Short-wave Mode Research Articles

Impact of wall-slip on the soluto-marangoni instability in a two-fluid system in a channel–Creeping flow scenario

The role of wall-slip on the soluto-Marangoni instability that emerges in a two-fluid creeping two-dimensional Poiseuille flow is assessed within the framework of Orr-Sommerfeld analysis and species-transport system. Different wall-slip scenarios, namely S1 (slip at the upper wall), S2 (slip at the lower wall), S1S2 (symmetric slip at the upper and lower walls) are considered. The system instability is characterized by identifying unstable and stable zones in the m-n (viscosity ratio - depth ratio) plane for each of the slip conditions at the wall using asymptotic analysis for long-wave disturbances. Numerical simulations based on Chebyshev spectral collocation method reveals the emergence of two modes (M1 and M2) and corresponding stability features are displayed for typical values of Marangoni numbers, n, m and slip lengths. The occurrence of short-wave modes and the features of exchanging dominance between the short-wave modes in the presence of wall-slip for different slip condition are elucidated and the physical mechanism responsible for triggering the instability in the system are revealed through energy budget analysis. The channel system hosting less viscous fluid adjacent to the upper wall demonstrates interesting characteristics such as (among other things): stabilizing/destabilizing the emerging M1/M2 modes in system with no-slip by imposing S1/S2/S1S2 wall conditions and increasing the slip length; exchange of dominance of unstable modes beyond a threshold slip length for S1 slip type. The study thus presents possible means of stabilizing/destabilizing a creeping channel flow system by designing the walls of the channel with appropriate slip type relevant to the application.

Influence of parametric forcing on Marangoni instability

We study a thin, laterally confined heated liquid layer subjected to mechanical parametric forcing without gravity. In the absence of parametric forcing, the liquid layer exhibits the Marangoni instability, provided the temperature difference across the layer exceeds a threshold. This threshold varies with the perturbation wavenumber, according to a curve with two minima, which correspond to long- and short-wave instability modes. The most unstable mode depends on the lateral confinement of the liquid layer. In wide containers, the long-wave mode is typically observed, and this can lead to the formation of dry spots. We focus on this mode, as the short-wave mode is found to be unaffected by parametric forcing. We use linear stability analysis and nonlinear computations based on a reduced-order model to investigate how parametric forcing can prevent the formation of dry spots. At low forcing frequencies, the liquid film can be rendered linearly stable within a finite range of forcing amplitudes, which decreases with increasing frequency and ultimately disappears at a cutoff frequency. Outside this range, the flow becomes unstable to either the Marangoni instability (for small amplitudes) or the Faraday instability (for large amplitudes). At high frequencies, beyond the cutoff frequency, linear stabilization through parametric forcing is not possible. However, a nonlinear saturation mechanism, occurring at forcing amplitudes below the Faraday instability threshold, can greatly reduce the film surface deformation and therefore prevent dry spots. Although dry spots can also be avoided at larger forcing amplitudes, this comes at the expense of generating large-amplitude Faraday waves.

Adaptation of conical liquid sheet and spray morphologies to cross-flowing gas

A variety of industrial devices use liquid injection into the traverse stream of air. Ambient flow changes the spray characteristics, which can alter a system's function. Two different spill-return pressure-swirl atomizers (SRA) were investigated under cross-flow. One of the tested atomizers generates a conical liquid sheet with shorter breakup lengths due to reduced internal air-core stability. Phase Doppler anemometer (PDA) was used for 2D velocity and droplet size measurements, along with high-speed visualization to record instantaneous spray behaviour. A wide range of operating parameters was tested, e.g., inlet pressure (pl) ranging from 0.25 MPa to 1 MPa, spill-to-feed ratio (SFR) from 0 to 0.9, and cross-flow velocity from 0 to 32 m/s. As the cross-flow velocity increases, the spray starts to tilt and the breakup length (lb) shortens as a result of increased aerodynamic forces. This reduces the differences between atomizers. Moreover, the droplet diameter depends on the lb, yet no semi-empirical model was found to accurately predict the droplet sizes. A map of breakup modes was established, and a transition point from long- to short-wave mode was identified. The Linear Stability Analysis of the liquid sheet breakup was used and compared with a semi-empirical approach for the first time for the SRA and cross-flow conditions. The results imply that considering only quiescent ambient conditions during atomizer development might not lead to the optimal design.

Micro-explosion characteristics and mechanism of multi-component fuel droplet with high volatility differential

Micro-explosion is considered as one of the effective ways to improve atomization, combustion and reduce emissions. The present study examined the micro-explosion characteristics and mechanism of multi-component fuel droplets using fiber-support method and high-speed backlit imaging technique. The multi-component fuel blends consist of 2, 5-dimethylfuran (DMF) as a lower volatile component, while Jatropha oil is used as the higher volatile constituents. The results show that the micro-explosion modes are categorized as puffing, breakup + puffing, vapor jetting, jetting + puffing according to the single micro-explosion intensity and droplet breakup index. The breakup + puffing mode is the dominant mode, and the jetting + puffing mode only appears in droplets with 25/75 and 50/50 composition. The formation mode of secondary droplets includes short-wave mode and long-wave mode. Two types of bubble formed during Jatropha oil/DMF blended droplets micro-explosion: bubbles caused by DMF superheating and bubbles caused by fatty acid pyrolysis. Moreover, the diameter and the velocity of secondary droplets obey Lorentz distribution and Weibull distribution respectively. The micro-explosion of Jatropha oil droplets experienced bubbles nucleation, bubbles growth, bubbles coalescence, bubbles movement and fragmentation, which are mainly caused by the pyrolysis of fatty acids. However, the micro-explosion of Jatropha oil/DMF blended droplets presents two mechanisms according to the different DMF content. The low DMF concentration leads to formation of a layer of Jatropha oil film on the droplet surface first, and then goes through a similar process with Jatropha oil droplets. The high DMF concentration leads to formation of a layer of DMF film on the droplet surface first. Then go through the same process as high DMF concentration.

Stability of a plane Couette flow over inhomogeneously stressed solids

In this paper, we investigate the stability of a plane Couette flow over non-linear solids undergoing homogeneous or inhomogeneous initial stresses. Almost all biological and engineering structures are subjected to complex initial residual stresses. We probe here the stability characteristics of a plane Couette flow over these stressed solid surfaces. Since initial stress is commonly inhomogeneous in Nature, our main focus is to analyze the stability of flow over inhomogeneously stressed solids at all Reynolds number regimes, which was not investigated earlier. We apply an initially stressed neo-Hookean solid model which precludes the necessity of using the stress-free reference. A linear perturbation analysis based on an Eulerian–Lagrangian formulation determines the stability associated with short and finite wave modes for zero, low, and high Reynolds number flows. In presence of a uniform initial stress field, the short wave modes are stabilized by tensile stresses and destabilized by compressive stresses in the limit of creeping flow. A similar influence of pre-stress is observed in buckling of columns. On the other hand, the case of spatially varying initial stress is far more intricate due to the inhomogeneous shearing of the solid in the unperturbed state. A linear perturbation introduced to this complicated unperturbed state presents several interesting observations. We find multiple unstable modes for low Reynolds number (Re≪1) creeping flows which were not reported earlier to the best of our knowledge. While literature demonstrates only downstream unstable modes for a plane Couette flow, both upstream and downstream unstable modes are observed for inhomogeneously stressed solids in various Reynolds number regimes. In the creeping flow limit (Re=0), the stability depends mainly on the tensile or compressive initial stress at the solid–fluid interface. When this initial stress is compressive at the interface, only the finite wave modes determine the stability for all thicknesses instead of the short-wave modes. At higher Reynolds number, we report many more interesting results for spatially varying stress-fields which includes an unusual scaling of wall-mode validated through eigenmode analysis.

Instability mechanisms in meandering streamwise vortex pairs of upswept afterbody wakes

Wakes of upswept afterbodies are often characterized by counter-rotating streamwise vortex pairs which meander in space. One application concerns aft regions of cargo aircraft, which are characterized by a relatively flat upswept base. Here we consider a canonical configuration comprised of a cylinder with upswept basal surface. The resulting longitudinal vortices, which are much closer to each other than wing-tip vortices, can adversely influence paratrooper and cargo drop operations as well as trailing aircraft. The unsteady dynamics of these vortices are examined using spatio-temporally resolved Large-Eddy Simulations (LES) and stability considerations. Emphasis is placed on understanding the potential instability dynamics responsible for meandering, which was observed, characterized and quantified at a representative location downstream of the body. The dynamics is then successfully mapped to a matched Batchelor vortex pair, and spatial and temporal stability analyses are performed with both counter-rotating vortices in the computational domain. Both spatial and temporal analyses reveal dipole structures associated with |m|=1 elliptic modes as dominant modes in afterbody vortices. A short-wave elliptic instability mode is found to dominate the meandering motion in the vortex pair; this mode was stable in the case of an isolated vortex. Further, the strain due to axial velocity plays a key role in the instability and therefore breakdown. The low frequency of the unstable mode (Strouhal number StD≃0.3 based on cylinder diameter) is consistent with the spectral analysis of meandering in the LES. Stability analyses at very low-wavenumber do not exhibit any unstable mode suggesting an absence of the Crow instability.

Diagnostic of small choroidal metastasis

Choroidal metastasis in 23–30 % of cases have multifocal growth. In 10–20 % of patients do not have subjective complaints, due to eccentrical localization of choroidal metastases. In these cases, they are detected by chance during examination. In the literature there is no information on the possibility of early diagnosis of “small” foci of metastatic lesions of the choroid using optical coherence tomography (OCT).The aim. To identify diagnostic signs of “small” choroidal metastases.Materials and methods. The study included 4 patients in whom “small” metastases (15 foci) were not visualized by ultrasound.Results. Choroidal metastases, which were not detected by ultrasound, mainly characterized by a multifocal growth pattern, and located mainly outside the central regions of the fundus. The OCT picture in these cases was characterized by the expansion of the choroidal complex up to 1300 μm with an asymmetric shape of the slopes, irregularities of its anterior surface with a moderate hyporeflective structure. At the same time, Bruch’s membrane was preserved, but a violation of the architectonics of the choriocapillary layer is characteristic with a flat profile of the anterior surface of the sclera. Secondary changes in the proper retina are represented by thickening of the retinal pigment epithelium, edema of the photoreceptor layer and of the nuclear layers, while neuroepithelium detachment (NED) appears mainly when the focus is more than 400 μm thick. Initially, choroidal metastasis can be detected by the fundus examination in MultiColor and OCT, as changes appear in the retina – edema of the photoreceptor layer with hyperreflective inclusions and NED, changes appear in the blue-peak autofluorescence (BAF) – hyperBAF with point hypoBAF inclusions, which leads to a change fundus pictures in MultiColor mode.Conclusion. For all patients with a burdened oncological history, even in the absence of visual complaints, in addition to an examination of the fundus of both eyes, it is necessary to provide an examination of the fundus in MultiColor and short-wave autofluorescence modes, followed by OCT in the zones of changes.

Wavy regime of a colloidal falling film

We explore the linear stability and subsequent formation of nonlinear waves in a colloidal, gravity-driven falling film flow. The problem of a gravity-driven falling film devoid of any microstructure has been well studied. However, the role of particulate suspensions in the stability and dynamics of such systems is less explored. We perform a linear stability analysis and observe that the presence of colloidal particles stabilizes both the long-wave surface and short-wave shear instability modes. We also derive nonlinear models in the framework of long-wave theory using Benney's gradient expansion and the Integral Boundary Layer (IBL) approach to study the systems' wavy dynamics.

Dynamics of nondegenerate vector solitons in a long-wave-short-wave resonance interaction system.

In this paper, we study the dynamics of an interesting class of vector solitons in the long-wave-short-wave resonance interaction (LSRI) system. The model that we consider here describes the nonlinear interaction of long wave and two short waves and it generically appears in several physical settings. To derive this class of nondegenerate vector soliton solutions we adopt the Hirota bilinear method with the more general form of admissible seed solutions with nonidentical distinct propagation constants. We express the resultant fundamental as well as multisoliton solutions in a compact way using Gram-determinants. The general fundamental vector soliton solution possesses several interesting properties. For instance, the double-hump or a single-hump profile structure including a special flattop profile form results in when the soliton propagates in all the components with identical velocities. Interestingly, in the case of nonidentical velocities, the soliton number is increased to two in the long-wave component, while a single-humped soliton propagates in the two short-wave components. We establish through a detailed analysis that the nondegenerate multisolitons in contrast to the already known vector solitons (with identical wave numbers) can undergo three types of elastic collision scenarios: (i) shape-preserving, (ii) shape-altering, and (iii) a shape-changing collision, depending on the choice of the soliton parameters. Here, by shape-altering we mean that the structure of the nondegenerate soliton gets modified slightly during the collision process, whereas if the changes occur appreciably then we call such a collision as shape-changing collision. We distinguish each of the collision scenarios, by deriving a zero phase shift criterion with the help of phase constants. Very importantly, the shape-changing behavior of the nondegenerate vector solitons is observed in the long-wave mode also, along with corresponding changes in the short-wave modes, and this nonlinear phenomenon has not been observed in the already known vector solitons. In addition, we point out the coexistence of nondegenerate and degenerate solitons simultaneously along with the associated physical consequences. We also indicate the physical realizations of these general vector solitons in nonlinear optics, hydrodynamics, and Bose-Einstein condensates. Our results are generic and they will be useful in these physical systems and other closely related systems including plasma physics when the long-wave-short-wave resonance interaction is taken into account.

Kinematic stability and simulations of the variational two-fluid model for slug flow

The two-fluid short-wave theory (TF-SWT) mode of the one-dimensional two-fluid model (TFM) [A. Clausse and M. Lopez de Bertodano, “Natural modes of the two-fluid model of two-phase flow,” Phys. Fluids 33, 033324 (2021)] showed that the incompressible kinematic and Kelvin–Helmholtz instabilities are the source of the long-standing ill-posed question. Here, the stability of the short wave mode is analyzed to obtain an unstable incompressible well-posed TFM for vertical slug flow, where inertial coupling and drag play the key role. Then, a computational method is implemented to perform non-linear simulations of slug waves. Linear stability analyses, i.e., characteristics and dispersion, of a variational TF-SWT for vertical slug flows are presented. The current TFM is constituted with a lumped-parameter model of inertial coupling between the Taylor bubble and the liquid. A characteristic analysis shows that this conservative model is parabolic, and it provides a base upon which other models can be constructed, including short-wave damping mechanisms, like vortex dynamics. The dispersion analysis shows that depending on the interfacial drag, the problem can be kinematic unstable. A new kinematic condition in terms of the inertial coupling and the interfacial drag is derived that is consistent with previous theoretical and experimental results. The material waves, which are predicted by linear stability theory, then develop into nonlinear slug waveforms that are captured by the numerical simulations. These and the horizontal stratified flow waves of previous research illustrate the TFM capability to model interfacial structures that behave like waves. Otherwise, when the physics of the TF-SWT waves is ignored, the model is ill-posed.

Stability of gravity-driven particle-laden flows – roles of shear-induced migration and normal stresses

In this paper, we study the role of shear-induced migration and particle-induced normal stresses in the formation and stability of a particle-laden, gravity-driven shallow flow. We first examine the modification of the base-state Nusselt flow due to the underlying microstructure, how shear-induced migration leads to viscosity stratification. We inspect the development of the base state via the boundary layer formation in the ‘shallow’ limit and find a reduction in entrance length with increasing bulk particle concentration and an increase in entrance length with increasing Péclet number ($Pe_p = \dot {\gamma } a^2 / D_0$, where $\dot{\gamma}$ is the average shear rate, a is the particle size and $D_0$ is the single particle diffusivity). A linear stability analysis is then performed on the fully developed state to identify two modes of instability typically found in gravity-driven falling films – the long-wave surface and the short-wave shear modes. We find that when the associated Péclet number is $Pe_p \ll 1$, increasing bulk particle volume fraction delays the onset of instability for both the surface mode and shear mode. However, with $Pe_p = {O}(1)$, we find an enhancement in both modes of instability. We also find that, beyond a critical Péclet number, for a fixed particle volume fraction, the surface mode is unstable even in the absence of fluid inertia. The enhanced destabilisation is attributed to the combined effects of base-state viscosity stratification and momentum forcing via particle concentration perturbations. We also show that the physics behind the enhancement of instability is independent of the choice of the constitutive model used to describe the dynamics of the particle phase, provided the chosen model has elements of shear-induced migration.

Stability of a plane Poiseuille flow in a channel bounded by anisotropic porous walls

Linear stability of a plane Poiseuille flow in a channel bounded by anisotropic permeable walls supported by rigid walls is studied. Characteristic instability features due to two-dimensional infinitesimal disturbances of the most unstable wall mode are investigated in detail. A detailed parametric study displays the existence of wall modes, porous modes, and center modes in both the presence and absence of inertial effects. The results reveal that an increase in mean permeability decreases the critical Reynolds number, destabilizing smaller wavenumbers. Although anisotropy has no significant effect on the growth rate at smaller wavenumbers, the impact is substantial at larger wavenumbers, particularly destabilizing short-wave modes and enlarging the bandwidth of unstable wavenumbers. Furthermore, in relation to the configuration with isotropic permeability, the one with larger (smaller) relative wall-normal permeability is more (less) unstable with a large bandwidth of unstable wavenumbers covering short-wave lengths when mean permeability is high and when the fluid channel thickness is the same as the thickness of each of the porous walls. The critical Reynolds number increases with an increase in anisotropic permeability, while the critical wavenumber decreases with an increase in anisotropic permeability. This demonstrates the possibility of enhancing (suppressing) instability by designing the channel walls as one with anisotropic permeability and appropriately tuning the relative wall-normal permeability to be higher (lower). Furthermore, anisotropic permeability can be used to control instabilities for any arbitrary relative thickness of the porous medium beyond a minimum relative thickness that depends on the relative magnitude of wall normal anisotropic permeability.

Effects of spatial periodic forcing on Turing patterns in two-layer coupled reaction diffusion system

Periodic forcing of pattern-forming systems is always a research hot spot in the field of pattern formation since it is one of the most effective methods of controlling patterns. In reality, most of the pattern-forming systems are the multilayered systems, in which each layer is a reaction-diffusion system coupled to adjacent layers. However, few researches on this issue have been conducted in the multilayered systems and their responses to the periodic forcing have not yet been well understood. In this work, the influences of the spatial periodic forcing on the Turing patterns in two linearly coupled layers described by the Brusselator (Bru) model and the Lengyel-Epstein (LE) model respectively have been investigated by introducing a spatial periodic forcing into the LE layer. It is found that the subcritical Turing mode in the LE layer can be excited as long as one of the external spatial forcing and the supercritical Turing mode (referred to as internal forcing mode) of the Bru layer is a longer wave mode. These three modes interact together and give rise to complex patterns with three different spatial scales. If both the spatial forcing mode and the internal forcing mode are the short wave modes, the subcritical Turing mode in the LE layer cannot be excited. But the superlattice pattern can also be generated when the spatial resonance is satisfied. When the eigenmode of the LE layer is supercritical, a simple and robust hexagon pattern with its characteristic wavelength appears and responds to the spatial forcing only when the forcing intensity is large enough. It is found that the wave number of forcing has a powerful influence on the spatial symmetry of patterns.

Convective instability in multicomponent mixtures with Soret effect

We study the two-dimensional modes of gravity-dependent convective instability arising in a ternary mixture in a plane horizontal layer. The gravity force is oriented perpendicular to the layer heated from below. It is assumed that the system is in the state of mechanical equilibrium of a mixture considered as the base state of the system, which can become unstable under certain conditions. The mathematical model uses two-dimensional Navier-Stokes equations, transfer equations for describing mixture components with the Soret effect, and a heat transfer equation. Under the influence of a concentration gradient, the heat transfer symmetric to the Soret effect is neglected because it is usually small in water-based mixtures. The possible concentration-dependent diffusion and cross-diffusion of dissolved components are also neglected. We investigate a convective stability using linear approximation and under finite-amplitude convection regimes. The stability analysis of the base state after linearization of the governing equations with respect to the state of mechanical equilibrium predicts various convection modes. For each case, a neutral curve and the dependences of the disturbance growth decrements on both the Rayleigh number and the wave number are plotted. We show that in the case of the layer being heated from below, there are ranges of governing parameters where both long-wave and short-wave modes of oscillatory instability occur. The numerical analysis of a nonlinear coupling between these modes has revealed that such instabilities develop in the ternary mixtures whose components are arranged (due to the Soret effect) in different directions with respect to the temperature gradient. The effect of the Rayleigh number on the flow structure and heat mass transfer is demonstrated.

Stability of plane Couette flow past an initially stressed solid

In this paper, we carry out linear stability analysis of a coupled solid–fluid system in a plane Couette flow past an initially stressed neo-Hookean solid at creeping flow limit (Re=0) and arbitrary Reynolds number (Re), as well as for different solid thicknesses. In biological and engineering systems, we often encounter flows past initially stressed deformable solids. For these cases, initial strain or initial stress appears as an additional symmetry representing tensor in the constitutive relation. Consequently, initial stress induces anisotropy (transverse isotropy in the present case) and affects material properties. We employ a hyperelastic model for the initially stressed deformable solid to study the effects of both uni-axial and equi-biaxial initial stresses on flow instability. This study also presents a case where anisotropy in the solid interferes with the stability of the solid–fluid coupled system. In contrast with the previous formulations with two or three state Eulerian–Lagrangian formulations, the present formulation requires four configurations for the initially stressed solid, viz. stress-free, initially stressed, deformed, and the perturbed state. This formulation applies to any fluid–solid coupled problems where the solid contains initial/residual stress. Our results show that initial tensile stress stabilizes the flow, while compressive initial stress destabilizes the same. Fortuitously, this observation of coupled fluid–solid stability is in agreement with the stability of solid column-like structures, where compressive axial stress leads to buckling. We report similar results for uni-axial and equi-biaxial initial stress, for different wave modes at creeping flow limit and their extensions at higher Re, and various solid thicknesses. Two modes of instability, viz., short-wave and finite-wave modes present in the creeping-flow limit are significantly affected by tensile/compressive initial stress for both uni-axial and equi-biaxial cases. For uni-axial tensile initial stress, the finite-wave mode does not extend to high Re. Instead of them, we observe multiple upstream modes to become unstable for higher Re, which show the wall mode scaling as O(Re−1/3). These upstream modes are not observed for stress-free solid. This behavior is triggered by the additional coupling terms between initial stress and perturbed variable in the governing equations of initially stressed solids. However, for the equi-biaxial case, the finite-wave mode does extend to higher Re to show wall mode scaling. This mode further stabilizes/destabilizes depending on the tensile/compressive nature of the initial stress present in the solid.

Effect of the duct and the pre-swirl stator on the wake dynamics of a pre-swirl pumpjet propulsor

A numerical study based on improved delayed detached eddy simulation is conducted to investigate the flow of a pre-swirl pumpjet propulsor (PJP). The PJP consists of a stator, a rotor, and a duct. In order to separate the roles played by the rotor, stator, and duct in determining the flow of PJP, three models are established: the R model (rotor only), the R–D model (rotor within a duct), and the PJP model (rotor and stator within a duct). Results show that the effect of the duct on the unsteady force acting on the rotor blades is weak, while the pre-swirl stator on it is strong due to the rotor–stator interference. In addition, the vortex structure of the three models are compared. The tip-duct mutual-inductance instability mode that the duct-induced vortex begins to affect adjacent tip vortices is reported. For the PJP model, a unique short-wave instability mode of the tip vortex caused by the existences of pre-swirl stator is discussed. More importantly, for the R–D and PJP model, the transition from stability to instability of the tip vortex depends on both the spiral-to-spiral distance and the strength of duct-induced vortex.

Stationary waves in a superfluid gas of electron-hole pairs in bilayers

Stationary waves in the condensate of electron-hole pairs in the $n-p$ bilayer system are studied. The system demonstrates the transition from a uniform (superfluid) to a nonuniform (supersolid) state. The precursor of this transition is the appearance of the roton-type minimum in the collective mode spectrum. Stationary waves occur in the flow of the condensate past an obstacle. It is shown that the roton-type minimum manifests itself in a rather complicated stationary wave pattern with several families of crests which cross one another. It is found that the stationary wave pattern is essentially modified under variation in the density of the condensate and under variation in the flow velocity. It is shown that the pattern is formed in the main part by shortwave modes in the case of a point obstacle. The contribution of longwave modes is clearly visible in the case of a weak extended obstacle, where the stationary wave pattern resembles the ship wave pattern.

Investigation of the stability of spatial modes in quarter-disk resonators

In this work, the stability of short-wavelength spatial modes in quarter-disk cavities was studied. It was found that in such resonators, short-wave modes (with wavelengths λ smaller than the radius R of the quarter-disk λ<<R) in space form figures similar to folded twice m-polygons. The m-order of allowed stable modes decreases rapidly with an increase in the δ/R parameter of deviation from the ideal quarter-disk shape. Unlike half-disk resonators, quarter-disk resonators with δ/R>0.1 lack total internal reflection modes.

Three-dimensional simulation of ligament formation and breakup caused by external vibration

Ligament formation followed by breakup is the primary process that controls external vibration-driven liquid atomization. In this paper, single-mode Faraday instabilities with detailed interfacial dynamics are studied via three-dimensional simulations with a validated numerical methodology. The detailed mechanisms of ligament formation and its breakup are illuminated. Colliding flow from adjacent troughs results in a pressure increase at the root of the crest. This nonlinear flow structure produces a local maximum pressure point that liberates the liquid region above it from the bulk liquid layer that synchronously moves with the bottom substrate. The appearance of the maximum pressure point can thus be recognized as the indicator of ligament formation. The freed ligament with capillary waves on its surface continues to grow until successive breakup occurs at its tip, which is driven by the “short-wave mode” breakup mechanism. It is found that the tip contraction dynamics of Faraday-type ligament can be well described by a one-dimensional theoretical model of a low-speed liquid jet under temporally periodic acceleration. Finally, the development behaviors of Faraday-type ligament and liquid jet are compared quantitatively, which reveals the analogy in their breakup dynamics in the tip regions.

The optimal oscillation mode in excitable small-world networks

The problem of oscillation mode recognition is one of the most important issues under investigation in the field of biological systems. In this paper, we have systematically investigated the optimal oscillation mode (OOM) identification in excitable small-world networks (ESWNs). It has been shown that rewiring probability, coupling strength and system size are the three determinants that can effectively determine the OOM in ESWN. The critical width is introduced to precisely identify the OOM, which is found to be dependent on the system size and independent of the coupling strength. It is revealed that the OOM will shift from the long-wave mode to the short-wave mode as the rewiring probability increases. On the contrary, it will drift toward the longer wave mode in two different manners with the increase of coupling strength and system size. Importantly, the mechanism of OOM selection in ESWN is also discussed. We hope our results will give people a deeper understanding of the key factors in determining OOM in ESWN.