Electromagnetic Wave Scattering from a Moving Medium with Stationary Interface across the Interluminal Regime

This paper extends current knowledge on electromagnetic wave scattering from bounded moving media in several regards. First, it complements the usual dispersion relation of moving media, ω(θk) (θk: phase velocity direction, associated with the wave vector, k), with the equally important impedance relation, η(θS) (θS: group velocity direction, associated with the Poynting vector, S). Second, it explains the interluminal-regime phenomenon of double-downstream wave transmission across a stationary interface between a regular medium and the moving medium, assuming motion perpendicular to the interface, and shows that the related waves are symmetric in terms of the energy refraction angle, while being asymmetric in terms of the phase refraction angle, with one of the waves subject to negative refraction, and shows that the wave impedances of the two transmitted waves are equal. Third, it generalizes the problem to the case where the medium moves obliquely with respect to the interface. Finally, it highlights the connection between this problem and a spacetime modulated medium.

Confinement-induced stabilization of the Rayleigh-Taylor instability and transition to the unconfined limit

The prevention of hydrodynamic instabilities can lead to important insights for understanding the instabilities’ underlying dynamics. The Rayleigh-Taylor instability that arises when a dense fluid sinks into and displaces a lighter one is particularly difficult to arrest. By preparing a density inversion between two miscible fluids inside the thin gap separating two flat plates, we create a clean initial stationary interface. Under these conditions, we find that the instability is suppressed below a critical plate spacing. With increasing spacing, the system transitions from the limit of stability where mass diffusion dominates over buoyant forces, through a regime where the gap sets the wavelength of the instability, to the unconfined regime governed by the competition between buoyancy and momentum diffusion. Our study, including experiment, simulation, and linear stability analysis, characterizes all three regimes of confinement and opens new routes for controlling mixing processes.

Integrated Fluxes in Magneto-Hydrodynamic Mixed Convection in a Cavity Sustained by Conjugate Heat Transfer

A numerical study of magneto-hydrodynamic mixed convection in a cavity has been conducted to investigate the influence of magnetic field on integrated flux of thermal energy, linear momentum, and kinetic energy. Shear force through lid motion establishes the forced convection effect and buoyancy force due to differential heating of the moving lid and the stationary interface ensures the natural convection phenomenon. Additionally, conduction through the solid slab with prescribed temperature at the outer surface attached to the cavity induces conjugate heat transfer. Further, the top and bottom walls throughout the domain are kept insulated and a uniform horizontal magnetic field is applied on the interface toward left. Fluid flow and heat transfer characteristics are examined for a range of Hartmann number (Ha): 0, 10, 50, and 120 at fixed values of Reynolds number, Grashof number, and Prandtl number of 300, 9 × 104 and 0.71, respectively. The result shows that the transport of heat in the near wall regions of the fluid domain is primarily governed by diffusion, whereas advection appears stronger in the central region of the cavity. Increase in magnetic field strength from Ha = 0 to 120 gradually suppresses the recirculating structure of the flow signifying a reduction in advective strength as depicted by the decrease in the value of total integrated heat flux from 25.15×10-3 to 6.0×10-3. The reduction in heat flux, momentum fluxes, and kinetic energy fluxes with increase in magnetic field has been well correlated in the range of 0≤Ha≤120.

Interface networks in models of competing species

We study a subclass of the May–Leonard stochastic model with an arbitrary, even number of species, leading to the rise of two competing partnerships where individuals are indistinguishable. By carrying out a series of accurate numerical stochastic simulations, we show that alliances compete each other forming spatial domains bounded by interfaces of empty sites. We solve numerically the mean field equations associated with the stochastic model in one and two spatial dimensions. We demonstrate that the stationary interface profile presents topological properties which are related to the asymptotic spatial distribution of species of enemy alliances far away from the interface core. Finally, we introduce a theoretical approach to model the formation of stable interfaces using spontaneous breaking of a discrete symmetry. We show that all the results provided by the soliton topological model, presented here for the very first time, are in agreement with the stochastic simulations and may be used as a tool for understanding the complex biodiversity in nature.

Buoyant miscible displacement flows in rectangular channels

Buoyant displacement flows of two miscible fluids in rectangular channels are studied, theoretically and experimentally. The scenario considered involves the displacement of a fluid by a slightly heavier one at nearly horizontal channel inclinations, where inertial effects are weak and laminar stratified flows may be expected. In the theoretical part, a lubrication approximation model is developed to simplify the displacement flow governing equations and furnish a semi-analytical solution for the heavy and light fluid flux functions. Three key dimensionless parameters govern the fluid flow motion, i.e. a buoyancy number, the viscosity ratio and the channel cross-section aspect ratio. When these parameters are specified, the reduced model can deliver the interface propagation in time, leading and trailing front heights, shapes and speeds, cross-sectional velocity fields, etc. In addition, the model can be exploited to provide various classifications such as single or multiple fronts as well as main displacement flow regimes at long times such as no sustained backflows, stationary interface flows and sustained backflows. Focusing on the variation of the buoyancy number, a large number of iso-viscous displacement experiments are performed in a square duct and the results are compared with those of the lubrication model. Qualitative displacement flow features observed in the theory and experiments are in good agreement, in particular, in terms of the main displacement flow regimes. The quantitative comparisons are also reasonable for small and moderate imposed displacement flow velocities. However, at large flow rates, a deviation of the experimental results from the model results is observed, which may be due to the presence of non-negligible inertial effects.

Buoyant displacement flows in slightly non-uniform channels

We consider displacement flows in slightly diverging or converging plane channels. The two fluids are miscible and buoyancy is significant. We assume that the channel is oriented close to horizontal. Employing a classical lubrication approximation, we simplify the governing equations to furnish a semi-analytical solution for the flux functions. Then, we demonstrate how the non-uniformity of the displacement flow geometry can affect the propagation of the interface between the heavy and light fluids in time, for various parameters studied, e.g. the viscosity ratio, a buoyancy number and rheological features. By setting the molecular diffusion effects to zero, certain solution behaviours at longer times can be practically predicted through the associated hyperbolic problem, using which it becomes possible to directly compute the interfacial features of interest, e.g. leading and trailing front heights and speeds. For a Newtonian displacement flow in a converging or uniform channel, as the buoyancy number increases from zero, we are able to classify three flow regimes based on the behaviour of the trailing front near the top of the channel: a no-back-flow regime, a stationary interface flow regime, and a sustained back-flow regime. For the case of a diverging channel flow, the sustained back-flow regime is replaced by an eventually stationary interface flow regime. In addition, as the displacement flow progresses, the leading front speed typically increases (decreases) in a converging (diverging) channel, while the opposite is usually true for the front height. For the no-back-flow regime (i.e. with small buoyancy), the solution of the displacement flow at long times in all the geometries considered converges to a similarity form, while no similarity form is found for the other flow regimes. As the displacement flow develops, frontal diffusive effects are reduced (enhanced) in a converging (diverging) channel and multiple fronts are progressively less (more) present in a converging (diverging) channel. Regarding non-Newtonian effects, a shear-thinning fluid displacing a Newtonian fluid exhibits an increasingly fast front that has a short height in a converging channel. When a yield stress is present in the displaced fluid, it is possible to find residual wall layers of displaced fluid that are completely static. These layers disappear at a certain critical downstream distance in a converging channel while they appear at a critical distance in a diverging channel. Finally, the combination of strong buoyant and yield-stress effects can modify the destiny of a second front that follows the leading front.

Wetting failure and contact line dynamics in a Couette flow

Liquid–liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the control parameters – capillary number, viscosity ratio and separation of scale – i.e. the slip length versus the macroscopic size of the system. The transition at a critical capillary number, from a stationary to a non-stationary interface, is studied while changing the control parameters. Comparisons with similar existing analyses for other geometries, such as the Landau–Levich problem, are also carried out. A numerical method of analysis is also presented, based on diffuse interface models obtained from multiphase extensions of the lattice Boltzmann equation. Sharp interface and diffuse interface models are quantitatively compared, indicating the correct limit of applicability of the diffuse interface models.

Phase Field Modeling of Interdiffusion Microstructure in Ni-Cr-Al Diffusion Couples

Evolution of interdiffusion microstructures was examined in ternary Ni-Cr-Al solid-tosolid diffusion couples using two-dimensional (2D) phase field simulation. Utilizing Cahn-Hilliard and Allen-Cahn equations, multiphase diffusion couples containing of fcc-γ and B2-β solid solution phases were simulated with alloys of different compositions and phase contents. Chemical mobility as a function of composition with constant gradient energy coefficients was used in the simulation. Simulated microstructures in γ+β/γ and γ+β/γ+β diffusion couples were compared with the experimental microstructures reported in literature. As observed experimentally, the model predicted the recession of γ+β region in the γ+β/γ couple and a stationary interface in γ+β/γ+β couple. Concentration profiles developed across the diffusion couples demonstrated that the interdiffusion occurs in the γ phase as well as in the γ+β region. Formation of single-phase γ and β layers near the interface of γ+β/γ+β couples was also investigated using the volume fraction profile obtained from the simulated microstructure.