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The fluid–solid coupling effect is more pronounced in the process of deep coal seam development compared to shallow coalbed methane, exerting a greater influence on production, and cannot be disregarded. Throughout the extraction process, the interaction between effective stress and gas desorption triggers deformation within the coal seam, leading to dynamic changes in both porosity and permeability. This paper has developed a fully coupled gas flow and deformation model that contains the coal matrix and discrete fractures to describe the dynamic gas seepage behavior and deformation of deep coal seams within a coupled wellbore–hydraulic fractures–matrix system. The model's validity is corroborated through the examination of fracture aperture, employing the finite element numerical simulation capabilities of COMSOL Multiphysics. Subsequent to the model's validation, an in-depth investigation into the permeability and production variations under diverse parametric conditions is conducted. This analysis also encompasses the assessment of hydraulic fracture geometry's impact. The simulation outcomes reveal that the permeability alterations during coal seam development are subject to the counteracting influences of gas desorption and effective stress. Moreover, it is observed that an increase in the Langmuir volume strain constant and initial porosity correlates with enhanced production, whereas a diminution in the hydraulic fracture compression coefficient leads to increased cumulative production. Notably, the optimal production is attained when hydraulic fractures are oriented vertically yet asymmetrically relative to the horizontal well. [ABSTRACT FROM AUTHOR]

It is a challenge to simulate the hydrodynamic problems covering the large deformation of the free surface arising in severe circumstances with intense flow. This paper investigates algorithms based on the moving particle semi-implicit method for simulating large deformation and impact loads. The algorithm discretizes the fluid domain into a series of particles, each representing a part of the fluid. The pressure field calculation is implicit, and the velocity field calculation is explicit. Three models, including the gradient model, source term, and free-surface detection, have been improved and compared to determine which improvement is the best to enhance the accuracy and stability. The enhanced pressure gradient guarantees that momentum conservation can be satisfied. Particle density and velocity divergence are incompressible conditions combined in the mixed source term approach. The arc approach is used in the free-surface judging process. The results show that the combination of three models is the most effective in exploring the problems of hydrodynamic pressure and dam break. The issue of liquid sloshing including roll and sway investigates the effect of the initial distance and time step. It is found that the simulation accuracy of impact pressure can be increased as the initial distance and the time step decrease. Finally, the free surface breaking and liquid splashing phenomena are easily observed, and the method can accurately simulate the massive deformation of the free surface. These findings are helpful for hazard assessments of the various fluid mechanics-related problems. [ABSTRACT FROM AUTHOR]

The optimization method provides an effective approach to enhance the low-speed lift of the vortex lift waveriders by deforming the aerodynamic shape refinedly. However, the vortex lift enhancement mechanism of the optimized configuration is unclear. In this study, the flow evolutions of the original and the optimized configurations are studied by employing the delayed detached-eddy simulation. Results indicate that the convex deformation of the leeward surface plays a dominant role in enhancing the vortex lift by enhancing the low-pressure suction at the upstream breakdown location and delaying the vortex breakdown. For the enhancement of the low-pressure suction, the convex deformation intensifies the streamwise vorticity below the axis of the primary vortex of the leading-edge vortex, in turn enhancing the downwash effect and causing the primary vortex to move downward. This reduces the pressure coefficient induced by the primary vortex on the leeward surface, thus enhancing the vortex lift. In terms of the delay of the vortex breakdown, the convex deformation compresses and accelerates the flow between the spanwise convex and the leading edge. These intensities enhance the washing effect along the spanwise direction on the outward wing and cause the primary vortex to deflect toward the outboard wing. Subsequently, the primary vortex and the shedding vortices generated by the shear layer instability merge, which increase the primary vortex intensity, and enhance the streamwise velocity in the vortex axis. Correspondingly, the primary vortex breakdown is delayed. Ultimately, the increased low-pressure region caused by the delay of the vortex breakdown enhances the vortex lift. [ABSTRACT FROM AUTHOR]

Experimental research findings are reported on the characteristics of surface transformation of droplets of promising fuel slurries in the air, as they move at subsonic velocities typical of combustion chambers of power plants. The main components of the fuels were water, coal processing waste, and coal. Typical shapes of droplets and the duration of their deformation cycles were identified. Droplets containing more than 70% of the solid phase remained practically undeformed. The lowest relative velocities of droplets leading to their fragmentation were determined. The key characteristics of secondary droplets (their number, sizes, velocities, and surface area of liquid) were calculated on the basis of the experimental findings. These characteristics were compared with those of initial droplets. Disruption conditions in the chosen range of the gas jet pressure (P ≤ 6 bars) can only be provided for fuel slurry droplets containing less than 60% of a coal component. The effect of a group of factors on deformation characteristics was identified. These include air jet and droplet velocities, droplet sizes, temperature, concentration, and type of components and additives. Approximation equations were derived for the mathematical description of the experimental data. Using certain criteria, the conditions necessary and sufficient for the disruption of water–fuel slurries on impact with an air jet were estimated. [ABSTRACT FROM AUTHOR]

The dynamic coupling between a Mach 2.0 shock-wave/turbulent boundary-layer interaction (STBLI) and a flexible panel is investigated. Wall-resolved large-eddy simulations are performed for a baseline interaction over a flat-rigid wall, a coupled interaction with a flexible panel, and a third interaction over a rigid surface that is shaped according to the mean panel deflection of the coupled case. Results show that the flexible panel exhibits self-sustained oscillatory behavior over a broad frequency range, confirming the strong and complex fluid–structure interaction (FSI). The first three bending modes of the panel oscillation are found to contribute most to the unsteady panel response, at frequencies in close agreement with natural frequencies of the mean deformed panel rather than those for the unloaded flat panel. This highlights the importance of the mean panel deformation and the corresponding stiffening in the FSI dynamics. The time-averaged flow shows an enlarged reverse-flow region in the presence of mean surface deformations. The separation-shock unsteadiness is enhanced due to the panel motion, leading to higher wall-pressure fluctuations in the coupled interaction. Spectral analysis of the separation-shock location and bubble-volume signals shows that the STBLI flow strongly couples with the first bending mode of the panel oscillation. This is further confirmed by dynamic mode decomposition of the flow and displacement data, which reveals variations in the reverse-flow region that follow the panel bending motion and appear to drive the separation-shock unsteadiness. Low-frequency modes that are not associated with the fluid–structure coupling, in turn, are qualitatively similar to those obtained for the rigid-wall interactions, indicating that the characteristic low-frequency unsteadiness of STBLI coexists with the dynamics emerging from the fluid–structure coupling. Based on the present results, unsteady FSIs involving STBLIs and flexible panels are likely to accentuate rather than mitigate the undesirable features of STBLIs. [ABSTRACT FROM AUTHOR]

Interfacial instability would be aroused on a spherical liquid droplet when it is subject to external vertical vibration. In this paper, a linear analysis was conducted on this instability problem. The polar-angle dependent acceleration in the spherical coordinate is strongly coupled with the temporal and spatial component of the surface deformation displacement, which gives a recursion equation that implicitly expresses the dispersion relation between the growth rate and the spherical mode numbers. The unstable regions (or unstable tongues) for the inviscid fluids considering the latitudinal mode (longitudinal mode number m = 0) were derived and presented in the parameter space. Compared to the solution of the spherical Faraday instability under radial vibration acceleration, the regions of harmonic unstable tongues for the mono-directional vibration cases become much narrower, and the subharmonic unstable tongues almost approach straight lines. The analysis shows that the latitudinal waves emerging on the spherical droplet surface ought to oscillate harmonically instead of subharmonically, which is opposite to the results for the case under radial vibration acceleration. A corresponding experiment of a liquid droplet lying on a vertically vibrating plate was conducted, and the observations substantiate our theoretical predictions. [ABSTRACT FROM AUTHOR]

This paper concerns the interaction of an oblique shock wave with a supersonic turbulent boundary layer over a thin panel surface, leading to shock–boundary layer interaction and panel buckling. We have performed high-order numerical simulations featuring various static two-dimensional surface deformations typically encountered in experiments. The deformation amplitudes we examined were at least half the height of the incoming turbulent boundary layer thickness. The results show that along the panel midspan, where the maximum deformation amplitude is located, the mean and root mean square pressure are affected by about 10%. Cases for which the pressure at the shock–boundary layer interaction was increased relative to the planar case showed to decrease downstream, and vice versa. Despite the weak response to the mean pressure amplitude, the mean pressure surface contour plots reveal that the streamwise, particularly the spanwise distribution, is affected more noticeably. For example, the surface deformation modes are shown to disrupt the spanwise constant mean pressure, forming higher (or lower) values at either the panel's midspan or edges, depending on the mode. Moreover, the surface curvature leads to a characteristic bending of the spanwise distribution, which can be concave or convex depending on the deformation mode. Analysis of the Reynolds stress anisotropy componentality at different heights from the buckled surface reveals a similar spanwise response of the turbulent velocity fluctuations. The results suggest that the deformation rate plays an important role alongside the deformation amplitude in the turbulent layer and shock–boundary layer interaction. [ABSTRACT FROM AUTHOR]

Xu and Davis [J. Fluid Mech. 161, 1–25 (1985)] examined the stability of long axisymmetric liquid jet subjected to an axial temperature gradient, finding capillary, surface-wave, and hydrodynamic modes. They showed that capillary breakup can be retarded or even suppressed for a small Prandtl number (Pr < 1) and a large Biot number (Bi ≥ 1). In the present work, the energy mechanism is carried out for these three kinds of flow instabilities, and the mechanism of suppressing capillary breakup is clarified. When the Reynolds number (RB) is not large, the work done by the pressure on the free surface (PS) is the main energy source of the capillary instability. At small Pr and large Bi, the phase difference between the radial velocity and surface deformation increases with RB, leading to the decrease in PS, which prevents the occurrence of capillary breakup. Meanwhile, the work done by thermocapillary force becomes the main energy source, making hydrodynamic modes unstable. The perturbation flow fields are displayed, which shows that the temperature fluctuations of three modes differ from each other. [ABSTRACT FROM AUTHOR]

A framework based on a continuous adjoint-based analysis of steady and unsteady flows to predict and control the drag force due to surface morphing is presented. By establishing a relation between perturbations in the body shape and in the boundary condition on a certain geometry, we derive an analytical expression of the sensitivity to changes in the geometry of the body and its relation to the sensitivity to the perturbation of the boundary conditions. The methodology is evaluated on the incompressible flow around a cylinder for steady and unsteady flows. A reduction of the drag coefficient was obtained and investigated by several surface deformations, conducted in the direction of the sensitivity vector field obtained by solving the derived adjoint problem. In unsteady flows, the sensitivity field is computed by integrating the unsteady adjoint problem backward in time from the unsteady flow solution. Two different types of deformations based on the calculated sensitivity were applied: time-averaged deformation and time-dependent. Attempting the latter, a deformation at each time step, did not yield the same satisfactory results as the time-averaged in terms of expected drag reduction. We provide a theoretical reasoning for the difference between both methodologies, together with an insight into the physics of the sensitivity vector field distribution relating it to the drag force sources. [ABSTRACT FROM AUTHOR]

This paper presents an analytical/numerical study of the evaporation characteristics of sessile drops deformed by the presence of the gravitational field, focusing on the specific case of superhydrophobic substrates. The effect is systematically analyzed for contact angles between 150° and 180° and water drops with volume varying between 2.7 μl and 14.0 ml for a total of 91 cases. The evaporation characteristics are analyzed in terms of the vapor fluxes on the drop surface and evaporation rates, and the effect of drop deformation is quantified by relating the evaporation rate to the contact angle and the Bond number, B o = ρ g R e q 2 / σ , where Req is the volume equivalent drop radius. Some peculiarities that characterize the superhydrophobic region are pointed out, like the existence of a relative large region of Bo (from 0 to 10–15), where the evaporation rate of the deformed drops is lower than that of a spherical cap of the same size, and an almost negligible effect of the contact angle on evaporation characteristics, when compared to the hydrophilic/hydrophobic substrate cases. A relatively simple correlation is defined as a correction to the well-known Picknett–Bexon correlation, valid for non-deformed drops, and it is proposed for a quick evaluation of the evaporation rates from sessile drops, deformed by the gravitational field, on superhydrophobic substrates. [ABSTRACT FROM AUTHOR]

As an aircraft flies through cloud at temperatures below freezing, it encounters ice particles and supercooled droplets, which results in the accretion of ice onto its surfaces and hence deformation of its aerodynamic shape. This can, in worst cases, cause series accidents. Here, we focus on tackling the common situation where there is a thin layer of water on the aircraft surface and the particles are similarly thin such as to be able to interact with the water layer. Three-way interaction occurs between air, water, and body motion: under suitable assumptions (including that the Reynolds and Froude numbers are large, and that the body is much denser than the air), the model allows the shape of the layer interface and pressure profile beneath the body to be calculated for a given body position. Simultaneously, this in turn allows the forces on the body to be calculated and hence the motion of the particle to be computed in full. The result is a wide range of possible motions of the particle, including both "sink" cases (the particle enters the water and becomes submerged) and "skim" cases (where the particle is launched back off the surface of the water following contact). The latter cases have analogy with traditional "stone skimming/skipping" games. Repeated skims and significant wakes are accommodated rationally. [ABSTRACT FROM AUTHOR]

A fluid droplet, in general, deforms if subject to active driving, such as a finite slip velocity or active tractions on its interface. Starting from Stokes equations, we show that these deformations and their dynamics can be computed analytically in a perturbation theory in the inverse of the surface tension γ, by using an approach based on vector spherical harmonics. We consider squirmer models and general active tractions, such as inhomogeneous surface tensions, which may result from the Marangoni effects. In the lowest order, the deformation is of order ε ∝ 1 / γ , yet it affects the flow fields inside and outside of the droplet in order to ε 0 . Hence, a correct description of the flow has to allow for shape fluctuations, —even in the limit of large surface tension. We compute stationary shapes and relaxation times and compare our results to an approach, which discards all effects of deformations on surface tensions. This approach leads to the same propulsion velocity but to significantly different flow fields. [ABSTRACT FROM AUTHOR]

Here, we present an analysis of the flow properties of second order Stokes waves in water. The description of the flow field is developed using the concept of fixed points and manifolds, which is commonly employed for the analysis of a nonlinear dynamic system. We find that the components of the velocity field are related to each other by an elliptic correlation, where the center of the ellipse represents the fixed points. Since an ellipse is not likely to pass through its center, the estimation of the fixed points in a second order Stokes wave seems challenging. However, we find that the fixed points can be found out in a degenerate case of the ellipse; such a case is observed at the bottom surface that is found to host all the fixed points. The vertical lines passing through the fixed points represent the manifolds. We find that, interestingly, the fixed points and the corresponding manifolds are not fixed but rather move with a speed that equals the wave celerity. Here, we show that the deformation of the free surface requires straining. The flow field evolves in a manner to sustain such straining. Despite the rigid nature, the flow straining is also observed at the bottom surface. Such straining is found to be generated by the fixed points at the bottom surface. The vertically oriented manifolds are found acting as the guides to mediate such flow and straining exchange between the free and bottom surface. [ABSTRACT FROM AUTHOR]

Thermocapillary migration of a deformed droplet in the combined vertical temperature gradient and thermal radiations with uniform and non-uniform fluxes is first analyzed. The creeping flow solutions show that the deformed droplet has a slender or a cardioid shape, which depends on the form of the radiation flux. The deviation from a sphere depends not only on the viscosity and the conductivity ratios of two-phase fluids but also on capillary and thermal radiation numbers. Moreover, in the roles of interfacial rheology on thermocapillary migration of a deformed droplet, only the surface dilatational viscosity and the surface internal energy can reduce the steady migration velocity, but the surface shear viscosity has not any effects on the steady migration velocity. The surface shear and dilatational viscosities affect the deformation of the droplet by increasing the viscosity ratio of two-phase fluids. The surface internal energy directly reduces the deformation of the droplet. However, the deformed droplet still keeps its original shape without the influence of interfacial rheology. Furthermore, it is found that, based on the net force balance condition of the droplet, the normal stress balance at the interface can be used to determine the steady migration velocity, which is not affected by the surface deformation in the creeping flow. From the expressions of the normal/the tangential stress balance, it can be proved that the surface shear viscosity does not affect the steady migration velocity. The results could not only provide a valuable understanding of thermocapillary migration of a deformed droplet with/without the interfacial rheology in a vertical temperature gradient controlled by thermal radiation but also inspire its potential practical applications in microgravity and microfluidic fields. [ABSTRACT FROM AUTHOR]

Analyzing the deformation of liquid surfaces to better understand, for example, wave generation in oceanology or the formation of industrial spray systems, requires a series of three-dimensional snapshots that temporally resolve such events. This requirement is challenging, especially when applied to transient liquid surfaces that deform rapidly. A technique called Fringe Projection-Laser Induced Fluorescence (FP-LIF), developed by the authors, generates three-dimensional surface reconstructions of irregular liquid structures using snapshots recorded via a single camera only. In this article, FP-LIF is associated, for the first time, with a high-speed detection system, allowing the three-dimensional visualization of liquid surface deformation and breakups at a kHz frame rate. The technique is applied here at 20 kHz for imaging the complete development of a wide hollow-cone water spray and analyzing, in detail, the transition from early injection to stabilization. The three-dimensional image series covered a total time window of 300 ms (6000 frames). It is observed during the first 100 ms that the initial liquid jet deforms into a stable tulip shaped sheet. Then, between 100 and 180 ms, the tulip shape gradually grows until its stabilization corresponds to the final conical shaped sheet. Once the stabilization is reached, the fluctuation of the final spray-angle—ranging from 40° to 50°—is extracted by post-processing 1000 consecutive three-dimensional images, providing a detailed analysis of the radial symmetry of the spray over time and three-dimensional space. The results provided in this article are relevant for the validation of Computational Fluid Dynamics spray models. [ABSTRACT FROM AUTHOR]

Remote light-induced free liquid surface deformation has been studied in various systems for decades. One of the mechanisms able to do this task is driven by the thermocapillary Marangoni effect. The strength of the light–matter interaction, which is usually weak, here is amplified by the light absorption and heat production that changes surface tension. Here, we report on an experimental study aimed at dynamical aspects of the deformation induced under conditions of chopped laser excitation light. The light-induced deformations are usually in the range of several micrometers. Therefore, we applied the interferometric technique to measure deformation profiles in real time. Experiments were performed in the shallow bath of the rapeseed oil with an azo-dye and excited with 514.5 nm and probed with 650 nm coherent laser beams, respectively. The mechanism of deformation driven by Marangoni effect was carefully modeled in 3D by computational fluid dynamic numerical simulations within the COMSOL Multiphysics package. The adaptive mesh technique used in the simulation together with solving the time-dependent coupled Navier–Stokes and heat transport differential equations allowed us to replicate the experimental findings. A satisfactory agreement between the results of the simulations and those of the experiment in terms of the dynamics, shape, and depth of the deformation has been obtained. The toroidal-like whirls accompanying the thermocapillary Marangoni effect were identified by the simulation results. We then experimentally proved that these toroidal-like vortices, which accompany laser heating in dyed oil, formed a kind of novel hydrodynamic trap, in the center of their quiet zone, in which microcrystals can be trapped. [ABSTRACT FROM AUTHOR]

A numerical analysis of the thermocapillary-driven dynamics of a free surface in microgravity is presented for an open container of liquid subjected to steady or oscillatory thermal excitation. The response to this forcing is analyzed for parameters representative of common silicone oils. In contrast to previous investigations, we permit large-scale unconstrained motion of the contact points and deformation of the free surface, which allows us to study the interaction between free surface dynamics and thermocapillary flow. First, the response of the free surface to steady thermal excitation is considered and characterized by the asymmetry of the contact points. Linear dependence of this asymmetry on the applied Marangoni number is found, which is amplified by the vibroequilibria effect when supplemental (high-frequency) vibrations are introduced. In low-viscosity liquids, the transient dynamics of the free surface includes sloshing modes, suggesting that thermal modulation may be used to excite them. The free surface response to oscillatory thermal excitation is then studied for a wide range of parameters, including variations in contact angle β, viscosity ν, container length L, and fluid height H. We perform a frequency analysis and obtain Bode-type diagrams for the contact point oscillations, characterizing the low-frequency response by its amplitude and phase with respect to the thermal forcing, and demonstrate a resonance peak corresponding to the principal sloshing mode. Overall, these results indicate the potential of oscillatory thermal excitation for fluid control in microgravity. [ABSTRACT FROM AUTHOR]

The vitreous undergoes physical and biochemical changes with age. The most important of such degenerative changes is vitreous liquefaction or synchysis, in which pockets of liquid known as lacunae form in the vitreous gel. The movement mechanism and characteristics of vitreous liquefaction are quite complex. In this study, the flow dynamics of partial vitreous liquefaction (PVL) as two-phase viscoelastic-Newtonian fluid flow are investigated in the human eye. A reliable three-dimensional (3D) numerical procedure is developed for capturing the interface effects and dynamic characteristics of these two-phase complex fluid flows. In the present work, two different configurations of the PVL including liquefied pocket in the central and the posterior portions of the vitreous cavity are considered. The effects of lens indentation on the flow field and interface deformation of PVL inside the vitreous cavity are investigated. The results show that the curvature of the vitreous cavity due to the lens capsule increases shear and normal stresses in comparison with those for the PVL in a sphere as a simplified model. It is observed that the presence of lens indentation and the location of liquefied region are two factors that can produce conditions of asymmetry inside the vitreous body. In a realistic model of vitreous cavity, although the velocity magnitude inside the liquefied vitreous region increases when the liquefied pocket is in the posterior portion of the vitreous cavity, the stress values and the asymmetric condition of flow field become more significant for the liquefied pocket located close to the posterior lens curvature. [ABSTRACT FROM AUTHOR]

Three-dimensional large-eddy simulations are carried out for flow past a cylinder beneath a deformable free surface at a fixed Reynolds number of Re = 7550. The results are examined for two Froude numbers of F r = 0.2 and 0.6 and a gap ratio of 0.4, to investigate the effects of the distortion of the free surface on the flow fields and hydrodynamics. At the low Froude number of F r = 0.2 , the deformation of the free surface is small with little influence on the wake characteristics, and an alternative vortex shedding modulated by the free surface is detected in the wake. As the Froude number increases to 0.6, intense interface distortion occurs, which can be divided into three different regions: a hydraulic jump in the region of overtopping, a well-defined long-wavelength wave generation region in the large-scale recirculation zone near the free surface, and a water level recovery slope further downstream. The sudden change in flow regime from locally supercritical to subcritical allows the occurrence of the hydraulic jump. The induced surface waves behind the cylinder are ascribed to the shedding process of three shear layers, two of which are separated from the cylinder surface and one from the free surface. In addition, a jet-like flow originated from the gap between the free surface and the top of the cylinder occurs, exerting a downward thrust on the cylinder and pushing the wake away from the free surface. The Kármán vortex shedding in the wake is suppressed due to the interruption of the jet-like flow. The fluctuations of the wake turbulence and hydrodynamic forces are also suppressed to a low level. [ABSTRACT FROM AUTHOR]

The nonlinear interaction between air and a water droplet just prior to a high-speed impingement on a surface is a phenomenon that has been researched extensively and occurs in a number of industrial settings. The role that the surface deformation plays in an air cushioned impact of a liquid droplet is considered here. In a two-dimensional framework, assuming small density and viscosity ratios between the air and the liquid, a reduced system of integrodifferential equations is derived governing the liquid droplet free-surface shape, the pressure in the thin air film, and the deformation of the surface, assuming the effects of surface tension, compressibility, and gravity to be negligible. The deformation of the surface is first described in a rather general form, based on previous membrane-type models. The coupled system is then investigated in two cases: a soft viscoelastic case where the surface stiffness and (viscous) damping are considered and a more general flexible surface where all relevant parameters are retained. Numerical solutions are presented, highlighting a number of key consequences of surface deformability on the pre-impact phase of droplet impact, such as reduction in pressure buildup, increased air entrapment, and considerable delay to touchdown. Connections (including subtle dependence of the size of entrapped air on the droplet velocity, reduced pressure peaks, and droplet gliding) with recent experiments and a large deformation analysis are also presented. [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]

Four configurations of a rotating magnetic dipole-driven turbulent flow in an electrically conducting liquid cylinder are considered by spectral direct numerical simulation. These configurations differ by parallel or perpendicular orientation of the dipole rotation vector with respect to the nearest surface of the cylinder or its axis. The rotating dipole generates electromagnetic force in a thin outer liquid layer facing it. A concentrated vortex is driven when the dipole rotation vector is perpendicular to the nearest surface. This vortex closely resembles the rotating disk-driven flow. When the dipole rotation vector is parallel to the nearest surface, then a distributed vortex occurs akin of the translating wall-driven cavity flow. The characteristic velocity is comparably little influenced by dipole orientation despite the electromagnetic force magnitude varying by a factor of three. Perpendicular orientation of the magnetic dipole rotation vector with respect to the cylinder's axis causes secondary corner eddies increasing the overall turbulent fluctuation. The simulations are supplemented by an experiment featuring a deep and narrow funnel-shaped quasi-stationary free surface deformation above a concentrated vortex. [ABSTRACT FROM AUTHOR]

Two-dimensional flow past a square cylinder close to a free surface is studied numerically to investigate the effect of Froude numbers (0.0–0.6) and gap ratios (0.2–1.2) on the wake behavior and integral parameters. The multiphase approach with the modified volume of fluid method is employed to study the flow. InterFoam, a two-phase incompressible flow solver in OpenFOAM, has been used to simulate the flow field. The surface deformation is found to increase with the increasing Froude number, which, in turn, produces substantial surface vorticity to cross-cancel the vorticity of the separated shear layer generated near the top surface of the cylinder. At high Froude numbers, merging of shed vortices in the cylinder downstream was encountered that possessed a period twice that in the formation region. For a fixed Froude number, with a decrease in the gap ratio, the amount of cross-cancellation between the top shear layer and the free surface increases. This enhanced interaction leads to diffusion of the vortices from the top shear layer to smaller downstream distances as the cylinder moves close to the free surface. Under such effects, the integral parameters (drag and lift coefficients and Strouhal number) are found to be a strong function of the Froude number and gap ratio. A comparison study of the wake structures with that of a circular cylinder shows the close resemblance in the large scale structures of the two flow fields. In terms of integral parameters, both the bluff bodies possess a similar behavior with the variations of the Froude number and gap ratio, but the magnitudes are quite different due to the differences in the separation points. [ABSTRACT FROM AUTHOR]

Physical experiments are conducted to study the interaction between a solitary wave and a finite horizontal plate submerged at a depth equal to 1/4 of the water depth. The spatial and temporal variation of the three-dimensional (3D) surface deformation is measured using a multi-lens stereo reconstruction system. The hydrodynamic loads are measured by underwater load cells. The plate-induced shoaling causes 3D wave focusing, leading to an increased maximum elevation along the streamwise centerline of the plate. The detailed wave focusing process and the influence of wave amplitude on focusing are presented based on the results obtained through image processing. The characteristics of the horizontal forces, vertical forces, and pitching moments are discussed. A 6-stage loading process based on the maxima of vertical wave force and pitching moment is proposed. It is coupled with the synchronous surface deformation to reveal the loading mechanism. It proves that the vertical wave force on the plate reduces apparently compared with the results from 2D experiments. The surface elevation and wave-induced load data provide an excellent benchmark for further studies on the 3D nonlinear interaction between a solitary wave and a submerged plate. [ABSTRACT FROM AUTHOR]

A lot of studies on the dynamics of a granular impact cratering by a liquid drop have been carried out. However, the results so far are controversial due to the complex impact dynamics of a liquid drop, such as deformation, splash, and penetration into the granular bed. In this study, we focused on the dynamics of the granular impact cratering by a hydrogel sphere, which deforms without splashing and penetrating. We investigated the maximal deformation time of the sphere and the lift-off time of the grains. Both the maximal deformation time and the lift-off time are similar to each other and depend on the −1/2 power of the Young's modulus of the hydrogel sphere. This power law of the maximum deformation time is the same as an impact of a gel sphere on a flat solid surface. The angle of the ejected curtain was evaluated. The angle is larger for the impact with small deformation of the sphere than that for the impact with large deformation, and the angle is less dependent on the free-fall height. We also investigated the distributions of the ejected grains using the grains dyed by a fluorescent dye. The distribution was visualized by the fluorescent images captured before and after the impact. At the crater rim, the number of the dyed grains flying to and away are balanced. The number of the dyed grains gathered at the dimensionless distance from the crater center of 1.15, where the distance is nondimensionalized by the crater radius, is the largest. This maximum value for the number of the gathered grains is larger for the impact with small deformation than that with large deformation. This result is consistent with the dependence of the impact mode on the angle of the ejected curtain. [ABSTRACT FROM AUTHOR]

This paper presents a combined experimental and numerical investigation designed to improve our understanding of how the shape of moving fluid threads evolves under asymmetrical confinements in both circular and square microchannels. Microfluidic devices with two junctions are designed to control the length of the fluid thread at the first junction and the deformation of the fluid thread at the second junction. Three different flow modes: nonbreakup, loosely confined breakup, and tightly confined breakup, are identified for varying lengths of fluid threads and capillary number, and two boundaries are identified between the three modes. The deformation dynamics of the fluid threads evolving as difference modes are addressed to consider the effects of thread length and capillary number. Numerical simulations are carried out to determine how the curvature evolves for different flow modes in the square microchannel. The evolution of interface profiles is obtained numerically over a wide range of capillary number. Stop-flow simulations are then carried out to identify both the critical shape for the onset of the capillary instability during tightly confined breakup and the corresponding curvature distribution. This critical shape is found to be corresponding to the fluid thread with the critical length at the transitive boundary between the loosely confined and tightly confined situations. [ABSTRACT FROM AUTHOR]

While rotating single phase fluid drops have been thoroughly investigated, the determination of the shape of a drop consisting of two immiscible liquid phases has not been previously considered. Recently, experiments using rotating micron-scale droplets of liquid helium have been carried out where the liquid can be in a normal or superfluid state depending on the isotope of helium used. Two phases can be present if the helium is a mixture of He3 and He4. Classical results have been very useful in aiding the analysis of single phase liquid helium drops and are similarly needed for two phase drops. In this contribution, the Navier–Stokes equations with surface tension are solved numerically using the finite-element method with surface tension effects on the inner and outer interfaces. The numerical models are time-dependent but are run to a steady state to determine equilibrium shapes. It is found that with an appropriate scaling of the density and surface tension coefficient, the relationships between the angular velocity and the angular momentum and of the outer surface dimensions with angular momentum become very similar to those of a single phase fluid for a broad range of parameters. However, the shapes of the inner drops vary significantly, particularly when the volume of the inner fluid is significantly less than that of the outer fluid. Increasing the relative magnitude of the interfacial surface tension coefficient or decreasing the relative density of the inner region leads to less deformation of the inner drop relative to the outer one. [ABSTRACT FROM AUTHOR]

The deformation of a vortex ring caused by its impingement on a sphere was numerically investigated using a proposed vortex-in-cell method. The method was validated by simulation of the collision of a vortex ring with a rigid planar surface and proved to be most satisfactory in the analysis of the dynamics of a vortex structure. In a coaxial collision, the behavior of the vortex structure is similar to that in the case of a planar surface. A secondary vortex ring is formed owing to the separation of the boundary layers on the sphere, caused by the effect of the primary vortex ring. The interaction between the secondary and primary vortex rings plays an important role in the dynamics of the vortex structure when the secondary vortex ring is completely formed. In a noncoaxial collision, the structure of the secondary vortex is moderately different from that in the coaxial collision. Moreover, the vortex structure in the coaxial collision is two-dimensional, in which the vorticity field is dominated by two transverse components, whereas that in the noncoaxial collision is three-dimensional. The total kinetic energy in both the cases decreases gradually during the entire period of evolution, whereas the enstrophy reduces in the early stage, then increases considerably, before a gradual reduction in the final stage. The enstrophy reaches a peak when the secondary vortex ring is completely formed, at which stage the effects of vortex stretching and vorticity production at the solid boundary are higher than that of vortex diffusion. [ABSTRACT FROM AUTHOR]

A generalized minimal residual method (GMRES) based immersed boundary-lattice Boltzmann flux solver (IB-LBFS) coupled with the finite element method (FEM) is presented in this paper for nonlinear fluid-structure interaction (FSI) problems. This approach effectively combines LBFS for the simulation of the flow field, the total Lagrangian FEM for the evaluation of nonlinear structural deformations, and the immersed boundary method (IBM) for the exchange of information on the fluid-solid interface and implementation of boundary conditions. Both the multidirect forcing and the implicit IBM are considered to examine their effects on numerical accuracy and efficiency. Through numerical simulations on flow past a cylinder, it is shown that the implicit IBM with the GMRES for the linear equation system is more efficient and accurate, which justify the conventional misunderstanding that implicit IBM is always less efficient than explicit methods. Numerical simulations on the lid-driven cavity flow in an inclined cavity, incompressible flows of a uniformly accelerated vertical plate, and the flow induced vibrations of a beam attached behind a cylinder in a channel are also successfully carried out and the obtained results are in good agreement with the published data, which verify the reliability and flexibility of the proposed solver for simulating nonlinear FSI problems. After that, the external flows past two hyperelastic cylinder-beam structures at the Reynolds number of 40–300 are studied and three different modes of static, linear, and nonlinear deformations of the beam are obtained, demonstrating its capability of simulating flows with nonlinear FSI problems with multiple deformable objects. [ABSTRACT FROM AUTHOR]

The dynamics of a bubble bypassing or passing between spherical obstacles, which is associated with many industrial applications, is investigated numerically. A gas–liquid–solid interaction model is established by combining the lattice Boltzmann method and the immersed boundary method. The deformation and the surface velocity of the bubble, as well as the streamlines of the flow field, are studied as the bubble bypasses a single spherical obstacle or passes between a pair of such obstacles. It is found that for the case of a single sphere, the rise velocity reaches a minimum value at the moment at which an annular bubble forms and the whole sphere is enveloped by the bubble. The initial distance between the bubble and the sphere, as well as the ratio of their sizes, has distinct influences on bubble shape and rise velocity. For a pair of spherical obstacles, the rise velocity of the bubble reaches a minimum value twice as the bubble rises between the obstacles. The distance between the two obstacles has a stronger influence on bubble motion than does their size, although when the two obstacles are of different sizes, the bubble will deviate toward the smaller one. [ABSTRACT FROM AUTHOR]

Second-mode instability plays an important role in the transition of a hypersonic boundary layer. The second-mode wave on a flared cone at Mach 6 has been investigated experimentally through the Nanoparticle-tracer based Planar Laser Scattering (NPLS) technique in this paper. Different behaviors of the second-mode wave ranging from linear growth to deformation are visualized under different unit Reynolds numbers. The propagation velocity of the second-mode wave is quantitatively calculated, and the spectral properties of the second-mode wave have been analyzed by the power spectrum density. The characteristic frequency of the second-mode wave calculated from the NPLS images agrees well with the results measured by the transducers. Evolution of the wall-normal distribution of disturbance shows that high frequency harmonics are generated during the growth process of the second-mode wave and its normal distribution range shrinks with the increase in its frequency. The bispectral analysis indicates that the high degree of phase coupling may be the reason for the deformation of the second-mode wave. The nonlinear interaction between the disturbance waves is strong during the deformation stage of the second-mode waves. [ABSTRACT FROM AUTHOR]

The rheological behaviors of complex emulsion globules (CEGs) and its three asymmetric daughter droplets (DDs) have been studied numerically in this paper. Unlike simple eccentric emulsion globules (SEEGs), two more DDs are added into the globules and the three DDs are located initially in an asymmetric distribution with a triangular shape. Through this investigation, an oriented shift and an inverse of CEGs are observed. Especially, the movement of CEGs under more conditions is still caused by the interaction of the asymmetric inner pressure distribution and the total outer drag force. Due to the asymmetric internal structure, the deformation of CEGs caused by the outer flow is asymmetric and so is the interfacial curvature which results in the oriented inner circulation. Compared to SEEGs, the addition of two extra DDs leads to the bigger deformation of CEGs, and more CEGs will shift to the left in the parameter range of our investigation. The increases of the parameters in the discussed ranges will promote CEGs to move to the right. In addition, DDs will move away from the original position and move away from or close to the interface of the mother droplet (MD), which may result in interface contact between DDs and MD. The results investigated in this paper further prove the mechanical mechanism of the oriented shift of the complex emulsions globules and are helpful to the controllable movement of soft globules driven by the asymmetric curvatures. [ABSTRACT FROM AUTHOR]

A solitary wave slamming on an Oscillating Wave Surge Converter (OWSC) is numerically investigated using a time-domain higher-order boundary element method with fully non-linear boundary conditions. A stretched coordinate is implemented to improve the numerical efficiency as long as the slamming peak pressure occurs. The potential of the thin long jet is assumed to vary linearly, while the process of jet detaching is simulated through the domain decomposition method so that the local highly oscillatory pressure can be avoided. Two auxiliary functions are applied simultaneously to decouple the mutual dependence between the flap motion and the fluid flow. A unique mesh scheme is employed to simulate the free surface with strong deformation, through which the smallest meshes are distributed near the largest pressure gradient on the body and the mesh size increases gradually at a ratio. The validity of the present model to simulate the solitary wave and the slamming event is verified, respectively, based on which relatively comprehensive parameter studies are then performed. Through analyzing the flap's motion states, the free surface profiles, and the pressure distributions, it is found that several unique phenomena and mechanisms exist in the solitary waves slamming on an OWSC. [ABSTRACT FROM AUTHOR]

For a floating bubble, in the range of Bond numbers based on an equivalent spherical radius, 0 < Boe < 1, we present analytical expressions for various shape parameters of the bubble as functions of Boe. Expressions are obtained for the radius of the rim Rr, the radius of the thin film cap Rc, the height of the top of the cap from the rim hcap, the height of the rim above the free surface hr, and the depth of the bubble cavity from the free surface Zc. To obtain these expressions, we solve equations formulated in terms of these shape parameters for the meniscus outside the bubble, the force balance of the bubble, the pressure balance at the centre line of the bubble, and geometrical constraints, after neglecting the deformation of the bubble cavity for Boe < 1. The obtained expressions are shown to match well with our experimental measurements of the shape of the bubble. In addition to these expressions, we also present simpler approximations that can be used accurately as scaling laws for these shape parameters up to Boe < 0.5. [ABSTRACT FROM AUTHOR]

The present study aims at investigating the deformation mechanism of liquid-liquid interfaces by both the experimental and numerical approaches. The experiments reveal that the topology of an initial flat interface composed of Newtonian aqueous and Newtonian oil phases can be modulated as climbing or descending along a rotating rod according to the ratio of the kinematic viscosity between these two liquid phases. The measurements of the fluid flow fields by particle image velocimetry highlight the relationship between the appearance of the Taylor-Couette instability in the less viscous phase and the interface's orientation. The increasing rod rotation speed expands the Taylor-Couette vortices and then intensifies the magnitude of the interface deformation. The numerical simulation by the volume of fluid method is in qualitative agreement with the experimental results, in particular the interface shape and the qualitative influence of different parameters, even under very high rotation speeds of the rod. [ABSTRACT FROM AUTHOR]

The liquid jet impact onto a clamped elastic plate is investigated. The two-dimensional jet of constant thickness and with flat vertical front is initially advancing towards the elastic plate along a flat, rigid, and horizontal plane at a constant uniform speed. The elastic plate of variable thickness is mounted perpendicular to the rigid plane. The maximum stress during the early impact stage is estimated for a given retardation time and a given relaxation time of the plate material. The stresses during the initial impact stage are compared with the static stresses in the plate placed in an equivalent uniform flow. It is shown that the static stresses are always smaller than the bending stresses during the early stage of impact for a given speed and thickness of the jet. This implies that if the stresses in the plate are smaller than the yield stress of the plate material with no plastic deformations in the plate occurring during the unsteady impact stage, then the plate behaves elastically after the impact and plastic deformations are not achieved. Approaching the plastic deformations is treated here as a damage to the plate. The maximum stress increases with an increase in jet thickness. A critical value of the jet velocity, below which the plate is not damaged by the jet impact, is obtained for given characteristics of the plate. [ABSTRACT FROM AUTHOR]

Droplet deformation is the first stage of all aerodynamically induced-breakups, considerably affecting the characteristics of the atomization. In the present study, using an adaptive volume of fluid method, two and three-dimensional direct numerical simulations have been performed to understand droplet deformation. A high Reynolds number and a range of relatively high Weber numbers are chosen, addressing the shear breakup of droplets in a stream. The study is focused on the initiation and growth of instabilities over the droplet. The role of Kelvin-Helmholtz and Rayleigh-Taylor instabilities in wave formation and azimuthal transverse modulation are shown and the obtained results for the most amplified wave-numbers are compared with instability theories for zero and non-zero vorticity layers. The present results for the most amplified wave-numbers and deformation topologies are in good agreement with the previous experimental results. [ABSTRACT FROM AUTHOR]

A low-dimensional parametric deformation model of a cancer cell under shear flow is developed. The model is built around an experiment in which MDA-MB-231 adherent cells are subjected to flow with increasing shear. The cell surface deformation is imaged using differential interference contrast microscopy imaging techniques until the cell releases into the flow. We post-process the time sequence of images using an active shape model from which we obtain the principal components of deformation. These principal components are then used to obtain the parameters in an empirical constitutive equation determining the cell deformations as a function of the fluid normal and shear forces imparted. The cell surface is modeled as a 2D Gaussian interface which can be deformed with three active parameters: H (height), σx (x-width), and σy (y-width). Fluid forces are calculated on the cell surface by discretizing the surface with regularized Stokeslets, and the flow is driven by a stochastically fluctuating pressure gradient. The Stokeslet strengths are obtained so that viscous boundary conditions are enforced on the surface of the cell and the surrounding plate. We show that the low-dimensional model is able to capture the principal deformations of the cell reasonably well and argue that active shape models can be exploited further as a useful tool to bridge the gap between experiments, models, and numerical simulations in this biological setting. [ABSTRACT FROM AUTHOR]

Droplets of de-ionized water and four aqueous surfactant solutions were generated in oil using a microfluidic flow-focusing device. The morphological developments of the drops in extensional flow and confinement-induced shear flow at various extension rates were studied using a hyperbolic contraction. This novel approach to droplet deformation within a microfluidic device allowed the probing of droplets within a nearly uniform extensional flow. The focus of this work was to study the effect of confinement-induced shear on droplet deformation and breakup in extensional flows. Droplet deformation was found to increase with both increasing capillary number and increasing confinement, for a fixed viscosity ratio of λ=0.1, with the effect of the shear induced by confinement being quite dramatic. The addition of surfactant to the droplets resulted in the production of tails, which streamed from the rear of the droplets and produced daughter droplets much smaller than the parent droplet. In the partially confined limit, where the flow was purely extensional, a single tail was formed at the center of the droplets trailing edge. With enhanced confinement, shear effects from the wall became important, the droplets were observed to take on a bullet-like shape, and two tails formed at the trailing edge of the droplet. The critical value of the capillary number and confinement needed for the formation of tails varied with the surfactant used. [ABSTRACT FROM AUTHOR]

Numerical computations have been performed to study the effects of thermocapillary convection and buoyancy convection, and free surface deformation induced by gravity on the migration behavior of a liquid droplet on a horizontal solid surface subjected to a uniform temperature gradient. Investigations are carried out by solving the Navier-Stokes equations coupled with the energy equation through the finite element method. The combined thermocapillary and buoyancy force driven convection produces complex dynamic behavior of fluid motion inside the droplet. The net momentum generated by a pair of asymmetric thermocapillary convection vortices inside the droplet drives the droplet to move in both small and middle droplet sized regimes. In the small sized regime, the quasisteady migration speed of the droplet is mostly linearly proportional to its size because of the stronger net thermocapillary momentum. When the droplet is in the middle sized regime, its quasisteady migration speed reaches a maximum, but this is gradually reduced as the droplet size increases due to the suppression of the net thermocapillary momentum by the buoyancy force. In the large droplet sized regime, two pairs of convection vortices exist inside the droplet as a result of the appearance of the buoyancy-driven convection accompanying the thermocapillary convection. The quasisteady migration speed quickly diminishes mainly due to the reduction of the net thermocapillary momentum from the stronger buoyancy convection. [ABSTRACT FROM AUTHOR]

Marangoni convection caused by a photochemical reaction of the type A⇋hνB in a thin liquid film with deformable interface is studied. A system of two coupled nonlinear evolution equations for the film thickness and the reactant concentration is derived in the long-wave approximation. Linear stability analysis is performed and the conditions for Marangoni convection to occur are obtained. It is shown that the type of instability depends on the ratio of diffusivities of the reactant and the product of the photochemical reaction: If the diffusivities are equal, the instability is always monotonic, while when they are significantly different the instability can be oscillatory. Numerical simulations of the derived system of equations are performed. It is shown that in the case of the monotonic instability, the system develops a spotty pattern that ultimately leads to the film rupture. In the case of oscillatory instability, it is shown that photo-Marangoni convection can result in sustained wavy patterns with a square symmetry. [ABSTRACT FROM AUTHOR]

Two-dimensional corotating vortex pairs are computed as equilibrium solutions of the Euler equations and the influence of one vortex on the other is characterized in terms of a deformation field acting on an isolated vortex region. It is shown, by computing equilibrium states for a single vortex within an equivalent strain field, that the external rotating strain accounts for the elliptic deformation of the streamlines near the center of each vortex. Critical states, as a function of the strain rate, are reached when stagnation points start to penetrate the vortex regions at the outer boundary. While critical states for a single vortex within a uniform external rotating strain field consist of elliptical corner solutions, the vortex shapes lose the elliptical symmetry in the corotating case. We show that these asymmetric equilibrium states can be captured by a single vortex model if we consider higher order terms in the deformation field. We also demonstrate that the critical strain rates are of the same order of magnitude for both the single-vortex model and the interacting vortex pair. [ABSTRACT FROM AUTHOR]

We derive exact solutions describing three-dimensional ellipsoidal drop deformation with zero surface tension in steady, planar linear flows. We apply the analysis to study the development of lamellar drop morphologies as observed in recent experiments. [ABSTRACT FROM AUTHOR]

Studies the effects of insoluble surfactants on the nonlinear deformation and breakup of stretching liquid bridges. Stretching and breaking of threads of liquid during the emission of single drops; Numerical solution for equations resulting from a slender-jet approximation of the Navier-Stokes system governing fluid flow.

Maps the experimental trajectories of two deformable drops in planar extensional flow. Comparison of experimental results with theoretical calculations for spherical drops; effect of deformation, initial position and viscosity ratio on the interaction of the two drops; Incorporation of deformation into trajectory calculations.

Examines buoyancy-driven viscous interaction of a rising drop with a smaller trailing drop. Spherical shape of drops when Bond number is small; Observation of significant deformation at higher Bond numbers; Stretching of trailing drop due to flow created by leading drop.

Describes the hydrodynamics and stability of a deformable body embedded in an inviscid irrotational nonuniform ambient flow field moving in the proximity of interfaces. Chaotization of a body's motion due to the presence of boundaries; Nonlinear control of a moving rigid body in an unbounded space based on a simple potential framework.