a physical point of view. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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14 pages, 289 KiB  
Article
Optimal Boundary Control of Non-Isothermal Viscous Fluid Flow
by Evgenii S. Baranovskii, Anastasia A. Domnich and Mikhail A. Artemov
Fluids 2019, 4(3), 133; https://doi.org/10.3390/fluids4030133 - 16 Jul 2019
Cited by 22 | Viewed by 2279
Abstract
We study an optimal control problem for the mathematical model that describes steady non-isothermal creeping flows of an incompressible fluid through a locally Lipschitz bounded domain. The control parameters are the pressure and the temperature on the in-flow and out-flow parts of the [...] Read more.
We study an optimal control problem for the mathematical model that describes steady non-isothermal creeping flows of an incompressible fluid through a locally Lipschitz bounded domain. The control parameters are the pressure and the temperature on the in-flow and out-flow parts of the boundary of the flow domain. We propose the weak formulation of the problem and prove the existence of weak solutions that minimize a given cost functional. It is also shown that the marginal function of this control system is lower semi-continuous. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
11 pages, 1912 KiB  
Article
Semi-Analytical Solutions for the Poiseuille–Couette Flow of a Generalised Phan-Thien–Tanner Fluid
by Ângela M. Ribau, Luís L. Ferrás, Maria L. Morgado, Magda Rebelo and Alexandre M. Afonso
Fluids 2019, 4(3), 129; https://doi.org/10.3390/fluids4030129 - 12 Jul 2019
Cited by 11 | Viewed by 3949
Abstract
This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille–Couette flows, described by the recently proposed (Ferrás et al., A Generalised Phan-Thien–Tanner Model, JNNFM 2019) viscoelastic model, known as the generalised Phan-Thien–Tanner constitutive equation. This generalised version considers the [...] Read more.
This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille–Couette flows, described by the recently proposed (Ferrás et al., A Generalised Phan-Thien–Tanner Model, JNNFM 2019) viscoelastic model, known as the generalised Phan-Thien–Tanner constitutive equation. This generalised version considers the Mittag–Leffler function instead of the classical linear or exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The analytical solutions derived in this work allow a better understanding of the model, and therefore contribute to improve the modelling of complex materials, and will provide an interesting challenge to computational rheologists, to benchmarking and to code verification. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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22 pages, 4868 KiB  
Article
A New Exact Solution for the Flow of a Fluid through Porous Media for a Variety of Boundary Conditions
by U. S. Mahabaleshwar, P. N. Vinay Kumar, K. R. Nagaraju, Gabriella Bognár and S. N. Ravichandra Nayakar
Fluids 2019, 4(3), 125; https://doi.org/10.3390/fluids4030125 - 8 Jul 2019
Cited by 41 | Viewed by 4877
Abstract
The viscous fluid flow past a semi-infinite porous solid, which is proportionally sheared at one boundary with the possibility of the fluid slipping according to Navier’s slip or second order slip, is considered here. Such an assumption takes into consideration several of the [...] Read more.
The viscous fluid flow past a semi-infinite porous solid, which is proportionally sheared at one boundary with the possibility of the fluid slipping according to Navier’s slip or second order slip, is considered here. Such an assumption takes into consideration several of the boundary conditions used in the literature, and is a generalization of them. Upon introducing a similarity transformation, the governing equations for the problem under consideration reduces to a system of nonlinear partial differential equations. Interestingly, we were able to obtain an exact analytical solution for the velocity, though the equation is nonlinear. The flow through the porous solid is assumed to obey the Brinkman equation, and is considered relevant to several applications. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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16 pages, 3457 KiB  
Article
Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid
by Masoud Jabbari, James McDonough, Evan Mitsoulis and Jesper Henri Hattel
Fluids 2019, 4(3), 124; https://doi.org/10.3390/fluids4030124 - 8 Jul 2019
Cited by 6 | Viewed by 2556
Abstract
In this paper, a first-order projection method is used to solve the Navier–Stokes equations numerically for a time-dependent incompressible fluid inside a three-dimensional (3-D) lid-driven cavity. The flow structure in a cavity of aspect ratio δ = 1 and Reynolds numbers [...] Read more.
In this paper, a first-order projection method is used to solve the Navier–Stokes equations numerically for a time-dependent incompressible fluid inside a three-dimensional (3-D) lid-driven cavity. The flow structure in a cavity of aspect ratio δ = 1 and Reynolds numbers ( 100 , 400 , 1000 ) is compared with existing results to validate the code. We then apply the developed code to flow of a generalised Newtonian fluid with the well-known Ostwald–de Waele power-law model. Results show that, by decreasing n (further deviation from Newtonian behaviour) from 1 to 0.9, the peak values of the velocity decrease while the centre of the main vortex moves towards the upper right corner of the cavity. However, for n = 0.5 , the behaviour is reversed and the main vortex shifts back towards the centre of the cavity. We moreover demonstrate that, for the deeper cavities, δ = 2 , 4 , as the shear-thinning parameter n decreased the top-main vortex expands towards the bottom surface, and correspondingly the secondary flow becomes less pronounced in the plane perpendicular to the cavity lid. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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17 pages, 11851 KiB  
Article
Lubrication Approximation for Fluids with Shear-Dependent Viscosity
by Bruno M.M. Pereira, Gonçalo A.S. Dias, Filipe S. Cal, Kumbakonam R. Rajagopal and Juha H. Videman
Fluids 2019, 4(2), 98; https://doi.org/10.3390/fluids4020098 - 28 May 2019
Cited by 4 | Viewed by 5504
Abstract
We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of [...] Read more.
We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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15 pages, 890 KiB  
Article
The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel
by D. Andrew S. Rees and Andrew P. Bassom
Fluids 2019, 4(2), 95; https://doi.org/10.3390/fluids4020095 - 24 May 2019
Cited by 8 | Viewed by 2894
Abstract
We study the steady free convective flow of a Bingham fluid in a porous channel where heat is supplied by both differential heating of the sidewalls and by means of a uniform internal heat generation. The detailed temperature profile is governing by an [...] Read more.
We study the steady free convective flow of a Bingham fluid in a porous channel where heat is supplied by both differential heating of the sidewalls and by means of a uniform internal heat generation. The detailed temperature profile is governing by an external and an internal Darcy-Rayleigh number. The presence of the Bingham fluid is characterised by means of a body force threshold as given by the Rees-Bingham number. The resulting flow field may then exhibit between two and four yield surfaces depending on the balance of magnitudes of the three nondimensional parameters. Some indication is given of how the locations of the yield surfaces evolve with the relative strength of the Darcy-Rayleigh numbers and the Rees-Bingham number. Finally, parameter space is delimited into those regions within which the different types of flow and stagnation patterns arise. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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13 pages, 8109 KiB  
Article
On the Interaction of Side-By-Side Circular Cylinders in Viscoplastic Fluids
by Naser Hamedi and Lars-Göran Westerberg
Fluids 2019, 4(2), 93; https://doi.org/10.3390/fluids4020093 - 21 May 2019
Cited by 3 | Viewed by 3162
Abstract
In this paper, the static interaction of a train of three cylinders in a Bingham fluid is studied numerically using Computational Fluid Dynamics. The variation of drag forces for the cylinders in several configurations is investigated. Positions of the particles in relation to [...] Read more.
In this paper, the static interaction of a train of three cylinders in a Bingham fluid is studied numerically using Computational Fluid Dynamics. The variation of drag forces for the cylinders in several configurations is investigated. Positions of the particles in relation to the reference particle are recognized by the separation distance between the cylinders. A steady state field is considered, with Bingham numbers between 5 and 150. Several separation distances (d) were considered, such that 2.0Dd ≤ 6.0D where D is the cylinder diameter. The Reynolds number was chosen in the range of 5 ≤ Re ≤ 40. In particular, the effect of the separation distance, Reynolds number and Bingham number on the shape and size of the unyielded regions was investigated. The functional dependence of this region and the drag coefficient is explored. The present results reveal the significant influence of the gap between the cylinders on the drag force and the shape of the unyielded regions surrounding the cylinders. It was found that there are several configurations in which the drag forces over the first and the third cylinders are almost equal depending on variation of the Bi, Re and the separation distance. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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16 pages, 876 KiB  
Article
Thin-Film Flow of an Inhomogeneous Fluid with Density-Dependent Viscosity
by Lorenzo Fusi, Angiolo Farina, Fabio Rosso and Kumbakonam Rajagopal
Fluids 2019, 4(1), 30; https://doi.org/10.3390/fluids4010030 - 18 Feb 2019
Cited by 10 | Viewed by 2599
Abstract
In this paper, we study the pressure-driven thin film flow of an inhomogeneous incompressible fluid in which its viscosity depends on the density. The constitutive response of this class of fluids can be derived using a thermodynamical framework put into place to describe [...] Read more.
In this paper, we study the pressure-driven thin film flow of an inhomogeneous incompressible fluid in which its viscosity depends on the density. The constitutive response of this class of fluids can be derived using a thermodynamical framework put into place to describe the dissipative response of materials where the materials’ stored energy depends on the gradient of the density (Mechanics of Materials, 2006, 38, pp. 233–242). Assuming a small aspect ratio for the channel, we use the lubrication approximation and focus on the leading order problem. We show the mathematical problem reduce to a nonlinear first order partial differential equation (PDE) for the density in which the coefficients are integral operators. The problem is solved numerically and plots that describe the evolution of the density in the fluid domain are displayed. We also show that it was possible to determine an analytical solution of the problem when the boundary data are small perturbations of the homogeneous case. Finally, we use such an analytical solution to validate the numerical scheme. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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Review

Jump to: Editorial, Research

24 pages, 4044 KiB  
Review
Wormlike Micellar Solutions, Beyond the Chemical Enhanced Oil Recovery Restrictions
by Emad Jafari Nodoushan, Taeil Yi, Young Ju Lee and Namwon Kim
Fluids 2019, 4(3), 173; https://doi.org/10.3390/fluids4030173 - 17 Sep 2019
Cited by 10 | Viewed by 4521
Abstract
While traditional oil recovery methods are limited in terms of meeting the overall oil demands, enhanced oil recovery (EOR) techniques are being continually developed to provide a principal portion of our energy demands. Chemical EOR (cEOR) is one of the EOR techniques that [...] Read more.
While traditional oil recovery methods are limited in terms of meeting the overall oil demands, enhanced oil recovery (EOR) techniques are being continually developed to provide a principal portion of our energy demands. Chemical EOR (cEOR) is one of the EOR techniques that shows an efficient oil recovery factor in a number of oilfields with low salinity and temperature ranges. However, the application of cEOR under the harsh conditions of reservoirs where most of today’s crude oils come from remains a challenge. High temperatures, the presence of ions, divalent ions, and heterogeneous rock structures in such reservoirs restrict the application of cEOR. Polymer solutions, surfactants, alkaline-based solutions, and complex multi-components of them are common chemical displacing fluids that failed to show successful recovery results in hostile conditions for various reasons. Wormlike micellar solutions (WMS) are viscoelastic surfactants that possess advantageous characteristics for overcoming current cEOR challenges. In this study, we first review the major approaches and challenges of commonly used chemical agents for cEOR applications. Subsequently, we review special characteristics of WMS that make them promising materials for the future of cEOR. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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