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Fluids
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Instabilities in Viscoelastic Fluid Flows
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Instabilities in Viscoelastic Fluid Flows

A special issue of Fluids (ISSN 2311-5521). This special issue belongs to the section "Non-Newtonian and Complex Fluids".

Deadline for manuscript submissions: closed (30 June 2022) | Viewed by 20022

Special Issue Editor

Dr. Silvia C. Hirata

E-Mail Website
Guest Editor
Laboratoire de Mécanique de Lille, Université Lille 1, Sciences et Technologies, 59655 Villeneuve d’Ascq Cedex, France
Interests: thermoconvective instabilities; instabilities in viscoelastic fluids; instabilities in porous media or in clear fluid layers; absolute/convective instabilities

Special Issue Information

Dear Colleagues,

Flows of complex fluids occur in a variety of industrial applications, as well as in nature. From blood to plastic melts, the presence of microstructures such as polymers, proteins, and particles can promote nonlinear material properties, giving rise to intriguing flow behavior and transport dynamics. Among different rheological behaviors, viscoelasticity in particular may promote instabilities in nearly inertialess flows. Such instabilities can be driven solely by the non-Newtonian behavior of complex fluids such as polymer melts and solutions. This Special Issue of Fluids aims to collect recent theoretical, numerical, and experimental developments in this research field. Specific topics may include thermo-hydrodynamical instabilities, instabilities in shear or extensional flows, interfacial instabilities, instabilities in porous media, instabilities in Taylor–Couette flows, and transition to elastic turbulence.

Dr. Silvia C. Hirata
Guest Editor

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Keywords

  • non-Newtonian fluids
  • viscoelastic fluids
  • instabilities
  • linear and non-linear analyses
  • transport phenomena

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Published Papers (7 papers)

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Research

17 pages, 983 KiB  
Article
A Numerical Analysis on the Unsteady Flow of a Thermomagnetic Reactive Maxwell Nanofluid over a Stretching/Shrinking Sheet with Ohmic Dissipation and Brownian Motion
by Stanford Shateyi and Hillary Muzara
Fluids 2022, 7(8), 252; https://doi.org/10.3390/fluids7080252 - 22 Jul 2022
Cited by 6 | Viewed by 2107
Abstract
The major objective of this current investigation is to examine the unsteady flow of a thermomagnetic reactive Maxwell nanofluid flow over a stretching/shrinking sheet with Ohmic dissipation and Brownian motion. Suitable similarity transformations were used to reduce the governing non-linear partial differential equations [...] Read more.
The major objective of this current investigation is to examine the unsteady flow of a thermomagnetic reactive Maxwell nanofluid flow over a stretching/shrinking sheet with Ohmic dissipation and Brownian motion. Suitable similarity transformations were used to reduce the governing non-linear partial differential equations of momentum, energy and species conservation into a set of coupled ordinary differential equations. The reduced similarity ordinary differential equations were solved numerically using the Spectral Quasi-Linearization Method. The influence of some pertinent physical parameters on the velocity, temperature and concentration distributions was studied and analysed graphically. Further investigations were made on the impact of the Eckert number, Prandtl number, Schmidt number, thermal radiation parameter, Brownian motion parameter, thermophoresis parameter and chemical reaction parameter on the skin friction coefficient, surface heat and mass transfer rates. The results were displayed in a tabular form. Obtained results reveal that the Maxwell parameter and the unsteadiness parameter reduce the Maxwell nanofluid velocity and the fluid temperature is increased with an increase in the Eckert number and thermal radiation parameter. Full article
(This article belongs to the Special Issue Instabilities in Viscoelastic Fluid Flows)
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19 pages, 9150 KiB  
Article
Viscoelasticity-Induced Instability in Plane Couette Flow at Very Low Reynolds Number
by Tomohiro Nimura and Takahiro Tsukahara
Fluids 2022, 7(7), 241; https://doi.org/10.3390/fluids7070241 - 13 Jul 2022
Cited by 4 | Viewed by 2201
Abstract
Elasto-inertial turbulence (EIT), a new turbulent state found in polymer solutions with viscoelastic properties, is associated with drag-reduced turbulence. However, the relationship between EIT and drag-reduced turbulence is not currently well-understood, and it is important to elucidate the mechanism of the transition to [...] Read more.
Elasto-inertial turbulence (EIT), a new turbulent state found in polymer solutions with viscoelastic properties, is associated with drag-reduced turbulence. However, the relationship between EIT and drag-reduced turbulence is not currently well-understood, and it is important to elucidate the mechanism of the transition to EIT. The instability of viscoelastic fluids has been studied in a canonical wall-bounded shear flow to investigate the transition process of EIT. In this study, we numerically deduced that an instability occurs in the linearly stable viscoelastic plane Couette flow for lower Reynolds numbers, at which a non-linear unstable solution exists. Under instability, the flow structure is elongated in the spanwise direction and regularly arranged in the streamwise direction, which is a characteristic structure of EIT. The regularity of the flow structure depends on the Weissenberg number, which represents the strength of elasticity; the structure becomes disordered under high Weissenberg numbers. In the energy spectrum of velocity fluctuations, a steep decay law of the structure’s scale towards a small scale is observed, and this can be recognized as a ubiquitous feature of EIT. The existence of instability in viscoelastic plane Couette flow supports the idea that the transitional path toward EIT may be mediated by subcritical instability. Full article
(This article belongs to the Special Issue Instabilities in Viscoelastic Fluid Flows)
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22 pages, 986 KiB  
Article
Electroviscoelstic Stability Analysis of Cylindrical Structures in Walters B Conducting Fluids Streaming through Porous Medium
by T. M. N. Metwaly and N. M. Hafez
Fluids 2022, 7(7), 224; https://doi.org/10.3390/fluids7070224 - 1 Jul 2022
Cited by 1 | Viewed by 2008
Abstract
In this research, the linear stability of a cylindrical interface between two viscoelstic Walters B conducting fluids moving through a porous medium is investigated theoretically and numerically. The fluids are influenced by a uniform axial electric field. The cylindrical structure preserves heat and [...] Read more.
In this research, the linear stability of a cylindrical interface between two viscoelstic Walters B conducting fluids moving through a porous medium is investigated theoretically and numerically. The fluids are influenced by a uniform axial electric field. The cylindrical structure preserves heat and mass transfer across the interface. The governing equations of motion and continuity are linearized, as are Maxwell’s equations in quasi-static approximation and the suitable boundary conditions at the interface. The method of normal modes has been used to obtain a quadratic characteristic equation in frequency with complex coefficients describing the interaction between viscoelstic Walters B conducting fluids and the electric field. In light of linear stability theory, the Routh–Hurwitz criteria are used to govern the structure’s stability. Several special cases are recoverd under suitable data choices. The stability analysis is conferred in detail via the behaviors of the applied electric field and the imaginary growth rate part with the wavenumbers. The effects of various parameters on the interfacial stability are theoretically presented and illustrated graphically through two sets of figures. Our results demonstrate that kinematic viscosities, kinematic viscoelasticities, and medium porosity improve stability, whereas medium permeability, heat and mass transfer coefficients, and fluid velocities decrease it. Finally, electrical conductivity has a critical influence on the structure’s stability. Full article
(This article belongs to the Special Issue Instabilities in Viscoelastic Fluid Flows)
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14 pages, 3796 KiB  
Article
Onset of Thermal Instabilities in the Plane Poiseuille Flow of Weakly Elastic Fluids: Viscous Dissipation Effects
by Silvia C. Hirata and Mohamed Najib Ouarzazi
Fluids 2021, 6(12), 432; https://doi.org/10.3390/fluids6120432 - 29 Nov 2021
Cited by 1 | Viewed by 2511
Abstract
The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the [...] Read more.
The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the external boundaries and/or from the volumetric heating induced by viscous dissipation. The rheological properties of the viscoelastic fluid are modeled using the Oldroyd-B constitutive equation. As in the Newtonian fluid case, the most unstable structures are found to be stationary longitudinal rolls (modes with axes aligned along the streamwise direction). For such structures, it is shown that the viscoelastic contribution to viscous dissipation may be reduced to one unique parameter: γ=λ1(1−Γ), where λ1 and Γ represent the relaxation time and the viscosity ratio of the viscoelastic fluid, respectively. It is found that the influence of the elasticity parameter γ on the linear stability characteristics is non-monotonic. The fluid elasticity stabilizes (destabilizes) the basic Poiseuille flow if γ<γ* (γ>γ*) where γ* is a particular value of γ that we have determined. It is also shown that when the temperature gradient imposed on the external boundaries is zero, the critical Reynolds number for the onset of such viscous dissipation/viscoelastic-induced instability may be well below the one needed to trigger the pure hydrodynamic instability in weakly elastic solutions. Full article
(This article belongs to the Special Issue Instabilities in Viscoelastic Fluid Flows)
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9 pages, 436 KiB  
Article
Stability of a Buoyant Oldroyd-B Flow Saturating a Vertical Porous Layer with Open Boundaries
by Stefano Lazzari, Michele Celli and Antonio Barletta
Fluids 2021, 6(11), 375; https://doi.org/10.3390/fluids6110375 - 21 Oct 2021
Cited by 5 | Viewed by 2067
Abstract
The performance of several engineering applications are strictly connected to the rheology of the working fluids and the Oldroyd-B model is widely employed to describe a linear viscoelastic behaviour. In the present paper, a buoyant Oldroyd-B flow in a vertical porous layer with [...] Read more.
The performance of several engineering applications are strictly connected to the rheology of the working fluids and the Oldroyd-B model is widely employed to describe a linear viscoelastic behaviour. In the present paper, a buoyant Oldroyd-B flow in a vertical porous layer with permeable and isothermal boundaries is investigated. Seepage flow is modelled through an extended version of Darcy’s law which accounts for the Oldroyd-B rheology. The basic stationary flow is parallel to the vertical axis and describes a single-cell pattern where the cell has an infinite height. A linear stability analysis of such a basic flow is carried out to determine the onset conditions for a multicellular pattern. This analysis is performed numerically by employing the shooting method. The neutral stability curves and the values of the critical Rayleigh number are evaluated for different retardation time and relaxation time characteristics of the fluid. The study highlights the extent to which the viscoelasticity has a destabilising effect on the buoyant flow. For the limiting case of a Newtonian fluid, the known results available in the literature are recovered, namely a critical value of the Darcy–Rayleigh number equal to 197.081 and a corresponding critical wavenumber of 1.05950. Full article
(This article belongs to the Special Issue Instabilities in Viscoelastic Fluid Flows)
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13 pages, 1877 KiB  
Article
Investigation of Non-Linear Rheological Characteristics of Barite-Free Drilling Fluids
by Ekaterina Leusheva, Nataliia Brovkina and Valentin Morenov
Fluids 2021, 6(9), 327; https://doi.org/10.3390/fluids6090327 - 13 Sep 2021
Cited by 15 | Viewed by 4979
Abstract
Drilling fluids play an important role in the construction of oil and gas wells. Furthermore, drilling of oil and gas wells at offshore fields is an even more complex task that requires application of specialized drilling muds, which are non-Newtonian and complex fluids. [...] Read more.
Drilling fluids play an important role in the construction of oil and gas wells. Furthermore, drilling of oil and gas wells at offshore fields is an even more complex task that requires application of specialized drilling muds, which are non-Newtonian and complex fluids. With regard to fluid properties, it is necessary to manage the equivalent circulation density because its high values can lead to fracture in the formation, loss of circulation and wellbore instability. Thus, rheology of the used drilling mud has a significant impact on the equivalent circulation density. The aim of the present research is to develop compositions of drilling muds with a low solids load based on salts of formate acid and improve their rheological parameters for wells with a narrow drilling fluid density range. Partially hydrolyzed polyacrylamide of different molecular weights was proposed as a replacement for hydrolized polyacrylamide. The experiment was conducted on a Fann rotary viscometer. The article presents experimentally obtained data of indicators such as plastic viscosity, yield point, nonlinearity index and consistency coefficient. Experimental data were analyzed by the method of approximation. Analysis is performed in order to determine the most suitable rheological model, which describes the investigated fluids’ flow with the least error. Full article
(This article belongs to the Special Issue Instabilities in Viscoelastic Fluid Flows)
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14 pages, 40248 KiB  
Article
Viscoelastic Thermovibrational Flow Driven by Sinusoidal and Pulse (Square) Waves
by Marcello Lappa and Alessio Boaro
Fluids 2021, 6(9), 311; https://doi.org/10.3390/fluids6090311 - 1 Sep 2021
Cited by 3 | Viewed by 2608
Abstract
The present study aims to probe the role of an influential factor heretofore scarcely considered in earlier studies in the field of thermovibrational convection, that is, the specific time-varying shape of the forcing used to produce fluid motion under the effect of an [...] Read more.
The present study aims to probe the role of an influential factor heretofore scarcely considered in earlier studies in the field of thermovibrational convection, that is, the specific time-varying shape of the forcing used to produce fluid motion under the effect of an imposed temperature gradient. Towards this end, two different temporal profiles of acceleration are considered: a classical (sinusoidal) and a pulse (square) wave. Their effects are analyzed in conjunction with the ability of a specific category of fluids to accumulate and release elastic energy, i.e., that of Chilcott–Rallison finitely extensible nonlinear elastic (FENE-CR) liquids. Through solution of the related governing equations in time-dependent, three-dimensional, and nonlinear form for a representative set of parameters (generalized Prandtl number Prg=8, normalized frequency Ω=25, solvent-to-total viscosity ratio ξ=0.5, elasticity number ϑ=0.1, and vibrational Rayleigh number Raω=4000), it is shown that while the system responds to a sinusoidal acceleration in a way that is reminiscent of modulated Rayleigh–Bénard (RB) convection in a Newtonian fluid (i.e., producing a superlattice), with a pulse wave acceleration, the flow displays a peculiar breaking-roll mode of convection that is in between classical (un-modulated) RB in viscoelastic fluids and purely thermovibrational flows. Besides these differences, these cases share important properties, namely, a temporal subharmonic response and the tendency to produce spatially standing waves. Full article
(This article belongs to the Special Issue Instabilities in Viscoelastic Fluid Flows)
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