Special Issue "Recent Advances in Mechanics of Non-Newtonian Fluids"

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

Deadline for manuscript submissions: 1 September 2019.

Special Issue Editors

Guest Editor
Prof. Wei-Tao Wu

School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Website 1 | Website 2 | E-Mail
Interests: multiphase flow; non-Newtonian fluid; hemodynamics; computational fluid mechanics; heat transfer
Guest Editor
Prof. Dr. Mehrdad Massoudi

Department of Biomedical Engineering and Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA
Website | E-Mail
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

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

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

Published Papers (10 papers)

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Research

Open AccessArticle
Investigation of Hydrodynamically Dominated Membrane Rupture, Using Smoothed Particle Hydrodynamics–Finite Element Method
Received: 28 June 2019 / Revised: 27 July 2019 / Accepted: 30 July 2019 / Published: 3 August 2019
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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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Open AccessFeature PaperArticle
A New Model for Thermodynamic Characterization of Hemoglobin
Received: 14 June 2019 / Revised: 3 July 2019 / Accepted: 5 July 2019 / Published: 17 July 2019
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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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Open AccessFeature PaperArticle
Optimal Boundary Control of Non-Isothermal Viscous Fluid Flow
Received: 29 June 2019 / Revised: 10 July 2019 / Accepted: 12 July 2019 / Published: 16 July 2019
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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)
Open AccessArticle
Semi-Analytical Solutions for the Poiseuille–Couette Flow of a Generalised Phan-Thien–Tanner Fluid
Received: 3 June 2019 / Revised: 3 July 2019 / Accepted: 9 July 2019 / Published: 12 July 2019
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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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Open AccessArticle
A New Exact Solution for the Flow of a Fluid through Porous Media for a Variety of Boundary Conditions
Received: 23 May 2019 / Revised: 28 June 2019 / Accepted: 29 June 2019 / Published: 8 July 2019
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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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Open AccessArticle
Application of a Projection Method for Simulating Flow of a Shear-Thinning Fluid
Received: 29 May 2019 / Revised: 1 July 2019 / Accepted: 3 July 2019 / Published: 8 July 2019
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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 (100 [...] 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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Open AccessArticle
Lubrication Approximation for Fluids with Shear-Dependent Viscosity
Received: 30 April 2019 / Revised: 16 May 2019 / Accepted: 20 May 2019 / Published: 28 May 2019
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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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Open AccessArticle
The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel
Received: 14 April 2019 / Revised: 10 May 2019 / Accepted: 16 May 2019 / Published: 24 May 2019
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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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Open AccessFeature PaperArticle
On the Interaction of Side-By-Side Circular Cylinders in Viscoplastic Fluids
Received: 12 April 2019 / Revised: 15 May 2019 / Accepted: 17 May 2019 / Published: 21 May 2019
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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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Open AccessArticle
Thin-Film Flow of an Inhomogeneous Fluid with Density-Dependent Viscosity
Received: 10 January 2019 / Revised: 19 January 2019 / Accepted: 19 January 2019 / Published: 18 February 2019
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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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