Numerical simulations of elastic-plastic Richtmyer-Meshkov instability of multiple interfaces.

The elastic-plastic Richtmyer-Meshkov instability of multiple interfaces is investigated by numerical simulation using a multimaterial solid mechanics algorithm based on an Eulerian framework. This Richtmyer-Meshkov instability problem is realized by a copper layer that is flanked by vacuum and a copper block of different material strength. The research efforts are directed to reveal the influence of the layer thickness and material strength on the deformation of the perturbed solid-vacuum interface impacted by an initial shock. By varying the initial thickness (x_{I}) of the copper layer and the yield stress (σ_{Y2}) of the copper block, two deformation modes, which have been identified as the broken mode and the stable mode, are closely scrutinized. For a fixed x_{I} and a decreasing σ_{Y2}, the reflected rarefaction waves (RRWs), developing after the initial shock impacts the perturbed interface 1 (I1) between vacuum and the copper layer, become stronger after traveling across the interface 2 (I2). Subsequently, the velocity of I2 becomes larger, causing the width of I1 to grow larger. This width growth of I1 leads to a final separation of the spike from I1 and, consequently, the deformation mode changes from the stable mode to the broken mode. For a fixed σ_{Y2} and a decreasing x_{I}, the RRWs impact I2 at an earlier moment with a greater strength and thus the deformation mode changes from the stable mode to the broken mode. Meanwhile, the comparison of the spike width of cases whose deformation mode is the broken mode shows that there exists a maximum value of rescaled spike width, at which the deformation mode changes from the stable mode to the broken mode.

Deep-reinforcement-learning-based self-organization of freely undulatory swimmers.

It is fascinating that fish groups spontaneously form different formations. The collective locomotions of two and multiple undulatory self-propelled foils swimming in a fluid are numerically studied and the deep reinforcement learning (DRL) is applied to control the locomotion. We explored whether typical patterns emerge spontaneously under the driven two DRL strategies. One strategy is that only the following fish gets hydrodynamic advantages. The other is that all individuals in the group take advantage of the interaction. In the DRL strategy, we use swimming efficiency as the reward function, and the visual information is included. We also investigated the effect of involving hydrodynamic force information, which is an analogy to that detected by the lateral line of fish. Each fish can adjust its undulatory phase to achieve the goal. Under the two strategies, collective patterns with different characteristics, i.e., the staggered-following, tandem-following phalanx and compact modes emerge. They are consistent with the results in the literature. The hydrodynamic mechanism of the above high-efficiency collective traveling modes is analyzed by the vortex-body interaction and thrust. We also found that the time sequence feature and hydrodynamic information in the DRL are essential to improve the performance of collective swimming. Our research can reasonably explain the controversial issue observed in the relevant experiments. The paper may be helpful for the design of bionic fish.

Comparative effects of cannabinoid CB1 receptor agonist and antagonist on timing impulsivity induced by d-amphetamine in a differential reinforcement of low-rate response task in male rats.

RATIONALE: In human beings and experimental animals, maladaptive impulsivity is manifested by the acute injection of psychostimulants, such as amphetamine. Cannabinoid CB1 receptors have been implicated in the regulation of stimulant-induced impulsive action, but the role of CB1 receptors in timing-related impulsive action by amphetamine remains unknown. METHODS: Male rats were used in evaluating the effects of CB1 receptor antagonist and agonist (SR141716A and WIN55,212-2, respectively) systemically administered individually and combined with d-amphetamine on a differential reinforcement of low-rate response (DRL) task, an operant behavioral test of timing and behavioral inhibition characterized as a type of timing impulsive action. RESULTS: A distinct pattern of DRL behavioral changes was produced by acute d-amphetamine (0, 0.5, 1.0, and 1.5 mg/kg) treatment in a dose-dependent fashion, whereas no significant dose effect was detected for acute SR141716A (0, 0.3, 1, and 3 mg/kg) or WIN55,212-2 (0, 0.5, 1, and 2 mg/kg) treatment. Furthermore, DRL behavior altered by 1.5 mg/kg d-amphetamine was reversed by a noneffective dose of SR141716A (3 mg/kg) pretreatment. The minimally influenced DRL behavior by 0.5 mg/kg d-amphetamine was affected by pretreatment with a noneffective dose of WIN55,212-2 (1 mg/kg). CONCLUSION: These findings reveal that the activation and blockade of CB1 receptors can differentially modulate the timing impulsive action of DRL behavior induced by acute amphetamine treatment. Characterizing how CB1 receptors modulate impulsive behavior will deepen our understanding of the cannabinoid psychopharmacology of impulsivity and may be helpful in developing an optimal pharmacotherapy for reducing maladaptive impulsivity in patients with some psychiatric disorders.

Scaling law of mixing layer in cylindrical Rayleigh-Taylor turbulence.

The nonlinear evolution of mixing layer in cylindrical Rayleigh-Taylor (RT) turbulence is studied theoretically and numerically. The scaling laws including the hyperbolic cosine growth for outward mixing layer and the cosine growth for inward mixing layer of the cylindrical RT turbulence are proposed for the first time and verified reliably by direct numerical simulation of the Navier-Stokes equations. It is identified that the scaling laws for the cylindrical RT turbulence transcend the classical power law for the planar RT turbulence and can be recovered to the quadratic growth as cylindrical geometry effect vanishes. Further, characteristic time- and length scales are reasonably obtained based on the scaling laws to reveal the self-similar evolution features for the cylindrical RT turbulence.

Hydrodynamic benefits of intermittent locomotion of a self-propelled flapping plate.

Intermittent locomotion is a widely used behavioral strategy for fish and birds to reduce the cost of movement. The intermittent locomotion performance of a self-propelled flapping plate is investigated numerically. Two intermittent swimming modes, namely, the multiple-tail-beat mode (MT mode) and the half-tail-beat mode (HT mode), as well as the continuous swimming mode (CT mode), are considered. Performance is evaluated from propulsive speed, efficiency, and cost of transport. The hydrodynamic performances of the intermittent modes are found to be better than the hydrodynamic performance of the CT mode when the bending stiffness K is moderate [i.e., K≈O(1)] and the duty cycle is not too small. For the two intermittent modes, the performance of the HT mode is better than that of the MT mode when K is small or moderate, while the situation is opposite when K is large. It is found that compared to the asymmetric wake of the MT mode, the symmetric wake of the HT mode is favorable to generate more thrust force and therefore achieve better performance. Besides, at moderate K, the largest bending deformation of the plate in the HT mode, as well as the large normal force, produces the largest thrust during the flapping. The present results can help us to better understand the intermittent locomotion of animals and may be helpful for bionic design.

Numerical study of droplet impact on a flexible substrate.

Droplets interacting with deformable moving boundaries is ubiquitous. The flexible boundaries may dramatically affect the hydrodynamic behavior of droplets. A numerical method for simulating droplet impact on flexible substrates is developed. The effect of flexibility is investigated. To reduce the contact time and increase the remaining upward momentum in the flexible cases, the Weber number should be larger than a critical value. Moreover, the ratio of the natural frequency of the plate to that of the droplet F_{r} should approximately equal to the reciprocal of the contact time of droplets impact on the rigid surfaces (t_{ctr}) at the same We, e.g., F_{r}≈1/t_{ctr}. Only under this circumstance would the kinetic energy convert into the surface energy of the droplet and the elastic energy of the plate simultaneously, and vice versa. Moreover, based on a double spring model, we proposed scaling laws for the maximal deflection of the plate and spreading diameter of the drop. Finally, the droplet impact under different wettability is qualitatively studied. We found that the flexibility may contribute to the droplet bouncing at a smaller contact angle.

Molecular Dynamics Study of Binary Nanodroplet Evaporation on a Heated Homogeneous Substrate.

The evaporation mechanism of miscible binary nanodroplets from heated homogeneous surfaces was studied by molecular dynamics simulations, which has never been studied before. The binary droplets contain a hydrophilic component (type-2 particles) and a hydrophobic component (type-3 particles). It is shown that liquid-liquid interaction strength (ε23) and hydrophilic particle number fraction (φ) have great influence on the surface tension, wetting characteristics, evaporation patterns, evaporation rate, and local mass flux. It is observed that when ε23 ≥ 1, or φ ≈ 0.5, the evaporation mode is the constant-contact-angle mode. Otherwise, it is the mixed mode. We found that the evaporation rate becomes faster when φ and ε23 increase. The droplets become more hydrophilic when φ increases, which promotes heat transfer efficiency between the liquid-solid interface. Besides, a larger ε23 promotes the heat transfer inside the droplet. The mass transfer to the vapor phase occurs preferentially in the vicinity of TPCL (three phase contact line) in the hydrophilic systems (θ < θc), where θc is the critical contact angle, while in most hydrophobic systems (θ > θc), the mass flux close to the TPCL is suppressed. We found that θc ∈ (102°-106°), which is different from the theoretical one, θc = 90°. The discrepancy is attributed to the existence of the adsorption layer near the TPCL.

Self-propelled plate in wakes behind tandem cylinders.

Fish may take advantage of environmental vortices to save the cost of locomotion. The complex hydrodynamics shed from multiple physical objects may significantly affect fish refuging (holding stationary). Taking a model of a self-propelled flapping plate, we numerically studied the locomotion of the plate in wakes of two tandem cylinders. In most simulations, the plate heaves at its initial position G_{0} before the flow comes (releasing Style I). In the typical wake patterns, the plate may hold stationary, drift upstream, or drift downstream. The phase diagrams of these modes in the G_{0}-A plane for the vortex shedding patterns were obtained, where A is the flapping amplitude. It is observed that the plate is able to hold stationary at multiple equilibrium locations after it is released. Meanwhile, the minimum amplitude and the input power required for the plate seem inversely proportional to the shedding vortex strength. The effect of releasing style was also investigated. If the plate keeps stationary and does not flap until the vortex shedding is fully developed (releasing Style II), then the plate is able to hold stationary at some equilibrium locations but the flapping plate has a very minor effect on the shedding vortices. However, in Style I, the released plate is able to achieve more equilibrium locations through adjusting the phase of vortex shedding. The effort of the preflapping in Style I is not in vain, because although it consumes more energy, it becomes easier to hold stationary later. The relevant mechanism is explored.

Pinning-Depinning Mechanism of the Contact Line during Evaporation of Nanodroplets on Heated Heterogeneous Surfaces: A Molecular Dynamics Simulation.

Droplet evaporation on heterogeneous or patterned surfaces has numerous potential applications, for example, inkjet printing. The effect of surface heterogeneities on the evaporation of a nanometer-sized cylindrical droplet on a solid surface is studied using molecular dynamics simulations of Lennard-Jones particles. Different heterogeneities of the surface were achieved through alternating stripes of equal width but two chemical types, which lead to different contact angles. The evaporation induced by the heated substrate instead of the isothermal evaporation is investigated. It is found that the whole evaporation process is generally dominated by the nonuniform evaporation effect. However, at the initial moment, the volume expansion and local evaporation effects play important roles. From the nanoscale point of view, the slow movement of the contact line during the pinning process is observed, which is different from the macroscopic stationary pinning. Particularly, we found that the speed of the contact line may be not only affected by the intrinsic energy barrier between the two adjacent stripes ( u) but also relevant to the evaporation rate. Generally speaking, the larger the intrinsic energy barrier, the slower the movement of the contact line. At the specified temperature, when u is less than a critical energy barrier ( u*), the speed of the contact line would increase with the evaporate rate. When u > u*, the speed of the contact line is determined only by u and no longer affected by the evaporation rate at different stages (the first stick and the second stick).

Measurement of a Richtmyer-Meshkov Instability at an Air-SF_{6} Interface in a Semiannular Shock Tube.

We report the first measurements of the perturbation amplitude in the converging Richtmyer-Meshkov instability in a semiannular shock tube. At early stages, the amplitude growth agrees well with the impulsive model considering the geometrical convergence effect. A quick decrease of the growth rate at late time, even to be negative, before the reshock is observed for the first time. The reduction of the growth rate is ascribed to the Rayleigh-Taylor stabilization caused by the interface deceleration motion only presented in the converging circumstance. By reasonably evaluating the Rayleigh-Taylor stabilization, a modified model based on the Bell equation is proposed, which well predicts the perturbation growth in a converging geometry from early to late stages before the reshock. It is also found that the flow compressibility is significant in the converging Richtmyer-Meshkov instability.

Self-propulsion of a flapping flexible plate near the ground.

The self-propulsion of a three-dimensional flapping flexible plate near the ground is studied using an immersed boundary-lattice Boltzmann method for fluid flow and a finite-element method for plate motion. When the leading edge of the flexible plate is forced into a vertical oscillation near the ground, the entire plate moves freely due to the fluid-structure interaction. The mechanisms underlying the dynamics of the plate near the ground are elucidated. Based on the propulsive behaviors of the flapping plate, three distinct regimes due to the ground effect can be qualitatively identified. These regimes can be described briefly as the expensive, benefited, and uninfluenced propulsion regimes. The analysis of unsteady dynamics and plate deformation indicates that the ground effect becomes weaker for a more flexible plate. We have found that a suitable degree of flexibility can improve propulsion near the ground. The vortical structure around the plate and the pressure distribution on the plate are analyzed to understand propulsive behaviors. The results obtained in this study can provide some physical insights into the propulsive mechanisms of a flapping flexible plate near the ground.

Viscous flow past a collapsible channel as a model for self-excited oscillation of blood vessels.

Motivated by collapse of blood vessels for both healthy and diseased situations under various circumstances in human body, we have performed computational studies on an incompressible viscous fluid past a rigid channel with part of its upper wall being replaced by a deformable beam. The Navier-Stokes equations governing the fluid flow are solved by a multi-block lattice Boltzmann method and the structural equation governing the elastic beam motion by a finite difference method. The mutual coupling of the fluid and solid is realized by the momentum exchange scheme. The present study focuses on the influences of the dimensionless parameters controlling the fluid-structure system on the collapse and self-excited oscillation of the beam and fluid dynamics downstream. The major conclusions obtained in this study are described as follows. The self-excited oscillation can be intrigued by application of an external pressure on the elastic portion of the channel and the part of the beam having the largest deformation tends to occur always towards the end portion of the deformable wall. The blood pressure and wall shear stress undergo significant variations near the portion of the greatest oscillation. The stretching motion has the most contribution to the total potential elastic energy of the oscillating beam.

Dewetting films with inclined contact lines.

A partially wetting plate withdrawn from a liquid reservoir causes the deposition of a liquid film that is characterized by inclined contact lines. It has been experimentally indicated that the normal component of the contact-line velocity relative to the plate remains constant and is independent of the inclination angles, a fact that has never theoretically been justified. We demonstrate, in the framework of lubrication theory, that the speed-angle independence is only approximate and the normal velocity actually exhibits a weak decrease with the inclination angle of the contact line. This correlation is attributed to the variation of the effective separation of microscopic and macroscopic length scales. In addition, the inclination of the contact line results in a tangential flux of the liquid, which is confined in the vicinity of the contact line. Simple scaling relations are provided for both the normal velocity and the tangential flux.

Sedimentation of an oblate ellipsoid in narrow tubes.

Sedimentation behaviors of an oblate ellipsoidal particle inside narrow [R/a∈(1.2,2.0)] infinitely long circular tubes are studied by the lattice Boltzmann method, where R and a are the radius of the tube and the length of the semimajor axis of the ellipsoid, respectively. The Archimedes numbers (Ar) up to 70 are considered. Four periodic and two steady sedimentation modes are identified. It is the first time that the anomalous mode has been found in a circular tube for an ellipsoidal particle. The phase diagram of the modes as a function of Ar and R/a is obtained. The anomalous mode is observed in the larger R/a and lower-Ar regime. Through comparisons between the anomalous and oscillatory modes, it is found that R/a plays a critical role for the anomalous mode. Some constrained cases with two steady modes are simulated. It is found that the particle settles faster in the unconstrained modes than in the corresponding constrained modes. This might inspire further study on why the particle adopts a specific mode under a certain circumstance.

Length effects of a built-in flapping flat plate on the flow over a traveling wavy foil.

Flow over the traveling wavy foil with a built-in rigid flapping plate at its trailing edge has been numerically studied using the multi-relaxation-time lattice Boltzmann method and immersed boundary method. The effect of the plate length on the propulsive performance such as the thrust force, energy consumption, and propeller efficiency has been investigated. Three modes (body force dominated, body and tail force competing and tail force dominated modes) have been identified that are associated with different hydrodynamics and flow structures. It is revealed that there exists a better performance plate length region and, within this region, a high propeller efficiency (close to its maximum value) is achieved due to a great increase in propulsive force at a cost of a slight increase in energy consumption. Furthermore, a weak stabilizing effect on locomotion movement is indicated by the slight decrease in the root-mean-square (rms) values of drag and lateral forces.

Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis.

Atherosclerotic plaque can cause severe stenosis in the artery lumen. Blood flow through a substantially narrowed artery may have different flow characteristics and produce different forces acting on the plaque surface and artery wall. The disturbed flow and force fields in the lumen may have serious implications on vascular endothelial cells, smooth muscle cells, and circulating blood cells. In this work a simplified model is used to simulate a pulsatile non-Newtonian blood flow past a stenosed artery caused by atherosclerotic plaques of different severity. The focus is on a systematic parameter study of the effects of plaque size/geometry, flow Reynolds number, shear-rate dependent viscosity and flow pulsatility on the fluid wall shear stress and its gradient, fluid wall normal stress, and flow shear rate. The computational results obtained from this idealized model may shed light on the flow and force characteristics of more realistic blood flow through an atherosclerotic vessel.

Scheme for contact angle and its hysteresis in a multiphase lattice Boltzmann method.

In this paper, a scheme for specifying contact angle and its hysteresis is incorporated into a multiphase lattice Boltzmann method. The scheme is validated through investigations of the dynamic behaviors of a droplet sliding along two kinds of walls: a smooth (ideal) wall and a rough or chemically inhomogeneous (nonideal) wall. For an ideal wall, the wettability of solid substrates is able to be prescribed. For a nonideal wall, arbitrary contact angle hysteresis can be obtained through adjusting advancing and receding angles. Significantly different phenomena can be recovered for the two kinds of walls. For instance, a droplet on an inclined ideal wall under gravity is impossible to stay stationary. However, the droplet on a nonideal wall may be pinned due to contact angle hysteresis. The steady interface shapes of the droplet on an inclined nonideal wall under gravity or in a shear flow quantitatively agree well with the previous numerical studies. Besides, the complex motion of a droplet creeping like an inchworm could be simulated. The scheme is found suitable for the study of contact line problems with and without contact angle hysteresis.

Shear viscosity of dilute suspensions of ellipsoidal particles with a lattice Boltzmann method.

The intrinsic viscosities for prolate and oblate spheroidal suspensions in a dilute Newtonian fluid are studied using a three-dimensional lattice Boltzmann method. Through directly calculated viscous dissipation, the minimum and maximum intrinsic viscosities and the period of the tumbling state all agree well with the analytical solution for particles with different aspect ratios. This numerical test verifies the analysis on maximum and minimum intrinsic viscosities. Different behavior patterns of transient intrinsic viscosity in a period are analyzed in detail. A phase lag between the transient intrinsic viscosity and the orientation of the particle at finite Reynolds number (Re) is found and attributed to fluid and particle inertia. At lower Re, the phase lag increases with Re. There exists a critical Reynolds number Rea at which the phase lag begins to decrease with Re. The Rea depends on the aspect ratio of the particle. We found that both the intrinsic viscosity and the period change linearly with Re when ReRea (high-Re regime). In the high-Re regime, the dependence of the period on Re is consistent with a scaling law, and the dependence of the intrinsic viscosity on Re is well described by second-degree polynomial fits.

Flow over a traveling wavy foil with a passively flapping flat plate.

Flow over a traveling wavy foil with a passively flapping flat plate has been investigated using a multiblock lattice Boltzmann equation and the immersed boundary method. The foil undergoes prescribed undulations in the lateral direction and the rigid flat plate has passive motion determined by the fluid structure interaction. This simplified model is used to study the effect of the fish caudal fin and its flexibility on the locomotion of swimming animals. The flexibility of the caudal fin is modeled by a torsion spring acting about the pivot at the conjuncture of the wavy foil and the flat plate. The study reveals that the passively oscillating flat plate contributes half of the propulsive force. The flexibility, represented by the nondimensional natural frequency F, plays a very important role in the movement and propulsive force generation of the whole body. When the plate is too flexible, the drag force is observed. As the flat plate becomes more rigid, the propulsive force that is generated when the undulation is confined to last part of the wavy foil becomes larger. The steady movement occurs at F=5. These results are consistent with the observations of some swimming animals in nature.

Propulsive performance of a body with a traveling-wave surface.

A body with a traveling-wave surface (TWS) is investigated by solving the incompressible Navier-Stokes equation numerically to understand the mechanisms of a novel propulsive strategy. In this study, a virtual model of a foil with a flexible surface which performs a traveling-wave movement is used as a free swimming body. Based on the simulations by varying the traveling-wave Reynolds number and the amplitude and wave number of the TWS, some propulsive properties including the forward speed, the swimming efficiency, and the flow field are analyzed in detail. It is found that the mean forward velocity increases with the traveling-wave Reynolds number, the amplitude, and the wave number of the TWS. A weak wake behind the free swimming body is identified and the propulsive mechanisms are discussed. Moreover, the TWS is a "quiet" propulsive approach, which is an advantage when preying. The results obtained in this study provide a novel propulsion concept, which may also lead to an important design capability for underwater vehicles.