Non-Newtonian Fluid Mechanics

A topical collection in Fluids (ISSN 2311-5521). This collection belongs to the section "Non-Newtonian and Complex Fluids".

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Editor

Department of Chemical Engineering, Transport Phenomena Research Center (CEFT), Faculty of Engineering of the University of Porto, Rua Dr. Roberto Frias s/n, CP 4200-465 Porto, Portugal
Interests: complex fluids; rheometry; modeling; simulations
Special Issues, Collections and Topics in MDPI journals

Topical Collection Information

Dear Colleagues,

Non-Newtonian Fluids exhibit a non-linear relationship between the applied stress and its rate of deformation. The spectrum of rheological behaviours is vast and there is not a unique constitutive equation able to express all their features. In fact, modelling specific rheological behaviours, viscoelasticity of polymeric solutions is challenging, and it is yet a matter of active research. The success in the development of these constitutive models relies on the accuracy of rheometrical data set, which depending on the nature of the complex fluid can also be rather difficult. Moreover, the success of the numerical simulations predicting the flow of these complex fluids in real applications also relies on the quality of the constitutive models. Therefore, the chain rheometry–modeling–simulations is sentenced to a feedback process so that Non-Newtonian fluid mechanics can expand its frontiers of knowledge.

This topic collection aims at gathering theoretical, computational and experimental studies where the non-Newtonian nature of the fluid is important.

We look forward to receiving your contributions.

Dr. Francisco J. Galindo-Rosales
Guest Editor

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Keywords

  • rheometry 
  • constitutive equations
  • numerical simulations 
  • complex fluids 
  • non-Newtonian fluid mechanics

Published Papers (11 papers)

2023

Jump to: 2022, 2021

17 pages, 1826 KiB  
Article
Interfacial Dynamics of Miscible Displacement of Shear-Thinning Fluid in a Vertical Channel
by Yao Zhang, Andrianifaliana H. Rabenjafimanantsoa and Hans Joakim Skadsem
Fluids 2023, 8(2), 35; https://doi.org/10.3390/fluids8020035 - 18 Jan 2023
Cited by 2 | Viewed by 1284
Abstract
The displacement of a shear-thinning fluid by a denser and less viscous Newtonian fluid in a vertical duct is investigated using experiments and numerical simulations. We study how shear-thinning and increased viscosity contrast between the fluids affect the displacement. Our results show that [...] Read more.
The displacement of a shear-thinning fluid by a denser and less viscous Newtonian fluid in a vertical duct is investigated using experiments and numerical simulations. We study how shear-thinning and increased viscosity contrast between the fluids affect the displacement. Our results show that the degree of shear-thinning significantly influences the development of interfacial patterns and the growth of perturbations. In the weakly shear-thinning regime, the displacement progresses as a stable displacement with no visible instabilities. Increasing the viscosity of the displaced fluids result in a Saffman–Taylor type instability with several finger-shaped channels carved across the width of the duct. In the strongly shear-thinning regime, a unique viscous finger with an uneven interface is formed in the middle of the displaced fluid. This finger eventually breaks through at the outlet, leaving behind considerably stagnant wall layers at the duct side walls. We link the onset of viscous fingering instability to the viscosity contrast between the fluids, and the stabilizing density difference, as expressed through a modified, unperturbed pressure gradient for the two fluids. Numerical simulations are performed with both an initial flat interface, and with a perturbed interface, and we find good qualitative agreement between experimental observations and computations. Full article
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2022

Jump to: 2023, 2021

21 pages, 3582 KiB  
Article
Performance Comparison of Newtonian and Non-Newtonian Fluid on a Heterogeneous Slip/No-Slip Journal Bearing System Based on CFD-FSI Method
by Mohammad Tauviqirrahman, J. Jamari, S. Susilowati, Caecilia Pujiastuti, Budi Setiyana, Ahmad Hafil Pasaribu and Muhammad Imam Ammarullah
Fluids 2022, 7(7), 225; https://doi.org/10.3390/fluids7070225 - 02 Jul 2022
Cited by 31 | Viewed by 2814
Abstract
It is a well-known fact that incorporating a slip boundary into the contact surfaces improves bearing performance significantly. Regrettably, no research into the effect of slip on the behavior of journal bearing systems operating with non-Newtonian lubricants has been conducted thus far. The [...] Read more.
It is a well-known fact that incorporating a slip boundary into the contact surfaces improves bearing performance significantly. Regrettably, no research into the effect of slip on the behavior of journal bearing systems operating with non-Newtonian lubricants has been conducted thus far. The main purpose of this work is to explore the performance comparison of Newtonian and non-Newtonian fluid on a heterogeneous slip/no-slip journal bearing system. The tribological and acoustic behavior of journal bearing is investigated in this study using a rigorous program that combines CFD (computational fluid dynamics) and two-way FSI (fluid–structure interaction) procedures to simulate Newtonian vs. non-Newtonian conditions with and without slip boundary. The numerical results indicate that irrespective of the lubricant type (i.e., Newtonian or non-Newtonian), an engineered heterogeneous slip/no-slip pattern leads to the improvement of the bearing performance (i.e., increased load-carrying capacity, reduced coefficient of friction, and decreased noise) compared to conventional journal bearing. Furthermore, the influence of the eccentricity ratio is discussed, which confirms that the slip beneficial effect becomes stronger as the eccentricity ratio decreases. It has also been noticed that the Newtonian lubricant is preferable for improving tribological performance, whereas non-Newtonian fluid is recommended for lowering bearing noise. Full article
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15 pages, 1985 KiB  
Article
Stability Analysis of Thin Power-Law Fluid Film Flowing down a Moving Plane in a Vertical Direction
by Wu-Man Liu and Cha’o-Kuang Chen
Fluids 2022, 7(5), 167; https://doi.org/10.3390/fluids7050167 - 10 May 2022
Viewed by 1721
Abstract
This paper analyses the stability of thin power-law fluid flowing down a moving plane in a vertical direction by using the long-wave perturbation method. Linear and nonlinear stability are discussed. The linear stable region increases as the downward speed increases and the power-law [...] Read more.
This paper analyses the stability of thin power-law fluid flowing down a moving plane in a vertical direction by using the long-wave perturbation method. Linear and nonlinear stability are discussed. The linear stable region increases as the downward speed increases and the power-law index increases. More accurate results are obtained on the coefficients of the nonlinear generalized kinematic equation in the power-law part. The regions of sub-critical instability and absolute stability are expanded when the downward movement of plane increases, or the power-law index increases, and meanwhile the parts of supercritical stability and explosive supercritical instability are compressed. By substituting the power-law index and moving speed into the generalized nonlinear kinematic equation of the power-law film on the free surface, the results can be applied to estimate the stability of the thin film flow in the field of engineering. Full article
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2021

Jump to: 2023, 2022

11 pages, 2668 KiB  
Article
Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary
by Pedro Vayssière Brandão, Michele Celli and Antonio Barletta
Fluids 2021, 6(12), 450; https://doi.org/10.3390/fluids6120450 - 11 Dec 2021
Cited by 3 | Viewed by 2060
Abstract
The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed [...] Read more.
The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non–Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid. Full article
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27 pages, 20733 KiB  
Article
Rheological Characterization of Non-Newtonian Mixtures by Pressure Pipe Tests
by Armando Carravetta, Oreste Fecarotta, Riccardo Martino and Maria Cristina Morani
Fluids 2021, 6(11), 419; https://doi.org/10.3390/fluids6110419 - 20 Nov 2021
Cited by 3 | Viewed by 1760
Abstract
The rheological behavior of non-Newtonian fluids in turbulent conditions is an important topic in several fields of engineering. Nevertheless, this topic was not deeply investigated in the past due to the complexity of the experimental tests for the assessment of the constitutive parameters. [...] Read more.
The rheological behavior of non-Newtonian fluids in turbulent conditions is an important topic in several fields of engineering. Nevertheless, this topic was not deeply investigated in the past due to the complexity of the experimental tests for the assessment of the constitutive parameters. Pressure pipe tests on Herschel-Bulkley mixtures were proven to be suitable for exploring turbulent conditions, but discrepancies with the results of tests performed in laminar flow were detected. These contradictions could be attributed to the inconsistencies of the Herschel-Bulkley model (HB) for high shear rate flows, proven by Hallbom and Klein, who suggested a more general “yield plastic” model (HK). Hence, in this study, a procedure for the estimation of the rheological parameters of both HB and HK models in pressure pipe tests is defined and rated on a complete set of experiments. The HK model performed much better than HB model in the turbulent range and slightly better than the HB model in the laminar range, confirming the consistency of the “yield plastic” model. The rheological parameters obtained by the proposed procedure were used to numerically model a dam-break propagation of a non-Newtonian fluid, showing significant differences in terms of process evolution depending on the constitutive model. Full article
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20 pages, 9132 KiB  
Article
Flow Structures Identification through Proper Orthogonal Decomposition: The Flow around Two Distinct Cylinders
by Ângela M. Ribau, Nelson D. Gonçalves, Luís L. Ferrás and Alexandre M. Afonso
Fluids 2021, 6(11), 384; https://doi.org/10.3390/fluids6110384 - 25 Oct 2021
Cited by 4 | Viewed by 2158
Abstract
Numerical simulations of fluid flows can produce a huge amount of data and inadvertently important flow structures can be ignored, if a thorough analysis is not performed. The identification of these flow structures, mainly in transient situations, is a complex task, since such [...] Read more.
Numerical simulations of fluid flows can produce a huge amount of data and inadvertently important flow structures can be ignored, if a thorough analysis is not performed. The identification of these flow structures, mainly in transient situations, is a complex task, since such structures change in time and can move along the domain. With the decomposition of the entire data set into smaller sets, important structures present in the main flow and structures with periodic behaviour, like vortices, can be identified. Therefore, through the analysis of the frequency of each of these components and using a smaller number of components, we show that the Proper Orthogonal Decomposition can be used not only to reduce the amount of significant data, but also to obtain a better and global understanding of the flow (through the analysis of specific modes). In this work, the von Kármán vortex street is decomposed into a generator base and analysed through the Proper Orthogonal Decomposition for the 2D flow around a cylinder and the 2D flow around two cylinders with different radii. We consider a Newtonian fluid and two non-Newtonian power-law fluids, with n=0.7 and n=1.3. Grouping specific modes, a reconstruction is made, allowing the identification of complex structures that otherwise would be impossible to identify using simple post-processing of the fluid flow. Full article
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13 pages, 6453 KiB  
Article
Effect of Magnetohydrodynamics on Heat Transfer Behaviour of a Non-Newtonian Fluid Flow over a Stretching Sheet under Local Thermal Non-Equilibrium Condition
by Konduru Sarada, Ramanahalli J. Punith Gowda, Ioannis E. Sarris, Rangaswamy Naveen Kumar and Ballajja C. Prasannakumara
Fluids 2021, 6(8), 264; https://doi.org/10.3390/fluids6080264 - 25 Jul 2021
Cited by 119 | Viewed by 4051
Abstract
A mathematical model is proposed to describe the flow, heat, and mass transfer behaviour of a non-Newtonian (Jeffrey and Oldroyd-B) fluid over a stretching sheet. Moreover, a similarity solution is given for steady two-dimensional flow subjected to Buongiorno’s theory to investigate the nature [...] Read more.
A mathematical model is proposed to describe the flow, heat, and mass transfer behaviour of a non-Newtonian (Jeffrey and Oldroyd-B) fluid over a stretching sheet. Moreover, a similarity solution is given for steady two-dimensional flow subjected to Buongiorno’s theory to investigate the nature of magnetohydrodynamics (MHD) in a porous medium, utilizing the local thermal non-equilibrium conditions (LTNE). The LTNE model is based on the energy equations and defines distinctive temperature profiles for both solid and fluid phases. Hence, distinctive temperature profiles for both the fluid and solid phases are employed in this study. Numerical solution for the nonlinear ordinary differential equations is obtained by employing fourth fifth order Runge–Kutta–Fehlberg numerical methodology with shooting technique. Results reveal that, the velocity of the Oldroyd-B fluid declines faster and high heat transfer is seen for lower values of magnetic parameter when compared to Jeffry fluid. However, for higher values of magnetic parameter velocity of the Jeffery fluid declines faster and shows high heat transfer when compared to Oldroyd-B fluid. The Jeffery liquid shows a higher fluid phase heat transfer than Oldroyd-B liquid for increasing values of Brownian motion and thermophoresis parameters. The increasing values of thermophoresis parameter decline the liquid and solid phase heat transfer rate of both liquids. Full article
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15 pages, 674 KiB  
Article
Re-Entrant Corner for a White-Metzner Fluid
by Stephen Chaffin, Nicholas Monk, Julia Rees and William Zimmerman
Fluids 2021, 6(7), 241; https://doi.org/10.3390/fluids6070241 - 02 Jul 2021
Cited by 1 | Viewed by 2017
Abstract
Viscoelastic fluids can be difficult to model due to the wide range of different physical behaviors that polymer melts can exhibit. One such feature is the viscous elastic boundary layer. We address the particular problem of a viscoelastic shear-dependent fluid flowing past a [...] Read more.
Viscoelastic fluids can be difficult to model due to the wide range of different physical behaviors that polymer melts can exhibit. One such feature is the viscous elastic boundary layer. We address the particular problem of a viscoelastic shear-dependent fluid flowing past a corner and investigate how the properties of the boundary layer change for a White-Metzner fluid. The boundary layer equations are derived and the upstream layer is matched with the far-field flow. It was found that if the fluid is sufficiently shear thinning then the viscoelastic boundary layer formulation fails due to the inertial forces becoming dominant. The depth of the boundary layer is controlled by the shear-thinning parameters. These effects are not a feature of other shear-thinning models, such as the Phan-Thien-Tanner model. This study provides insight in the different effects of some commonly used viscoelastic models in corner flows in the upstream boundary layer, the downstream boundary layer is not addressed. Full article
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9 pages, 8863 KiB  
Article
Turbulence Intensity Modulation by Micropolar Fluids
by George Sofiadis and Ioannis Sarris
Fluids 2021, 6(6), 195; https://doi.org/10.3390/fluids6060195 - 22 May 2021
Cited by 2 | Viewed by 1727
Abstract
Fluid microstructure nature has a direct effect on turbulence enhancement or attenuation. Certain classes of fluids, such as polymers, tend to reduce turbulence intensity, while others, like dense suspensions, present the opposite results. In this article, we take into consideration the micropolar class [...] Read more.
Fluid microstructure nature has a direct effect on turbulence enhancement or attenuation. Certain classes of fluids, such as polymers, tend to reduce turbulence intensity, while others, like dense suspensions, present the opposite results. In this article, we take into consideration the micropolar class of fluids and investigate turbulence intensity modulation for three different Reynolds numbers, as well as different volume fractions of the micropolar density, in a turbulent channel flow. Our findings support that, for low micropolar volume fractions, turbulence presents a monotonic enhancement as the Reynolds number increases. However, on the other hand, for sufficiently high volume fractions, turbulence intensity drops, along with Reynolds number increment. This result is considered to be due to the effect of the micropolar force term on the flow, suppressing near-wall turbulence and enforcing turbulence activity to move further away from the wall. This is the first time that such an observation is made for the class of micropolar fluid flows, and can further assist our understanding of physical phenomena in the more general non-Newtonian flow regime. Full article
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17 pages, 2910 KiB  
Article
Rheological Characterization of a Concentrated Phosphate Slurry
by Souhail Maazioui, Abderrahim Maazouz, Fayssal Benkhaldoun, Driss Ouazar and Khalid Lamnawar
Fluids 2021, 6(5), 178; https://doi.org/10.3390/fluids6050178 - 02 May 2021
Cited by 5 | Viewed by 3565
Abstract
Phosphate ore slurry is a suspension of insoluble particles of phosphate rock, the primary raw material for fertilizer and phosphoric acid, in a continuous phase of water. This suspension has a non-Newtonian flow behavior and exhibits yield stress as the shear rate tends [...] Read more.
Phosphate ore slurry is a suspension of insoluble particles of phosphate rock, the primary raw material for fertilizer and phosphoric acid, in a continuous phase of water. This suspension has a non-Newtonian flow behavior and exhibits yield stress as the shear rate tends toward zero. The suspended particles in the present study were assumed to be noncolloidal. Various grades and phosphate ore concentrations were chosen for this rheological investigation. We created some experimental protocols to determine the main characteristics of these complex fluids and established relevant rheological models with a view to simulate the numerical flow in a cylindrical pipeline. Rheograms of these slurries were obtained using a rotational rheometer and were accurately modeled with commonly used yield-pseudoplastic models. The results show that the concentration of solids in a solid–liquid mixture could be increased while maintaining a desired apparent viscosity. Finally, the design equations for the laminar pipe flow of yield pseudoplastics were investigated to highlight the role of rheological studies in this context. Full article
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29 pages, 468 KiB  
Article
Implicit Type Constitutive Relations for Elastic Solids and Their Use in the Development of Mathematical Models for Viscoelastic Fluids
by Vít Průša and K. R. Rajagopal
Fluids 2021, 6(3), 131; https://doi.org/10.3390/fluids6030131 - 22 Mar 2021
Cited by 2 | Viewed by 1891
Abstract
Viscoelastic fluids are non-Newtonian fluids that exhibit both “viscous” and “elastic” characteristics in virtue of the mechanisms used to store energy and produce entropy. Usually, the energy storage properties of such fluids are modeled using the same concepts as in the classical theory [...] Read more.
Viscoelastic fluids are non-Newtonian fluids that exhibit both “viscous” and “elastic” characteristics in virtue of the mechanisms used to store energy and produce entropy. Usually, the energy storage properties of such fluids are modeled using the same concepts as in the classical theory of nonlinear solids. Recently, new models for elastic solids have been successfully developed by appealing to implicit constitutive relations, and these new models offer a different perspective to the old topic of the elastic response of materials. In particular, a sub-class of implicit constitutive relations, namely relations wherein the left Cauchy–Green tensor is expressed as a function of stress, is of interest. We show how to use this new perspective in the development of mathematical models for viscoelastic fluids, and we provide a discussion of the thermodynamic underpinnings of such models. We focus on the use of Gibbs free energy instead of Helmholtz free energy, and using the standard Giesekus/Oldroyd-B models, we show how the alternative approach works in the case of well-known models. The proposed approach is straightforward to generalize to more complex settings wherein the classical approach might be impractical or even inapplicable. Full article
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