Journal ArticleDOI
Effect of inertia on the Marangoni instability of two-layer channel flow, Part II: normal-mode analysis
Mark Blyth,C. Pozrikidis +1 more
TLDR
In this article, the effect of inertia on the Yih-Marangoni instability of the interface between two liquid layers in the presence of an insoluble surfactant was assessed for shear-driven channel flow by a normal-mode linear stability analysis.Abstract:
The effect of inertia on the Yih–Marangoni instability of the interface between two liquid layers in the presence of an insoluble surfactant is assessed for shear-driven channel flow by a normal-mode linear stability analysis. The Orr–Sommerfeld equation describing the growth of small perturbations is solved numerically subject to interfacial conditions that allow for the Marangoni traction. For general Reynolds numbers and arbitrary wave numbers, the surfactant is found to either provoke instability or significantly lower the rate of decay of infinitesimal perturbations, while inertial effects act to widen the range of unstable wave numbers. The nonlinear evolution of growing interfacial waves consisting of a special pair of normal modes yielding an initially flat interface is analysed numerically by a finite-difference method. The results of the simulations are consistent with the predictions of the linear theory and reveal that the interfacial waves steepen and eventually overturn under the influence of the shear flow.read more
Citations
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Journal ArticleDOI
A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects
Zhenlin Guo,Ping Lin +1 more
TL;DR: In this article, a phase-field model for binary incompressible (quasi-incompressible) fluid with thermocapillary effects was developed, which allows for the different properties (densities, viscosities and heat conductivities) of each component while maintaining thermodynamic consistency.
Journal ArticleDOI
A lattice Boltzmann method for axisymmetric thermocapillary flows
Haihu Liu,Lei Wu,Yan Ba,Guang Xi +3 more
TL;DR: In this paper, a two-phase lattice Boltzmann method was developed to simulate axisymmetric thermocapil- lary flows by an improved color-gradient model.
Book ChapterDOI
Instability of Multi-Layer Channel and Film Flows
TL;DR: In this paper, the authors discuss the instability of multi-layer channel and film flows and present a boundary-integral formulation that allows simulating the evolution of periodic waves in the limit of Stokes flow in the absence and presence of surfactants.
Journal ArticleDOI
Stability of axisymmetric core–annular flow in the presence of an insoluble surfactant
TL;DR: In this paper, the effect of insoluble surfactant on the stability of the core-annular flow of two immiscible fluids is investigated by a normal-mode linear analysis and by numerical simulations based on the immersed-interface method for axisymmetric perturbations.
Journal ArticleDOI
Linear instability of two-fluid Taylor–Couette flow in the presence of surfactant
Jie Peng,Ke-Qin Zhu +1 more
TL;DR: In this article, the effect of insoluble surfactant on the centrifugal and shear instability of a pair of radially stratified immiscible liquids in the annular gap between concentric two-fluid Taylor-Couette flow is investigated by a normal-mode linear analysis and complementary energy analysis.
References
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MonographDOI
Numerical analysis of spectral methods : theory and applications
David Gottlieb,Steven A. Orszag +1 more
TL;DR: Spectral Methods Survey of Approximation Theory Review of Convergence Theory Algebraic Stability Spectral Methods Using Fourier Series Applications of algebraic stability analysis Constant Coefficient Hyperbolic Equations Time Differencing Efficient Implementation of Spectral Method as discussed by the authors.
Journal ArticleDOI
Accurate solution of the Orr–Sommerfeld stability equation
TL;DR: In this article, the Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the QR matrix eigenvalue algorithm.
Book
Numerical analysis of spectral methods
David Gottlieb,Steven A. Orszag +1 more
TL;DR: In this article, a mathematical analysis of spectral methods for mixed initial-boundary value problems is given, and the development of a mathematical theory that explains why spectral methods work and how well they work.
Journal ArticleDOI
Instability due to viscosity stratification
TL;DR: In this article, it was shown that the variation of viscosity in a fluid can cause instability, however small the Reynolds number is, and that the unstable modes are in the neighbourhood of a hidden neutral mode for the case of a single fluid, which is entirely ignored in the usual theory of hydrodynamic stability.
Book
Introduction to Theoretical and Computational Fluid Dynamics
TL;DR: The FDLIB software library as mentioned in this paper provides a comprehensive overview of numerical methods for hydrodynamic stability analysis of a flow and the equation of motion and vorticity transport of flow.