Article
Acoustics
Anna Katsiavria, Demetrios T. Papageorgiou
Summary: This article considers the stability of immiscible two-fluid Couette flows with slip present at the liquid-liquid interface. A nonlinear asymptotic theory is developed for a flow geometry in which a thin layer slips over a thick fluid layer. A nonlocal, nonlinear evolution equation is derived, valid at finite Reynolds numbers, slip lengths, viscosity and density ratios. The linear spectrum is calculated and it is shown that slip introduces dispersion, reducing instability or enhancing stability in geometries containing a thin layer.
Article
Mathematics, Applied
Fucai Li, Ronghua Pan, Zhipeng Zhang
Summary: This paper investigates the stability and instability of the steady state for the 3D homogeneous incompressible viscous flow in a bounded simply connected domain with a smooth boundary. It is shown that there exists a critical slip length, below which the steady state is unstable, and above which it is stable.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mechanics
Sanghasri Mukhopadhyay, Asim Mukhopadhyay
Summary: This study discusses the hydrodynamic instability and wave formation of a thin viscous film flowing down a slippery inclined substrate with broken time-reversal-symmetry. Numerical calculations reveal that odd-viscosity stabilizes the film flow, while slip on the substrate has a destabilizing effect.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2021)
Article
Computer Science, Interdisciplinary Applications
Jiangming Zhao, Adam Larios, Florin Bobaru
Summary: In this study, we derive the Eulerian formulation of a peridynamic model for Newtonian viscous flow based on the conservation principles of mass and momentum. The nonlocal nature of this formulation distinguishes it from viscous flow models that rely on numerical methods. By enforcing linear consistency with the classical Navier-Stokes equations, we calibrate the peridynamic model and validate it through various flow scenarios. The constructive approach used in deriving the model allows for seamless integration with peridynamic models for corrosion or fracture, enabling complex simulations of fluid-structure interaction problems involving solid degradation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Stephen J. Walters, Ross J. Turner, Lawrence K. Forbes
Summary: A novel technique is presented for solving flow problems of viscous multi-fluid systems with interfaces, utilizing exact Navier-Stokes equations and a Boussinesq-type approach. The technique is illustrated through a case study of classical Rayleigh-Taylor flow and compared with other models, showing strong support for its effectiveness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mechanics
Christopher C. Tisdell
Summary: Recently, Mandal and Ghosh (Phys. Fluids 35, 047121, 2023) presented perturbation solutions for viscous flow in porous channels with a slip condition limited to slow wall dilation-contraction rates. In this study, we demonstrate that this slowness assumption can be completely eliminated. By doing so, we develop a more widely applicable and accurate perturbation scheme for all dilation-contraction rates. Our approach involves generating new exact solutions to the linear, inviscid problem with slip condition and utilizing them to construct more accurate perturbation expansions for the nonlinear flow model.
Article
Mathematics, Applied
Claudia Gariboldi, Takeo Takahashi
Summary: In this study, we investigated the optimal control problem of the Navier-Stokes system with Navier slip boundary conditions. We analyzed the asymptotic behavior of the problem when the friction coefficient a tends to 0.8. The results showed that by choosing an optimal control for each a, we can obtain a sequence of optimal controls that converge to the optimal control problem of the Navier-Stokes system with Dirichlet boundary conditions. We also demonstrated the convergence of the corresponding direct and adjoint states.
ASYMPTOTIC ANALYSIS
(2022)
Article
Mechanics
Artem N. Nuriev, Andrey G. Egorov, Ayrat M. Kamalutdinov
Summary: This paper investigates the periodic rectilinear motion of an elliptic cylinder at an arbitrary angle of attack in a viscous incompressible fluid according to an arbitrary multi-harmonic law. The study develops the classical method of inner and outer asymptotic expansions to determine the hydrodynamic force acting on the cylinder, considering parameters such as the thickness of the Stokes boundary layer and the Reynolds number.
JOURNAL OF FLUID MECHANICS
(2021)
Article
Mathematics
Eugene Talygin, Alexander Gorodkov
Summary: This study presents analytical expressions for centripetal swirling viscous fluid flows, describing the dynamic geometric configuration and velocity components related to the direction of the streamlines. These expressions provide insight into the dynamic changes of swirling flow in channels.
Article
Mechanics
Oleg Bogoyavlenskij
Summary: A new effect has been discovered in viscous fluid dynamics that satisfies the three-dimensional Navier-Stokes equations without external forces. This effect consists of oscillations of the total angular momentum vector. Exact solutions for viscous flows obeying the no-slip boundary condition are derived, with an arbitrary number of oscillations of the total angular momentum vector on any given interval of time. The stability of these oscillations under small perturbations of the exact solutions has been proven.
Article
Mechanics
C. Y. Wang
Summary: This study examines slip flow in a rectangular cavity and finds that slip has a significant effect on flow properties, eliminating stress singularity at velocity discontinuity corners. Slip eigenfunctions are used to determine exact series solutions for sliding lids in both longitudinal and transverse directions.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2021)
Article
Mathematics, Applied
Zilai Li, Hao Liu, Yulin Ye
Summary: In this paper, we consider the viscous two-phase flow model with Navier-type slip boundary condition in a two-dimensional simply connected bounded domain with C-infinity boundary partial derivative Omega. By using new estimates of effective viscous flux on boundary integrals related to the Navier-type slip boundary condition, we establish the global existence and large time behavior of classical solutions to the two-phase flow model in time, provided that the initial energy is suitably small even if the density contains vacuum and has large oscillations. This is the first result concerning the global existence of classical solutions to the viscous two-phase flow model with density containing vacuum initially for general 2D bounded smooth domain.
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2022)
Article
Thermodynamics
Ashwini Bhat, Nagaraj N. Katagi
Summary: This study examined a two-dimensional viscous flow between porous discs under an external magnetic field, simplifying the problem to nonlinear differential equations with suitable boundary conditions. The Keller-box method was used to obtain solutions, showing the impact of non-zero tangential slip velocity on velocity, temperature profiles, and shear stress for different parameters. Results revealed that the presence of slip velocity altered the effects of flow parameters.
CASE STUDIES IN THERMAL ENGINEERING
(2021)
Article
Physics, Applied
Walid Aich, Hisam-Uddin Shaikh, Abid Ali Memon, Liaquat Ali Lund, Sami Ullah Khan, Muapper Alhadri, Lotfi Ben Said, Lioua Kolsi
Summary: The objective of this study is to investigate the heat transfer phenomenon for slip flow of viscous fluid in a wavy channel with general cosine function boundaries. The relationship between Reynolds number, geometry of the channel, and shear rate is rigorously studied. The variations of pressure gradient in the channel under periodic flow conditions are also analyzed.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Mathematics, Applied
Anthony Suen
Summary: The study presents a Serrin type blow-up criterion for 3-D viscous compressible flows with large external potential force, and proves the global existence of strong solutions for the Cauchy problem of the 3-D compressible Navier-Stokes system with a potential force term. It further discusses the removal of the Serrin condition on velocity in the case of isothermal flows with no vacuum.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
