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We perform two-dimensional particle resolved direct numerical simulations of the steady cross flow past a pair of interacting circular and non-circular cylinders with the cut-cell method, a sub-class of non-body-conforming methods that provides a sharp description of the boundary, is strictly mass and momentum conservative, and can be easily extended to adaptive grids. We use hierarchically refined Cartesian meshes where we place a reference cylinder (i) at the center of the domain and vary the location of a neighboring cylinder (j). We consider a large parameter space defined by the radius of curvature 2 / ζ i and 2 / ζ j ranging from 1 to 0, the angles of incidence α i and α j at values of 0 ° and 45 ° , the center-to-center gap ratio G ranging from 1.5 to 20, the alignment angle θ measured between the free-stream flow and the line connecting the centers of the cylinders, ranging from 0 ° to 360 ° , and finally the Reynolds number Re varied from 1 to 20. Specifically, we investigate the force and flow disturbances introduced by the neighboring cylinder on the reference cylinder, with a focus on the normalized hydrodynamic drag and lift coefficients and the associated prevailing flow regimes. Our study highlights the substantial impact of both the gap ratio G and the alignment angle θ in delineating distinct flow regimes, each exhibiting distinctive flow characteristics and consistent trends in pressure distributions and variations of the normalized drag and lift coefficients. Generally, the flow and force disturbances become more pronounced when significant interactions between the cylinders occur, whether due to proximity, wake interference, or both. We identify a critical threshold for G, beyond which the flow and force disturbances induced by the neighboring cylinder markedly diminish, except in scenarios dominated by significant wake interactions. Our investigation shows that the documented trends in the flow and force variations exhibit remarkable similarity at Re of 10 and 20, but expectedly deviate at R e = 1. Finally, we propose an empirical model to predict the hydrodynamic disturbances between two circular cylinders based on the modulation of the drag C d , i and lift C l , i coefficients. Leveraging the periodic nature of C d , i and C l , i as a function of the relative angular alignment θ of the neighboring cylinder, we use Fourier series expansions demonstrating accurate reconstruction of the data across a wide parameter space. Furthermore, our model exhibits promising predictive capabilities when applied to unexplored parameter ranges, encompassing scenarios involving non-circular cylinders and interpolated regions of Re and G. [ABSTRACT FROM AUTHOR]

The volume of fluid method is widely used for interface capturing in two-phase flows including surface tension. Calculation of surface forces requires accurate local interfacial curvature, which, despite receiving considerable attention, remains a challenge due to the abrupt variation of volume fraction near the interface. Based on recent studies showing the potential of data-driven techniques, a machine learning (ML) model using a multi-layered artificial neural network is initially developed to predict curvature on structured grids. Known shapes in the form of circular interface segments are used to generate a synthetic training dataset consisting of interfacial curvature and volume fractions. An optimum model configuration is carefully obtained, with a larger 5 × 5 input stencil showing increased accuracy for test data along with analytical test cases. However, an extension of the model to unstructured grids, required in simulations involving complex geometries, is non-trivial. To overcome the limitations, a local interface remapping algorithm is proposed where the stencil around a target cell is transformed into a structured stencil for the generation of the input dataset. The algorithm enables using the same ML model developed for structured grids to predict curvature on unstructured grids, thereby maintaining the simplicity of the ML strategy. The algorithm accurately predicts curvature for some analytically known shapes on quadrangular and triangular grids. Eventually, the ML model with the remapping algorithm is integrated into a two-phase flow solver to assess the performance in dynamic simulation environments, where satisfactory results are obtained for a benchmark rising bubble problem on both structured and unstructured grids. [ABSTRACT FROM AUTHOR]

In this study, we focus on the collective dynamics of polar active particles navigating across three distinct surfaces, each characterized by its own unique blend of topological and geometrical properties. The behavior of these active particles is influenced by a multitude of factors, including self-propulsion, inter-particle interactions, surface constraints, and under-damped stochastic forces simulated via Ornstein–Uhlenbeck processes. Our exploration unveils the prevailing collective patterns observed within these systems across three surface types: a sphere, a torus, and a landscape featuring hills and valleys, each distinguished by its specific topological and geometrical attributes. We underscore the profound impact of surface curvature and symmetry on the sustainable spatial-temporal dynamics witnessed. Our findings illuminate how the interplay between substantial surface curvature and particular symmetrical characteristics gives rise to a diverse spectrum of spatial-temporal patterns. Notably, we discern that high curvature tends to drive collective motion toward cyclic rotation on spheres and tori, or spatial-temporal periodic traveling ring patterns on landscapes with hills and valleys. Additionally, we observe that rough surfaces and the incorporation of excluded volume effects can disrupt the complexity of these collective spatial-temporal patterns. Through this investigation, we provide invaluable insight into the intricate interplay of curvature and symmetry, profoundly shaping collective behaviors among active particles across varied surfaces. [ABSTRACT FROM AUTHOR]

This study investigates the initial acceleration process of low-speed flames in curved channels. It also examines how the curvature and width of the channels influence flame propagation patterns and mechanisms. Previous research has highlighted the advantages of curved channels in facilitating flame acceleration. Subsequent studies have explored the interaction between pressure waves and flames, particularly in the later stages of flame propagation, leading to a high-speed flame phase. However, the effects of curvature and channel width on the initial acceleration phase of low-speed flames remain unclear. To address this gap, the present study utilizes theoretical methods to analyze the early acceleration phase of flames in curved channels with fixed curvature and width, from the closed end to the open end. Semi-analytical theoretical solutions are derived to determine the shape of the unburned gas flow field, flame front, and flame acceleration rate. The results demonstrate that the flow field shape deviates from axial symmetry to conserve angular momentum, favoring the inner wall of the curved channel and causing the flame front to adhere to it. In channels with small curvature, increasing the width leads to a decrease in the flame acceleration rate. Conversely, in channels with large curvature, widening the channel results in an increased flame acceleration rate. These findings provide theoretical insights for optimizing the design of the front-stage structure of curved detonation channels. [ABSTRACT FROM AUTHOR]

The modification of the dynamics on the f-plane due to the inclusion of the latitudinal variation of the Coriolis frequency, quantified by β, is examined by comparing steady and time-dependent solutions for different values of β, including 0. The comparisons are made for analytic expressions and numerical simulations of the solutions of two physical problems: geostrophic adjustment and Ekman transport. By varying the extent of the meridional domain, L, and the value of β, while keeping the same value of the deformation radius, Rd, we find that the relative change of the Coriolis frequency across L is not a uniformly valid predictor of the effect of β on the dynamics. Instead, the magnitude of this effect varies with the physical problem, the type of dynamics, i.e., steady or time dependent, and with the particular values of β and L. In contrast to the effect of β, the effect of curvature on the zonally invariant f-plane dynamics is negligible in all cases for L ≤ 1200 km and R d = 30 km employed here. [ABSTRACT FROM AUTHOR]

In practical aerodynamic scenarios, interactions between curved shock waves and boundary layers with composite shock curvatures in both streamwise and spanwise directions are encountered more frequently than those induced by planar oblique shocks. To gain a more systematic understanding of this phenomenon in physics, internal and external axisymmetric curved shock wave/boundary layer interactions (AC-SBLI) are being studied analytically by establishing the underlying relations within the flow structures. Specifically, based on reconstructing the dominant structures of AC-SBLI as a semi-analytical model, this study focuses on the impacts of shock spanwise curvatures on separation and the mechanism of their action. It reveals that spanwise curvatures affect the separation in both internal and external AC-SBLI, but each exhibits a different influence pattern, emphasizing apparent axisymmetric characteristic. The spanwise curvatures exert influence indirectly by altering the compression ratio and directly by affecting the distribution of streamwise shock intensities. These findings propose a new approach to estimating the flow structures in AC-SBLI, where analyzing the spanwise curvatures will assist with comprehending other more intricate three-dimensional separation phenomena. [ABSTRACT FROM AUTHOR]

Laminar submerged free jet theory still falls short in the near-nozzle region and transition to Schlichting's self-similar jet. The author's recent solution, based on mass conservation, is found lacking beyond the near-nozzle jet-core region. Instead, it is here constrained to conserve momentum, resulting in a locally linearized convection-diffusion equation, valid over jet width and up to self-similarity, when compared to simulations. This new solution leads to profile-specific values of virtual-origin correction to Schlichting's solution. Additionally, extensive jet characteristics are examined: (1) curvature core, (2) radial inflection location, (3) radial velocity, (4) vorticity field, (5) issuing mass, and (6) jet width. All are well predicted, and new insights are gained for a variety of issuing profiles: from uniform, through a non-monotonous profile and up to fully developed. The issuing mass of all non-uniform profiles undergoes an initial contraction proportional to the profile's level of development. Interestingly, the submerged jet contracts identically to the free-surface jet in the very near-nozzle region, before significant influence of their differing boundary conditions. Moreover, unless the issuing profile contains a radial inflection point, the inflection always occurs in the entrained fluid, just beyond the bounds of the issuing mass. It also follows an initial contraction and only later a widening toward the self-similar trend. Despite this contraction, the entrained fluid causes monotonous total jet-widening, at a rate inversely proportional to the level of development. Finally, this new solution correctly captures additional jet features, such as the local radial velocity and decay of the primary vorticity. [ABSTRACT FROM AUTHOR]

Drop surface interaction is omnipresent in nature and vital to many engineering applications. Most previous studies on drop impact dynamics on superhydrophobic cylindrical surfaces have focused on low-impact Weber (We) numbers, wherein the asymmetric bouncing behavior is the prominent outcome. However, it is observed that an impacting drop at higher impact We numbers (>100) exhibits more complex dynamics. The asymmetric post-impact lamella evolution in axial, and azimuthal directions are analyzed in detail. At higher impact velocities, the lamella expands in an azimuthal direction over the solid cylindrical surface, sweeping a certain angle followed by further expansion in air and over the solid surface until attaining the critical detachment angle or swiping angle, which is found to be a function of surface curvature and impact velocity. Thereafter, the expansion proceeds only in the air until the lamella completely shatters away, indicating the absence of a retraction phase in the azimuthal direction contrary to that during low-velocity impact. Lamella nucleation and film rupturing together, along with the ejection of satellite droplets, further add complexity. The present experimental study comprehensively evaluates the effect of higher Weber numbers (We up to 660) and surface curvature. Universal scaling relations are proposed for the lamella evolution in the axial and azimuthal directions based on the impact parameters to rationalize the same. A minimization of the surface energy approach has been hypothesized to predict the detachment angle utilizing the proposed scaling relations and is found to predict well with the experimental data. [ABSTRACT FROM AUTHOR]

Plant tendril inspired helical structures hold significant promise in various applications. In this study, we advance the understanding of factors influencing the morphology of helical fibers fabricated during co-electrospinning, which is grounded in the mechanism of inducing strain mismatch within the polymer components. Our investigation encompasses a comprehensive analysis of the intrinsic curvature through an updated bilayer strip physical model. Potential factors affecting the resulting curvature of the electrospun helical fibers, including flexibility difference and charge difference within the component pair as well as the evaporation behavior of the chosen solvents for polymers, are explored through numerical simulations and experimental validation. [ABSTRACT FROM AUTHOR]

The present work investigates the three-dimensional flow of a thin liquid film distributed on the outer surface of an ellipsoid, rotating around the vertical axis at constant angular velocity. The lubrication approximation expressing the evolution of the film thickness, originally developed for stationary curved substrates, has been re-derived by including the non-inertial forces associated with the rotation. This comprehensive model, which incorporates the gravitational, centrifugal, and capillary forces, is employed for a parametric investigation via numerical simulations. The results validate and extend the conclusions of our former study covering the axisymmetric case and bring about an advanced understanding by exploring non-axisymmetric effects. The parametric analysis sheds light on the significance of rotation on a non-constant curvature substrate by comparing the thickness profiles with the static case. [ABSTRACT FROM AUTHOR]

The effect of curvature on the three-dimensional instabilities of lid-driven flow in a toroidal square cavity is numerically studied using the linear stability analysis based on the spectral element method. The critical stability curves are determined, and four types of instability modes are predicted. For small curvatures (δ ≤ 0.2), the most dangerous mode is a steady short-wavelength mode (λc ≈ 0.4), which is consistent with that in the straight square cavity. In a narrow range of 0.22 ≤ δ ≤ 0.28, the critical mode is oscillatory and of medium wavelength (0.84 < λc < 1.07). For δ ≥ 0.29, two types of steady long-wavelength modes (λc > 1.26) become the critical mode. The disturbance energy analyses show that all the instabilities are caused by the centrifugal instability mechanism. [ABSTRACT FROM AUTHOR]

Manipulations of "complex" drops and their interactions with "complex" surfaces have attracted much attention in recent years. Here, we hypothesize that Janus drop impact on curved superhydrophobic surfaces can be highly affected by the curvature, Weber number (We), and viscosity difference between Janus components. The main objective is to predict the splitting of the low-viscosity component from the Janus drop. The study forms regime maps for the transition of non-splitting/splitting as a function of the parameters. It is shown that the We threshold, above which splitting occurs, can be tuned by altering the surface curvature and viscosity difference between low- and high-viscosity components. Asymmetric behavior observed in the two components is elucidated by establishing the relationship of the residence time and characterizing the dynamics by means of the horizontal momenta. The underlying mechanism for bouncing on asymmetric structures can provide a meaningful guidance on the designs of liquid purification or multi-material printing. [ABSTRACT FROM AUTHOR]

Clinical observations indicate that the shape and tortuosity of the carotid siphon are some of the contributing factors to the initiation and growth of an aneurysm. The present study explores the validity of this observation by performing systematic numerical simulations. Computational fluid dynamics (CFD) based calculations are performed to compare and contrast four different types of patient-specific carotid siphons, viz., C-, S-, U-, and helical shape, to investigate the hemodynamic influences on flow features, secondary flow patterns, and helicity. Fewer curved regions and the presence of local acute curvature were found to result in higher velocity magnitude, leading to giant sidewall aneurysms in the distal end of this curvature. In contrast, a larger number of curved regions in the parent vessel resulted in disturbed flow and reduced maximum streamwise velocity. When the velocity is lower, smaller aneurysms are observed at the bifurcation carina. The influence of siphon tortuosity, which is exemplified through the Dean number and linked to secondary flows, causes higher helicity when the vessel is more tortuous. It is hypothesized that a highly tortuous vessel protects the further growth of an aneurysm. This is in contrast to a less tortuous vessel with single acute curvature and prone to further expansile behavior of an aneurysm. [ABSTRACT FROM AUTHOR]

Mach reflection (MR) is an essential component in the development of the shock theory, as the incident shock curvature is found to have a significant effect on the MR patterns. Curved-shock Mach reflection (CMR) is not yet adequately understood due to the rotational complexity behind curved shocks. Here, CMR in steady, planar/axisymmetric flows is analyzed to supplement the well-studied phenomena caused by oblique-shock Mach reflection (OMR). The solution from the von Neumann's three-shock theory does not fully describe the CMR case. A CMR structure is presented and characterized by an incident shock, reflected shock, Mach stem, and expansion/compression waves over the slipline or occasionally an absence of waves due to pressure equilibrium. On the basis of this CMR structure, an analytical model for predicting the Mach stem in the CMR case is established. The model reduces to the OMR case if the shock curvature is not applicable. Predictions of the Mach stem geometry and shock structure based on the model exhibit better agreement with the numerical results than predictions using previous models. It is found that the circumferential shock curvature plays a key role in the axisymmetric doubly curved CMR case, which results in a different outcome from the planar case. [ABSTRACT FROM AUTHOR]

In this work, we analyze the flow of a thin layer of viscous liquid over the outer surface of a sphere due to inertia and gravity. We use the classical problem of a circular hydraulic jump as a starting point and observe the changes in the flow structure as the gravity component along the surface becomes significant. We assume that the flow is stationary and axisymmetric, the curvature of the spherical surface is small, and the capillary forces are negligible. The depth-averaged thin-layer equations describe the flow. We perform a qualitative analysis using a one-parametric representation of the longitudinal velocity distribution and find the necessary conditions for the hydraulic jump existence. The intensity of the jump monotonically decreases, and its radius grows to a certain finite value. The jump vanishes at a finite distance from the axis of symmetry. Using a two-parametric representation, we locate zones of recirculating flow and find the condition of their existence. We find the optimal strategy of averaging by comparing the results of our calculations with the data obtained experimentally and by using simulations in the framework of the full Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

In practical aerodynamic problems, curved shock/boundary layer interaction (CSBLI) is more frequently encountered than the canonical shock/boundary layer interaction (SBLI). Owing to the topological complexity of the flow field brought about by shock curvature, accurate prediction of the interaction length scale of CSBLI is a challenging task. In this work, streamwise and spanwise curvatures are introduced, in turn, with the aim of establishing an analytical model for the interaction length scale of CSBLI based on conservation of mass. The validity and universality of the model are verified, which reveal the impact of the shock curvatures on the interaction, acting as the form of non-uniformity. As an example, the CSBLI with different curvatures is compared, demonstrating that a streamwise curvature of 0.071 will bring a reduction of about 16.5% of the interaction length. The proposed method can be regarded as providing a foundation for further research on CSBLI, opening new perspectives for the investigation of SBLI flow structures. [ABSTRACT FROM AUTHOR]

In this study, we experimentally and numerically investigate the activity of a rebounding droplet on a spherical particle and the effects of surface curvature on its rebounding behavior. We report that the rebound of the droplet can be promoted in smaller particles. As the droplet-to-particle size ratio increases, the critical Weber number is significantly reduced, and the restitution coefficient is much increased. The underlying physical mechanism for the promotion of the rebound is the reduced energy dissipation on the smaller particles in the very early stages of the collision, and this reduction mainly occurs as the liquid is being squeezed. This reduced energy loss allows larger liquid–gas interfacial deformation at the maximum spreading state and also allows more drastic retractions during the recoiling stage, which eventually leads to the promotion of the rebound. [ABSTRACT FROM AUTHOR]

Thermal stratification can lead to the damping of turbulence, which reduces the mixing of solutes in a fluid body. A series of direct numerical simulation (DNS) solutions sweeping through a range of four different meandering channel curvatures, from a sharp to mild curvature range, are obtained to investigate the effect of curvature on stratification in meandering thermally stratified turbulent open channel flow with an internal heat source that models radiative heating from above. Based on the DNS results, the present paper addresses two issues. First, the influence of changing curvature on the complex bi-cellular pattern of the secondary flow is investigated, including the distribution of the temperature field. Second, the effects of changing curvature on the degree of stratification are analyzed. Stratification can be characterized by the friction Richardson number R i τ and the bulk Richardson number Rib. Stratification can also be viewed in terms of the transfer of energy from mean flow kinetic energy to potential energy via buoyancy fluxes. We study the effect of curvature on stratification by investigating its effect on the friction and bulk Richardson numbers. We also study the transfers between the global potential and kinetic energy reservoirs, including the global available Ea, background Eb, and total potential energy Ep, and the domain-averaged mean kinetic and turbulent kinetic energy. It is found that, in meandering channels, with the increase in curvature, Ep increases and R i τ and Rib decrease, indicating that increasing curvature leads to a decrease in the level of stratification. On the other hand, we also find that a low curvature meandering channel has a higher level of stratification than a straight channel. [ABSTRACT FROM AUTHOR]

Current analyses of curved detonations are mostly limited to the dynamics along the wall or the symmetry axis due to the lack of efficient approaches for reliably tracking stream tubes with curved shock fronts. To address this lack, the present work proposes a novel curved ray-tracking algorithm with two implementation methods. The curved ray is characterized by a specific arc of constant curvature perpendicularly intersecting both successive fronts. The methods were validated against Whitham's exact geometrical shock dynamics solutions of the self-similar shock diffraction problem. As compared to the typical forward straight-ray method, which is of the first order, the proposed methods demonstrate convergence rates greater by more than one order of magnitude and tend to be of the second order. The convergence analysis enabled to determine the range of time resolution required for the proposed methods to provide reliable results. This range is comparable to the acquisition rate of a modern high-speed camera that is commonly used in detonation visualization experiments. Differences between the proposed curved ray-tracking methods and the typical forward straight-ray method have been further examined by analyzing the ray dynamics during the weakly unstable hydrogen–oxygen–argon detonation diffraction. The ray-tube-based velocity-curvature relationship showed satisfactory agreement with those already well-established in quasi-steady experiments and predicted by the generalized Zeldovich–von Neumann–Doering model. This suggests the limited role of unsteadiness and cellular structure in the macro-scale dynamics of weakly unstable detonations. [ABSTRACT FROM AUTHOR]

We study the dynamics of an erodible sinuous channel subject to combined curvature and autogenic width oscillations. We find that generic grain transport (both bedload and suspended load transport) amplifies lateral stretching of the channel centerline and enhances the maximum width-variation amplitude and curvature ratio in their temporal dynamics by displaying a phase lag. However, in the initial and mature stages, the planform dynamics asymptotically approaches the conventional limits. The planform evolution is found to be influenced by four key parameters: Shields number, relative roughness, channel aspect ratio, and shear Reynolds number. The findings of this study, to the best of our knowledge, represent the first analytical investigation of the planform evolution of a sinuous channel driven by generic grain transport. [ABSTRACT FROM AUTHOR]

Capillary-wave propellers (CWPs) based on the phenomenon of electrowetting-on-dielectric (EWOD) have shown great potential for floating-object propulsion, heat-transfer enhancement, and fluid thermophysical property measurement. However, the small amplitude of the EWOD-induced capillary-wave limits the performance of the CWP in practical applications. Herein, a CWP with a concave curvature is proposed to enlarge the capillary-wave amplitude. The formation and propagation of the capillary wave are visualized by using a high-speed camera and a free-surface synthetic schlieren method. The wave amplitude and wave propagation are modeled theoretically. The effects of the concave curvature and the frequency of the electrical signal are investigated, and the results show that the concave curvature increases the wave amplitude, velocity vector, and wave intensity as compared with flat EWOD units. In addition, the results show that 20 Hz electrical signals are favorable for pursuing large wave energy density. The underlying mechanism for increasing the wave energy via concave CWPs is revealed experimentally and explained theoretically. The proposed concave CWP is helpful for increasing the propulsion speed of small-scale floating objects and is promising for improving the performance of CWPs in other applications. [ABSTRACT FROM AUTHOR]

In this article, we report the experimental evidence and an analytical model for the first time to predict the evaporation kinetics of sessile droplets seated on generic curved surfaces, either concave or convex. We appeal to the steady state, isothermal vapor diffusion theory, and incorporate conditions suitable to the geometry of curved substrates in a toroidal coordinate system, which is inherently different and more complicated than flat surfaces. We portray the mannerism in which the nature and magnitude of the curvature may dictate the evaporation behavior compared to a flat substrate. To validate the analytical model, we experimentally delineate the droplet evaporation phenomenon under the influence of substrate curvature. Convex cylinders and concave grooves of different radii have been employed for this purpose, and optical diagnostics of the droplet profile has been carried out to monitor evolution of the evaporation progress. Our model predicts that substrate convexity leads to substantial increase in evaporation rates due to augmented vapor diffusion domain over the liquid–vapor interface, whereas on a concave surface there is a decrease in evaporation rates due to droplet confinement phenomenon. The present model also addresses the fact that on the concave surface, the evaporation rate is not directly governed by substrate curvature, as discussed in the literature. The predictions from the model are found to be in good agreement with our detailed experimental observations. [ABSTRACT FROM AUTHOR]

The stability of copolymer tethers is investigated theoretically. Self-assembly of diblock or triblock copolymers can lead to tubular polymersomes, which are known experimentally to undergo shape instability under thermal, chemical, and tension stresses. It leads to a periodic modulation of the radius, which evolves to assembly line pearls connected by tiny tethers. We study the contributions of shear surface viscosity and spontaneous curvature and their interplay to understand the pearling instability. The performed linear analysis of stability of this cylinder-to-pearls transition shows that such systems are unstable if the membrane tension is larger than a finite critical value contrary to the Rayleigh–Plateau instability, an already known result, or if the spontaneous curvature is in a specific range, which depends on membrane tension. For the case of spontaneous curvature-induced shape instability, two dynamical modes are identified. The first one is analog to the tension-induced instability with a marginal mode. Its wavenumber associated with the most unstable mode decreases continuously to zero as membrane viscosity increases. The second one has a finite range of unstable wavenumbers. The wavenumber of the most unstable mode tends to be constant as membrane viscosity increases. In this mode, its growth rate becomes independent of the bulk viscosity in the limit of high membrane viscosity and behaves as a pure viscous surface. [ABSTRACT FROM AUTHOR]

In this Perspective, we explore the instability of a meandering channel with variable width and curvature. The analysis employs the depth-averaged formulations for the flow and sediment transport. Unlike the conventional instability analysis that considers mainly the bedload transport, we consider the generic sediment transport including both the bedload and suspended load. The analysis addresses the variations of the near-bank excess azimuthal velocity and the bed topography deviation with the meander wavenumber for different pertinent parameters, such as Shields number, relative roughness number, channel aspect ratio, width-variation amplitude, and shear Reynolds number. The analysis detects a resonance phenomenon for certain critical values of the pertinent parameters and explores the sensitivity of the resonant wavenumber to the pertinent parameters. In a hydraulically smooth flow regime, the sediment suspension is found to play a stabilizing role. On the contrary, in hydraulically transitional and rough flow regimes, the sediment suspension offers a destabilizing effect. The stability diagrams reveal that the stable zone enlarges as the Shields number and relative roughness number increase, while it contracts with an increase in width-variation amplitude. For a given shear Reynolds number in a hydraulically smooth flow regime, the stability diagram predicts various stable zones. By contrast, for a given shear Reynolds number in hydraulically transitional and rough flow regimes, a unique stable zone exists. [ABSTRACT FROM AUTHOR]

The present study compares the critical initiation energy predicted by the critical curvature (CC) and critical decay rate (CDR) models. To ensure a fair and meaningful comparison between these two theoretical approaches, the Taylor–Sedov blast wave model, which enables us to relate the critical state to the energy of the point source, has been employed in both models. Simplified as well as detailed chemical mechanisms were employed for the comparison. By using the same blast wave model, the ratio of critical initiation energy calculated with the CC and CDR models was found to be one to two orders of magnitude smaller than the results in previous studies. Although the choice of the blast wave model is important, the critical energy predicted by the CC model is invariably larger than the one predicted by the CDR model. This was explained by analyzing the relationship between the shock front radius and decay time, as well as the ignition delay-time around the critical conditions of the two models. It was demonstrated that the critical conditions of the CDR model can be fulfilled more easily than those of the CC model. As a result, the main source of discrepancy between the CDR and CC models is that they adopt different initiation failure mechanisms, namely, curvature for the CC model against unsteadiness for the CDR model. [ABSTRACT FROM AUTHOR]

A finite-volume solver is used to describe the cyclonic motion in a cylindrical vortex chamber comprising eight tangential injectors and a variable nozzle size. The simulations are performed under steady, incompressible, and inviscid flow conditions with air as the working fluid. First, we apply a fine tetrahedral mesh to minimize cell skewness, particularly near injectors. Second, this mesh is converted into a polyhedral grid to improve convergence characteristics and precision. After achieving convergence, the velocity components are evaluated and compared to existing analytical solutions. We find that well-resolved numerical simulations can accurately predict the expected forced vortex behavior in the core region as well as the free vortex tail in the outer region. We also confirm that the swirl velocity remains axially invariant irrespective of the outlet radius. Similarly, we are able to ascertain that the axial and radial velocities embody the bidirectional nature of the motion. As for the computed pressure distribution, it is found to agree quite well with both theoretical formulations and experimental measurements of cyclone separators. Then using a parametric trade study, the effect of nozzle variations on the internal flow character, mantle structure, and recirculation zones is systematically investigated. Apart from the exit diameter, we find that the nozzle length and inlet curvature can substantially affect the internal flow development including the formation of backflow regions, recirculation zones, and mantle excursions. Finally, an empirical relation is constructed for the nozzle radius of curvature and shown to effectively suppress the emergence of recirculation and backflow regions. [ABSTRACT FROM AUTHOR]

This study uses the level contour reconstruction method to numerically investigate the maximum spreading due to droplet collision with a dry, stationary, spherical particle. We consider a broad range of impact conditions: Weber number 30–90, Ohnesorge number 0.0013–0.7869, and droplet-to-particle size ratio 1/10–1/2, and quantitatively and systematically analyze 120 collision cases to understand how liquid viscosity and surface curvature affect the maximum spreading. The maximum spreading increases on the smaller particles for both the capillary and viscous regimes, but the underlying physics clearly differ. The increase in maximum spreading is governed mainly by the surface deformation of the rim for the capillary regime and viscous dissipation for the viscous regime. An empirical correlation that can be applied to the droplet impact on both a particle and a flat surface is also presented. The model shows good agreement with existing experimental data as well as our simulation results within a deviation range of ±15%. [ABSTRACT FROM AUTHOR]

We study theoretically the self-propulsion dynamics of a small droplet on general curved surfaces by a variational approach. A new reduced model is derived based on careful computations for the capillary energy and the viscous dissipation in the system. The model describes quantitatively the spontaneous motion of a liquid droplet on general surfaces. In particular, it recovers previous models for droplet motion on the outside surface of a cone. In this case, we derive a scaling law of the displacement s ∼ t 1 / 3 of a droplet with respect to time t by asymptotic analysis. Theoretical results are in good agreement with experiments in previous literature without adjusting the friction coefficient in the model. [ABSTRACT FROM AUTHOR]

Droplets and bubbles are thought to be two sides of the same coin; this work determines how true this is at the molecular scale. Stable cylindrical nanodroplets and nanobubbles are obtained in Molecular Dynamics (MD) simulations with three-phase contact lines pinned by alternate hydrophobic and hydrophilic patterns. The surface tension and Tolman length for both types of curved interfaces are obtained with the Kirkwood–Buff method, based on the difference between normal and tangential pressure components. Both bubble and droplet cases are compared to the flat interface case for reference. Results show that the surface tension decreases linearly while the Tolman length increases linearly with the gas/liquid density ratio. By running a careful parameter study of the flat interface over a range of densities, the effect of the density ratio can be corrected isolating the effects of curvature on the surface tension and Tolman length. It is found that such effects start to be seen when the equimolar curvature radius goes down to 20 reduced Lennard–Jones (LJ) units. They have the same magnitude but act with opposite signs for nanodroplet and nanobubble interfaces. Considering effects of the density ratio and curvature, a fitted Tolman equation was obtained, which predicts the surface tension of a curved interface. Results obtained by the fitted Tolman equation agree well with those obtained by the MD simulations except at very small curvature radius (<10 reduced LJ units) due to the accumulation of the curvature dependence of the Tolman length. [ABSTRACT FROM AUTHOR]

When two liquid droplets approach at negligible velocity in air, their coalescence spontaneously occurs by jump-to-contact instability and a connecting bridge joining the two facing interfaces at the nanoscale is created. We report experimental investigations of the expansion of this initial bridge by means of high-speed imaging. By considering droplets of water, polydimethylsiloxane, or paraffin of a few hundred micrometers, we investigate regimes where inertia takes a major role. Depending on the Ohnesorge number (Oh), the dynamics of the bridge differs a lot. For Oh ≈ 1, the initial flow is rapidly attenuated and the connecting bridge between the two droplets adopts a smooth parabolic shape. The maximum interface curvature and the minimum liquid pressure remain at the bridge center. The expansion is thus caused by the capillary pressure that drives the fluid toward the center. At small Oh, in the inertial regime, the length of the initial bridge grows at constant speed and the bridge expansion can be described by the propagation of nondispersive capillary wave packets. The central part of the bridge takes a cylindrical shape connected to the droplets by a narrow region of very large curvature. At the resolved scale, the interface exhibits slope discontinuities. By considering dihedral potential flows that result in the presence of the slope discontinuities, we show that the apparent angle made by the interface controls the flow rate that enters the bridge and thus determines its radial expansion. [ABSTRACT FROM AUTHOR]

The incompressible flow of a Maxwell fluid through a curved duct with a rectangular cross section is numerically investigated over a wide range of the Dean number and curvature of the duct. Unsteady solutions, such as periodic, multi-periodic, and chaotic solutions, are obtained by using the spectral method. The combined effects of the large Dean number, Deborah number, and curvature on fluid flow behaviors are discussed in detail. It is found that increasing the Deborah number accelerates the occurrence of the four-cell structure of secondary flow no matter what the Dean number is. Periodic solutions are found to appear for the case of a smaller Dean number due to the presence of elasticity. The periodic solution turns to a chaotic solution if the Dean number is further increased. The chaotic solution is weak for a smaller Deborah number, while it becomes strong for a larger Deborah number. In addition, time evolution calculations at Dn = 300 show that the flow state changes significantly if the curvature δ is increased to be the critical value of the curvature δc = 0.26, while it remains almost unchanged for δ > δc or δ < δc. [ABSTRACT FROM AUTHOR]

Understanding the effect of the artery curvature on the pressure drop inside the arteries is of great importance due to the existence of several curved portions inside the coronary arterial system. In this paper, an experimental model is developed to account for the effect of the curvature of the coronary arteries on the pressure drop and Fractional Flow Reserve (FFR). FFR is an index for the evaluation of the functional significance of coronary stenosis and is defined as the ratio of the coronary pressure downstream of the stenosis to its upstream value. To measure the pressure drop and FFR across curved artery models, three-dimensional-printed curved artery models are fabricated and installed in the test section of the experimental rig. For ratios of curvature radius over the artery diameter ranging from 2 to 7, there are a minimum value for the pressure drop and, hence, a corresponding maximum value for FFR at a ratio of approximately 3. For the curved arteries with larger curvature radii, the pressure drop increases, and consequently, FFR decreases with an increase in the radius. The results showed that an accurate evaluation of the pressure drop and FFR inside a curved coronary artery can only be achieved by accounting for the effect of curvature parameters including the curvature angle and radius, such that neglecting the effect of the artery curvature results in an underestimation of the pressure drop by about 25%–35%. The developed equation is able to determine the pressure drop inside a curved coronary artery model noninvasively. [ABSTRACT FROM AUTHOR]

A pore network model of isothermal drying is presented. The model takes into account the capillary effects, the transport of vapor by diffusion, including Knudsen effect, in the gas phase, and the Kelvin effect. The model is seen as a first step toward the simulation of drying in mesoscopic porous materials involving pore sizes between 4 nm and 50 nm. The major issue addressed with the present model is the computation of the menisci mean curvature radius at the boundary of each liquid cluster in conjunction with the Kelvin effect. The impact of Kelvin effect on the drying process is investigated, varying the relative humidity in the ambient air outside the medium. The simulations indicate that the Kelvin effect has a significant impact on the liquid distribution during drying. The evaporation rate is found to fluctuate due to the menisci curvature variations during drying. The simulations also highlight a noticeable non-local equilibrium effect. [ABSTRACT FROM AUTHOR]

In this paper, the impact of successive double droplets on a super-hydrophobic tube surface is numerically studied using a three-dimensional model by the coupled level set and volume of fluid method. The effect of impact velocity on double droplets impact under different curvature ratios is studied. With the increase in impact velocity, two kinds of impact models (out-of-phase and in-phase impact) are obtained, and the coalescent liquid film presents rebound, breakup-rebound, and splash-rebound. With the increase in the curvature ratio, the spread of the liquid film along the circumferential direction is promoted, and the rim of leading liquid film up-warp can be observed earlier. The breakup of an extending liquid film is discussed in detail under the curvature ratio of 1, which is mainly influenced by the combined effects of local negative pressure, air flow motion, surface tension, and gravity of the gathering liquid. The air entrainment occurs for the impact velocity between 0.75 m/s (We = 15.4) and 1.25 m/s (We = 42.9), while no air entrainment occurs for the impact velocity exceeding 1.5 m/s (We = 61.7). The entrapped air bubbles would cause a center breakup of the liquid film or escape from the liquid film. The escaping direction is mainly determined by the pressure distribution in the liquid film. [ABSTRACT FROM AUTHOR]

We numerically investigate the curvature effect on the self-propelled capability of coalesced drops. The numerical method is based on a well validated multiphase flow solver that solves the three-dimensional Navier–Stokes equations. The liquid–air interface is captured using the moment of fluid method, and a direction splitting method is applied to advect the interface. Afterward, an approximate projection method is used to decouple the calculation of velocity and pressure. Different cases were validated by comparing the experimental results with the simulation results. The coalescence-induced jumping behavior on a flat surface is carefully captured using this numerical method. To investigate the effect of curvature of a curvy substrate on the self-jumping behavior, a case with a single drop impinging on a convex surface and a case with two drops' coalescence on a fiber are also studied and compared with the experimental results. The asymmetric bouncing of a single drop on the convex surface leads to 40% reduction in contact time, as found in our study. Our study also reveals that due to the curvature of the wedge, the drop forms a lobe shaped region on the symmetric sides of the wedge. The lobed region forces the drop to convert more surface energy into kinetic energy in the upward direction. The jumping capability is improved by increasing the surface curvature. Our study also shows that at lower angles of contact, the drops can easily get attached to the substrate and, at the same time, have difficulty detaching from the substrate. [ABSTRACT FROM AUTHOR]

Analytical relationships describing droplet deformation in external magnetic (electric) fields rely on spheroidal and ellipsoidal shape approximations. We show that the ellipsoidal shape approximations that assume a uniform internal magnetic field are only valid for small deformations (aspect ratio a/b ≈ 4). For large droplet deformations, the non-uniformity in the field within the droplet becomes substantial, rendering such approximations to be invalid. To overcome the limitations of ellipsoidal theory, we perform numerical simulations to determine volume averaged demagnetization factor and fields. Based on the numerical simulations, we propose semi-analytical relationships to describe small and large deformations for magnetic droplets using volume averaged methods. We test and validate our results with the existing experimental results and find an excellent agreement between our model and experimental studies. We extend our analysis and investigate static and dynamic droplets with conical tips. We show that droplets with conical tips could be defined solely by the characteristic half cone angle. We analyze unstable droplets with extremely high susceptibility χ → ∞ and find that conical tips with a half cone angle of θc ≈ 30° and an aspect ratio of ≈3.7 are formed prior to breakup, in agreement with the prior experimental studies of charged electric droplet breakup. We show that the volume averaged methods derived for droplets with finite tip curvature are also valid and in good agreement with the computational and previous experimental studies of magnetic droplets with conical tips. [ABSTRACT FROM AUTHOR]

The physical characteristics inside shock waves with nonequilibrium molecular motion are difficult to describe using conventional macroscopic methods. In this paper, nonequilibrium hydrodynamic and thermodynamic effects caused by the strong nonequilibrium molecular velocity distribution at a shock wave are studied using a mesoscopic kinetic approach. This approach is based on a lattice Boltzmann method and a kinetic nonequilibrium method. The former adopts a compressible double-distribution-function model with separated density and total energy distribution functions. The latter represents the nonequilibrium effects through nonequilibrium kinetic moments based on the nonequilibrium molecular velocity distribution. The nonequilibrium effects in the steady state and the process of the formation of a regular reflection shock wave are presented. Nonequilibrium effects inside the shock wave are further investigated. First, the curvature pattern during the formation of a regular reflection shock wave is addressed. The curvature characteristic leads to distinct features of nonequilibrium effects compared with the linear pattern. A vector-based approach for visualizing nonequilibrium effects is proposed to study the curvature pattern. Second, the influence of viscosity on nonequilibrium effects, which is related to the average collision time among molecules at the shock wave, is explored. The results obtained in this paper provide mesoscopic physical insight into the flow mechanisms occurring in shock waves. [ABSTRACT FROM AUTHOR]

Hemodynamics plays an important role in the cause of atherosclerotic disease. In this work, we simulated the flow fields in six human carotids using the sharp-interface immersed boundary method. We compare the axial velocity, the secondary flow, the vortex structures, the area with reversed flows, and the standard deviation of velocity fluctuations for different carotids. The computed results show similarities among different carotids for the overall pattern of different flow characteristics. More importantly, differences are observed in terms of the details of the area of the reversed flow region, the size and shape of the region dominated by reversed flows, and the length of time with reversed flow or dominated by secondary flows, which are strongly correlated with the formation of plaques. Further analysis shows that patient-specific features of the carotid geometry, e.g., the flare and proximal curvature of the carotid, have significant effects on these flow characteristics. This suggests that a patient-specific program is needed for the prevention and treatment of atherosclerosis. [ABSTRACT FROM AUTHOR]

The instability of an elastic interface separating a ferrofluid and a nonmagnetic fluid subjected to an applied magnetic field perpendicular to the initially undisturbed interface is investigated in the effectively two-dimensional environment of a vertical, rectangular Hele-Shaw cell. By using a third-order mode-coupling perturbative scheme, and considering that the elastic interface has a curvature-dependent bending rigidity, the emergence of elastic ferrofluid peaks is detected at the onset of nonlinearities. In this context, the approximate profile of the interface is obtained. It is also shown that the morphology of the resulting peaks is sensitive to changes in a dimensionless magnetoelastic number (relative measure of magnetic and elastic forces), as well as in a bending rigidity fraction parameter, which expresses variations in the bending rigidity with the local interface curvature. [ABSTRACT FROM AUTHOR]

The Richtmyer–Meshkov instability of a three-dimensional (3D) minimum-surface featured SF6/air interface subjected to a planar weak incident shock is numerically studied. The focus is placed on presenting more intuitive details of the complex shock-interface interactions. In the present work, 3D Euler equations are solved. The fifth-order weighted essentially non-oscillatory scheme and the level-set method combined with the real ghost fluid method are adopted. The gas interface morphologies are precisely reproduced according to the previous experimental images, the wave systems in 3D space are illustrated, and the velocity distribution in a characteristic plane is depicted. Based on which, the unknown lagging structure in the previous experiment can be reasonably explained. It is actually the soap fog driven by the flow field. The baroclinic vorticity generation and the perturbation amplitude growth histories are measured. The present numerical study well confirms the 3D curvature effect and supports the extended 3D theoretical model for the heavy/light interface scenario. [ABSTRACT FROM AUTHOR]

Bénard-Marangoni convection can be used to self-organize hexagonal convective cells, but defects easily emerge in the hexagonal pattern, which hinders its application in industry. The dynamics of front propagation and defect generation are studied in this paper. We focus especially on the onset process of a local disturbance of a hexagonal pattern, named the "nucleus." The front propagation of the nucleus has been researched through numerical simulations of a model equation and experiments. In the numerical simulations, a single nucleus can evolve into a perfect hexagon pattern under critical or subcritical conditions, and a random disturbance can generate multiple nuclei which evolve into grain boundaries. In addition, under supercritical conditions, defects also emerge as a single nucleus grows. The instability of front propagation is considered to be the mechanism for the generation of irregular patterns. The curvature effect makes the protrusion of the front have a larger velocity in supercriticality, which results in a wavy front, and defects are generated in the concave portion of the front. Also, because of the curvature effect, the front of an irregular pattern has a larger velocity than that of the regular pattern since the protrusion of the front in the irregular pattern increases the average velocity. Experiments have also been carried out by using an infrared camera to analyze front propagation. The results are qualitatively in agreement with the results of numerical simulations. Through the study of defect generation in front propagation, we put forward a method for generating a hexagon pattern which greatly reduces the number of defects. [ABSTRACT FROM AUTHOR]

The bifurcation and instability of nonisothermal annular Poiseuille flow (NAPF) of air as well as water is studied. We have emphasized the impact of a gap between cylinders in terms of curvature parameter (C) for axisymmetric as well as nonaxisymmetric disturbances. The results from the linear stability analysis reveal that the first azimuthal mode acts as a least stable mode of the NAPF of air for relatively small values of C. In this situation, even though for some values of C, the NAPF has supercritical bifurcation, but the same flow may experience subcritical bifurcation under zero azimuthal mode. It has also been observed that for relatively larger values of the Reynolds number (Re) and lower values of C, the NAPF under axisymmetric disturbance always exhibits subcritical bifurcation. However, for small values of Re, the NAPF exhibits only supercritical bifurcation. The finite amplitude analysis predicts only supercritical bifurcation of NAPF of water. The influence of nonlinear interaction of different harmonics on the amplitude profile as well as kinetic energy spectrum is investigated. The amplitude profile possesses a jump in the vicinity of a point where the type of bifurcation is changed. In the subcritical regime, the induced shear production due to modification of the gradient production acts as a main destabilizing factor balanced by the gradient production of kinetic energy. [ABSTRACT FROM AUTHOR]

Oscillatory shearing is a popular method to understand transient nonlinear rheology. Various viscoelastic metrics have been used to analyze oscillatory rheology with different perspectives. We present a translation between various viscoelastic metrics for oscillatory rheology, using the framework of sequence of physical processes (SPPs) as a basis. The relation between the SPP metrics and Fourier-based metrics, such as Fourier sine and cosine coefficients, and large and minimum strain and rate metrics is provided. The meaning of the curvature in elastic and viscous Lissajous figures is explained with the sign of the SPP viscoelastic metrics. A low dimensional interpretation of the SPP framework is presented, featuring the center, size, and orientation of a deltoid in a transient Cole-Cole plot. Finally, we show how statistical information regarding the amount of change exhibited by the SPP metrics over a period of oscillation can be used to enhance the presentation and understanding of traditionally performed amplitude sweep experiments. [ABSTRACT FROM AUTHOR]

In this study, coalescence dynamics of two unequal sized drops of the same liquid have been investigated using the coupled level set and volume of fluid method. A broad range of fluid properties is considered with two orders of magnitude variation of Ohnesorge numbers and Atwood number ranging between 0.01 and 0.9976. The pinch-off process and controlling parameters that lead to satellite generation have been investigated. The capillary waves are generated as a result of the sharp curvature produced near the contact region. Here we demonstrate that the capillary waves propagating along the interface of the lower drop can affect the eventual pinch-off of the satellite. The local curvature of the neck plays a crucial role in the pinch-off process. A sharper axial curvature of the neck increases the local capillary pressure which restricts the pinch-off. The critical diameter ratio above which a satellite pinches off during the coalescence of two free-falling drops increases with increasing relative strength of the viscous force and the gravity force. The critical ratio can be as low as 1.2 at a lower relative strength of the viscous and the gravity forces. The coalescence of two unequal sized drops may produce much smaller satellite drops, on account of coalescence in successive steps, with or without intermediate detachment. [ABSTRACT FROM AUTHOR]

The statistical behavior of the surface density function (SDF, the magnitude of the reaction progress variable gradient) and the strain rates, which govern the evolution of the SDF, have been analyzed using a three-dimensional flame-resolved simulation database of a turbulent lean premixed methane-air flame in a bluff-body configuration. It has been found that the turbulence intensity increases with the distance from the burner, changing the flame curvature distribution and increasing the probability of the negative curvature in the downstream direction. The curvature dependences of dilatation rate ∇ ⋅ u → and displacement speed Sd give rise to variations of these quantities in the axial direction. These variations affect the nature of the alignment between the progress variable gradient and the local principal strain rates, which in turn affects the mean flame normal strain rate, which assumes positive values close to the burner but increasingly becomes negative as the effect of turbulence increases with the axial distance from the burner exit. The axial distance dependences of the curvature and displacement speed also induce a considerable variation in the mean value of the curvature stretch. The axial distance dependences of the dilatation rate and flame normal strain rate govern the behavior of the flame tangential strain rate, and its mean value increases in the downstream direction. The current analysis indicates that the statistical behaviors of different strain rates and displacement speed and their curvature dependences need to be included in the modeling of flame surface density and scalar dissipation rate in order to accurately capture their local behaviors. [ABSTRACT FROM AUTHOR]

Mechanical mechanisms of the directional movement and inverse of an eccentric compound droplet in a modest extensional flow are investigated in this paper by spectral boundary element methods. In this work, a phenomenon is revealed that the shift of a compound droplet is driven by the asymmetric interfacial curvature, not just the outer drag. The asymmetric layout of the daughter droplet leads to the asymmetric drags from the continuous phase and the asymmetric deformation of the compound droplet with different interface curvatures. As the inner droplet has both enhancing and suppressing effects on the globule deformation (during different stages), the interface curvatures will vary when the relative size and location of the inner droplet are changed. The curvature difference results in the asymmetric pressure distribution and circulation inside the compound droplet. Eventually, the interaction of the inner driving force (curvature difference) and the outer drags results in the directional shift and inverse of the compound droplet. The shift direction is affected by the structural asymmetry parameter ε (eccentricity) and some flow features such as the capillary number. The conclusion could enlighten potential applications for the movement of soft globules driven by the curvature difference. [ABSTRACT FROM AUTHOR]

In this paper, a novel geometric approach for studying steady, two-dimensional, incompressible flows has been thoroughly developed. The continuity and momentum equations were expressed in the flow's intrinsic coordinate system in order to "accommodate" the geometric parameters characterizing it, namely, the local curvatures of the streamlines and their orthogonal trajectories. As a result, a new description of the governing equations was obtained, in which the concerned variables are the velocity magnitude v and a new quantity which was named geometric vorticity, Γ. The latter is defined by the curl of the global curvature vector KG and can be interpreted as the geometric signature of the known vorticity Ω This approach leads to a new formulation of the Navier-Stokes and Euler equations, the so-called "velocity-curvature" formulation. In this framework, an expression for the flow velocity as a function of geometric parameters only was developed. This reveals that the physical information of a steady incompressible flow is imprinted in its geometry. It is this insight that makes the aforementioned formulation not only conceptually different to the existing classical descriptions, traditionally employed in both analytical and numerical applications, but also attractive, due to the advantages that it could provide at a theoretical and an experimental level. Finally, the derived results are briefly discussed, while emphasizing the implications that the identified geometry-physics interface might have in the future for planar flowanalysis. [ABSTRACT FROM AUTHOR]

The impact ofwater drops on spherical soft surfaces is investigated experimentally through high-speed imaging. The effect of a convex compliant surface on the dynamics of impacting drops is relevant to various applications, such as 3D ink-jet printing, where drops of fresh material impact on partially cured soft substrates with arbitrary shape. Several quantities which characterize the morphology of impacting drops are measured through image-processing, including the maximum and minimum spreading angles, length of the wetted curve, and dynamic contact angle. In particular, the dynamic contact angle is measured using a novel digital image-processing scheme based on a goniometric mask, which does not require edge fitting. It is shown that the surface with a higher curvature enhances the retraction of the spreading drop; this effect may be due to the difference of energy dissipation induced by the curvature of the surface. In addition, the impact parameters (elastic modulus, diameter ratio, and Weber number) are observed to significantly affect the dynamic contact angle during impact. A quantitative estimation of the deformation energy shows that it is significantly smaller than viscous dissipation. [ABSTRACT FROM AUTHOR]

The effect of initial densities in a free energy based two-phase-flow lattice Boltzmann method for non-ideal fluids with a curved interface was investigated in the present work. To investigate this effect, the initial densities in the liquid and gas phases coming from the saturation points and the equilibrium state were adopted in the simulation of a static droplet in an open and a closed system. For the purpose of simplicity and easier comparison, the closed system is fabricated by the implementation of the periodic boundary condition at the inlet and outlet of a gas channel, and the open system is fabricated by the implementation of a constant flux boundary condition at the inlet and a free-out boundary condition at the outlet of the same gas channel. By comparing the simulation results from the two types of initial densities in the open and closed systems, it is proven that the commonly used saturation initial densities setting is the reason for droplet mass and volume variation which occurred in the simulation, particularly in the open system with a constant flux boundary condition. Such problems are believed to come from the curvature effect of the surface tension and can be greatly reduced by adopting the initial densities in the two phases from equilibrium state. [ABSTRACT FROM AUTHOR]

This article was originally published online on 2 November 2022 with an error in the footnotes. The author footnotes are correct as they appear above. Publisher's Note: "Analytical model for predicting the length scale of shock/boundary layer interaction with curvature" [Phys. [Extracted from the article]