Force Balance Relation Research Articles

An analytical model for ice accretion on the engine strut surface

To predict flight icing more widely and practically, an ice accretion numerical framework that incorporates both the water droplet splash and the ice crystal sticking is developed. By proposing a deformation hypothesis, we deduce the modified energy conservation expression and the force balance relation for water droplet impingement. Subsequently, a new threshold determination and the probabilities for the droplet splash and ice crystal sticking are obtained, which are applicative across a wide range of Weber number after the validation. Through the interface tracking for a single droplet with the volume of fluid method, the droplet impingement dynamics are further explored, and the results of interaction with the wall serve the boundary treatments of droplet impingement in the discrete phase model. Additionally, the probability statistics method is employed to determine the parameters of the secondary droplets. Through the dynamic mesh technique, the retentive water droplets and the collected ice crystals are transformed into the accumulated ice in real time to update the ice accretion on the strut surface. Results demonstrate that the diameter, velocity, and content of droplets or crystals play significant roles in the impingement and the icing phenomena. Based on our numerical model, the predictions show that the ice accretion on the engine strut is influenced by flight parameters and environmental conditions, providing crucial guidance for the icing protection processes.

Theory of mean E B shear in a stochastic magnetic field: ambipolarity breaking and radial current

The mean E B shear in a stochastic magnetic field is calculated, using the radial force balance relation and transport equations. This analysis is relevant to the L → H transition with resonant magnetic perturbations, and special focus is placed upon the physics of non-ambipolar transport and radial current. The key physical process is the flow of fluctuating currents along wandering magnetic fields. The increments in poloidal and toroidal rotation, density and ion pressure are calculated. The radial envelope of the magnetic perturbations inside the plasma defines a new scale , which is the characteristic scale of the magnetic fluctuation intensity profile. The net particle outflow due to stochastic magnetic fields is calculated and is determined by the net radial current through the separatrix. Implications for the L → H transition are discussed.

Research on Insurance Method for Energetic Materials on Information Self-Destruction Chips.

Detonation waves released by energetic materials provide an important means of physical self-destruction (Psd) for information storage chips (ISCs) in the information insurance field and offer advantages that include a rapid response and low driving energy. The high electrical sensitivity of energetic materials means that they are easily triggered by leakage currents and electrostatic forces. Therefore, a Psd module based on a graphene-based insurance actuator heterogeneously integrated with energetic materials is proposed. First, the force–balance relation between the electrostatic van der Waals force and the elastic recovery force of the insurance actuator’s graphene electrode is established to realize physical isolation and an electrical interconnection between the energetic materials and the peripheral electrical systems. Second, a numerical analysis of the detonation wave stress of the energetic materials in the air domain is performed, and the copper azide dosage required to achieve reliable ISC Psd is obtained. Third, the insurance actuator is prepared via graphene thin film processing and copper azide is prepared via an in situ reaction. The experimental results show that the energetic materials proposed can release physical isolation within 14 μs and can achieve ISC Psd under the application of a voltage signal (4.4–4.65 V). Copper azide (0.45–0.52 mg) can achieve physical damage over an ISC area (23.37–35.84 mm2) within an assembly gap (0.05–0.25 mm) between copper azide and ISC. The proposed method has high applicability for information insurance.

Quantifying the solid-fluid interfacial tensions depending on the substrate curvature: Young's equation holds for wetting around nanoscale cylinder.

By extending the theoretical framework derived in our previous study [Imaizumi et al., J. Chem. Phys. 153, 034701 (2020)], we successfully calculated the solid-liquid (SL) and solid-vapor (SV) interfacial tensions of a simple Lennard-Jones fluid around solid cylinders with nanometer-scale diameters from single equilibrium molecular dynamics systems in which a solid cylinder was vertically immersed into a liquid pool. The SL and SV interfacial tensions γSL - γS0 and γSV - γS0 relative to that for bare solid surface γS0, respectively, were obtained by simple force balance relations on fluid-containing control volumes set around the bottom and top ends of the solid cylinder, which are subject to the fluid stress and the force from the solid. The theoretical contact angle calculated by Young's equation using these interfacial tensions agreed well with the apparent contact angle estimated by the analytical solution to fit the meniscus shape, showing that Young's equation holds even for the menisci around solids with nanoscale curvature. We have also found that the curvature effect on the contact angle was surprisingly small while it was indeed large on the local forces exerted on the solid cylinder near the contact line. In addition, the present results showed that the curvature dependence of the SL and SV interfacial free energies, which are the interfacial tensions, is different from that of the corresponding interfacial potential energies.

An Energetic Variational Approach for the Cahn–Hilliard Equation with Dynamic Boundary Condition: Model Derivation and Mathematical Analysis

The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range interactions of the material with the solid wall. Our first aim in this paper is to propose a new class of dynamic boundary conditions for the Cahn--Hilliard equation in a rather general setting. The derivation is based on an energetic variational approach that combines the least action principle and Onsager's principle of maximum energy dissipation. One feature of our model is that it naturally fulfills three important physical constraints such as conservation of mass, dissipation of energy and force balance relations. Next, we provide a comprehensive analysis of the resulting system of partial differential equations. Under suitable assumptions, we prove the existence and uniqueness of global weak/strong solutions to the initial boundary value problem with or without surface diffusion. Furthermore, we establish the uniqueness of asymptotic limit as $t\to+\infty$ and characterize the stability of local energy minimizers for the system.

Effect of Moving Contact Line's Curvature on Dynamic Wetting of non-Newtonian Fluids.

The curvature of the contact line is always changing with the dynamic wetting condition. Using a modified Wilhelmy plate method and the sessile drop method, this study experimentally investigated the dynamic wetting process of several kinds of Newtonian and non-Newtonian fluids. The results show that the curvature of the moving contact line strongly affects the relationship θD = f( U) for non-Newtonian fluids but has no effect on Newtonian fluids. The effect is more obvious with the stronger non-Newtonian fluids. The theoretical relationship derived from the Navier-Stokes equations established for spontaneous spreading indicates that the moving contact line curvature affects the relationship θD = f( U) for shear-thinning fluids and shear-thickening fluids in a different way, which agrees with the forced wetting experimental results for shear-thinning fluids in both this work and the previous one on the fluid showing shear-thickening rheology. A force balance relation of the braking force and driving force for the moving contact line is used to explain the internal mechanism about how the curvature of the contact line affects θD during wetting process.

A controllable way to measure the interfacial strength between carbon nanotube and polymer using a nanobridge structure

The interfacial strength between an embedded carbon nanotube (CNT) and a polymer matrix is a direct indicator of the interfacial load transfer which significantly impacts the effective mechanical properties of CNT/polymer nanocomposites. However, unavoidable kinks or entanglement of the CNTs in the polymer may complicate the characterization of the interface as measured through nanopullout experiments. In the current work a CNT/polymer nanobridge structure in a suspended polymer film is developed to allow the observation of the embedded portion of the CNT after the pullout process. The nanobridge structure was created on the basis of phase separation of a polymer blend, self-assembly of the CNTs in liquid flow, and ductile fracture of the polymer under thermal and solvent treatment. This structure accommodates a nanomechanical interfacial characterization method where a transverse force applied on the suspended CNT using an atomic force microscope results in an axial pullout force, which is obtained by the force-distance curves and a force balance relation. The high resolution of the AFM in the loading process and the ability to observe the embedded portion of the CNT eliminate uncertainties of the nanopullout process and provide a more controllable approach for measuring the interfacial strength in CNT/polymer nanocomposite systems.

The Cassie-Wenzel transition of fluids on nanostructured substrates: Macroscopic force balance versus microscopic density-functional theory.

Classical density functional theory is applied to investigate the validity of a phenomenological force-balance description of the stability of the Cassie state of liquids on substrates with nanoscale corrugation. A bulk free-energy functional of third order in local density is combined with a square-gradient term, describing the liquid-vapor interface. The bulk free energy is parameterized to reproduce the liquid density and the compressibility of water. The square-gradient term is adjusted to model the width of the water-vapor interface. The substrate is modeled by an external potential, based upon the Lennard-Jones interactions. The three-dimensional calculation focuses on substrates patterned with nanostripes and square-shaped nanopillars. Using both the force-balance relation and density-functional theory, we locate the Cassie-to-Wenzel transition as a function of the corrugation parameters. We demonstrate that the force-balance relation gives a qualitatively reasonable description of the transition even on the nanoscale. The force balance utilizes an effective contact angle between the fluid and the vertical wall of the corrugation to parameterize the impalement pressure. This effective angle is found to have values smaller than the Young contact angle. This observation corresponds to an impalement pressure that is smaller than the value predicted by macroscopic theory. Therefore, this effective angle embodies effects specific to nanoscopically corrugated surfaces, including the finite range of the liquid-solid potential (which has both repulsive and attractive parts), line tension, and the finite interface thickness. Consistently with this picture, both patterns (stripes and pillars) yield the same effective contact angles for large periods of corrugation.

Nature of Driving Force on an Isolated Moving Vortex in Dirty Superconductors

We reconsider the force-balance relation on an isolated vortex in the flux flow state within the scheme of time-dependent-Ginzburg-Landau (TDGL) equation. We define force on the vortex by the total force on superconducting electrons in the region $S$ surrounding the vortex. We derive the local momentum balance relation of superconducting electrons and then find the force-balance relation on isolated vortex with taking account of the fact that the transport current in charged superconductors are inherently spatially varying with the scale of penetration depth $\lambda$. We also find that nature of the driving force is hydrodynamic when $S$ is the disk with radius $R$ satisfying $\xi\ll R\ll \lambda$ ($\xi$ is the coherence length) while the hydrodynamic and magnetic parts contribute equally to the driving force for $\lambda \lesssim R$.

Development of a free-boundary tokamak equilibrium solver for advanced study of tokamak equilibria

A free-boundary Tokamak Equilibrium Solver (TES), developed for advanced study of tokamak equilibra, is described with two distinctive features. One is a generalized method to resolve the intrinsic axisymmetric instability, which is encountered after all in equilibrium calculation with a free-boundary condition. The other is an extension to deal with a new divertor geometry such as snowflake or X divertors. For validations, the uniqueness of a solution is confirmed by the independence on variations of computational domain, the mathematical correctness and accuracy of equilibrium profiles are checked by a direct comparison with an analytic equilibrium known as a generalized Solovev equilibrium, and the governing force balance relation is tested by examining the intrinsic axisymmetric instabilities. As a valuable application, a snowflake equilibrium that requires a second order zero of the poloidal magnetic field is discussed in the circumstance of KSTAR coil system.

On the origin of viscoelastic Taylor-Couette instability resulted from normal stress differences

In this paper, the effect of normal stress differences on the viscoelastic Taylor-Couette instability is studied numerically. The governing equations are discretized using FTCS finite difference method on a staggered mesh based on the artificial compressibility algorithm. Using the CEF model as the constitutive equation and the Carreau-Yasuda model as the viscometric functions, the flow between rotating cylinders has been studied for a range of radius ratios, Taylor numbers and rheological properties. It is shown that increasing the first normal stress difference destabilizes the flow field while increasing the negative second normal stress difference stabilizes the flow field. The main contribution of the current study is an answer to this question: How do the first and second normal stress differences affect the stability of viscoelastic flow between rotating cylinders? For this reason, we used the order of magnitude technique to obtain a force balance relation in the core region of flow. Based on this relation and numerical simulation, the origin of viscoelastic Taylor-Couette instability resulted from normal stress differences are studied in detail. Furthermore, a two dimensional analytical solution for the main flow velocity component between finite rotating cylinders is carried out considering the end effect of stationary walls.

Regulation of the membrane wrapping transition of a cylindrical target by cytoskeleton adhesion.

The adsorption of external objects to the cell membrane often triggers cellular responses involving large deformations. In phagocytosis, upon contact with the target, the cell creates large extensions that wrap around the target and ultimately lead to its engulfment. Although active force generation, in particular by actin polymerization, is required for completion of this process, the elastic deformation of the cell membrane upon adhesion to an external object might play an important part in its initiation. In this paper, the elastic deformation of a bilayer owing to the binding of a cylindrical object is studied, taking into account the membrane bending rigidity and the surface tension, the membrane adhesion to both the external target and inner cytoskeleton. The problem is studied within the framework of the Helfrich-Hamiltonian and using force balance relations and the proper boundary conditions that are related to the adhesion energy coefficients. It is shown that membrane wrapping around the target may be a continuous or abrupt transition upon increasing the target binding energy, depending on the value of the parameter. The degree of wrapping and the shape of the membrane in the vicinity of the object are computed numerically, and analytical expressions are given for the boundaries separating the different wrapping regimes in the parameter space.

Flow and force-balance relations in a natural channel with bank vegetation

ABSTRACTThe typical flow dynamics of meandering streams related to curvature and associated bed topography can be altered by stream width variations and vegetation. This paper presents laboratory experiments conducted in a reduced-scale model of a low-sinuosity, variable-width bend with and without vegetation on the outer bank. Measurements of velocities and water surface elevations on a dense grid allowed, for the first time, the quantification of fluxes and forces that influence flow structure. Experiments without vegetation showed superelevation of water surface along the outer bank due to centrifugal effects, accompanied by longitudinal variations in water-surface gradients associated with width changes, as the channel was narrower near the bend inflection and wider near the apex. High outer bank velocities developed in the downstream part of the bend due to the absence of well-developed bed topography. Vegetation reduced centrifugal effects at the bend entrance but enhanced them at the bend exit, affecting flow in the downstream bend.

Collisionality scaling of main-ion toroidal and poloidal rotation in low torque DIII-D plasmas

In tokamak plasmas with low levels of toroidal rotation, the radial electric field Er is a combination of pressure gradient and toroidal and poloidal rotation components, all having similar magnitudes. In order to assess the validity of neoclassical poloidal rotation theory for determining the poloidal rotation contribution to Er, Dα emission from neutral beam heated tokamak discharges in DIII-D (Luxon 2002 Nucl. Fusion 42 614) has been evaluated in a sequence of low torque (electron cyclotron resonance heating and balanced diagnostic neutral beam pulse) discharges to determine the local deuterium toroidal rotation velocity. By invoking the radial force balance relation the deuterium poloidal rotation can be inferred. It is found that the deuterium poloidal flow exceeds the neoclassical value in plasmas with collisionality , being more ion diamagnetic, and with a stronger dependence on collisionality than neoclassical theory predicts. At low toroidal rotation, the poloidal rotation contribution to the radial electric field and its shear is significant. The effect of anomalous levels of poloidal rotation on the radial electric field and cross-field heat transport is investigated for ITER parameters.

Plasma size scaling of avalanche-like heat transport in tokamaks

The influence of plasma size on global ion temperature gradient turbulence is studied with the full-f Eulerian code GT5D (Idomura et al 2009 Nucl. Fusion 49 065029). The gyrokinetic model includes a consistent neoclassical electric field as well as a fixed-power source operator, enabling long-time simulations with self-consistent turbulent transport and equilibrium profiles. The effects of plasma size (from ρ* = 1/100 to ρ* = 1/225) are studied by scaling the minor radius a and the input power. For the first time, worse-than-Bohm scaling is observed under experimentally realistic conditions. For all plasma sizes, avalanches propagate over significant radii but their propagation depends on the radial electric shear. It is found that this quantity does not scale with ρ* due to the building up of intrinsic momentum. Such a dependence can be inferred from a force balance relation, which remains approximately valid in nonlinear simulations. An adaptive parallel momentum source has been implemented in GT5D to damp the parallel momentum profile. The new scan then reveals that the radial electric shear scales with ρ* while the transport is globally higher. These simulations therefore suggest that intrinsic momentum reduces heat transport. This work also addresses another important issue in gyrokinetics: it is shown that for fixed initial physical parameters the turbulent quasi-steady-state is statistically independent of the initial conditions.

High spatial resolution equilibrium reconstruction

The extension of the EFIT equilibrium reconstruction code to fine spatial-grid resolutions is discussed. The residue in the force-balance relation of the Grad–Shafranov (G–S) equation and the convergence property of these fine spatial-grid EFIT equilibria are studied in detail. The results suggest that fine spatial-grid equilibria generally better satisfy the force-balance constraint described by the G–S equation. Finer spatial-grid equilibria have typically smaller average error in satisfying the force-balance equation than coarse-grid equilibria and those extrapolated from coarse-grid results. Analysis of the equilibrium iteration algorithm employed in EFIT reveals that the iteration process is related to the spatial feedback stabilization of the plasma with flux control at various specified locations. Thus, for a converged equilibrium, axisymmetric stability is generally expected with feedback. The iteration error decreases self-similarly in the final stage of the iteration process and is related to the least stable axisymmetric mode in the feedback-stabilized equilibrium.

Flow of second-order fluid in a curved duct with square cross-section

This paper investigates the inertial and creeping flow of a second-order fluid in a curved duct with a square cross-section. Numerical modeling is employed to analyze fluid flow, and the governing equations are discretized using the finite difference method on a staggered mesh. The marker-and-cell method is employed to allocate the parameters on the staggered mesh, and static pressure is calculated using the artificial compressibility approach. The effect of centrifugal force due to the curvature of the duct and the opposing effects of the first and second normal stress difference on the flow field are investigated. In addition, the order-of-magnitude technique is used to derive the force balance relations for the core region of flow. Based on these relations, the performance mechanism of centrifugal force and normal stress differences on the generation of secondary flows is considered. We also present an analytical relation for the axial velocity profile and flow resistance ratio of creeping flow. For this kind of flow, previous studies have investigated the effect of the first normal stress difference on the transition from one pair to two pairs of vortices while we show that the negative second normal stress difference has the opposite effect on this transition and can stabilize the flow.

Equilibrium paradigm for field-reversed configurations and application to experiments

Fresh insights on field-reversed configurations (FRCs) are incorporated in a new paradigm for equilibria. In particular four new or unappreciated properties are accounted for: an empirically based scrape-off layer thickness; a new, more accurate axial force balance relation; viscous force regularity at the O-point; and the broken-surface effect. The new paradigm corrects glaring defects of previous models (rigid rotor, Hill’s vortex). Further, the new paradigm is simple enough to be easily used as an interpretive tool despite the limited data suite in most experiments. It is applied to the newly enhanced FRC data compendium, a database of 69 records from 15 facilities. Several important observations and corrections on the previous understanding of FRCs follow, three of which stand out. (1) The traditional axial force balance (“average-β” relation) gives an inaccurate scaling with the separatrix-to-wall radius ratio. (2) The improved equilibrium paradigm yields separatrix particle transport rates of 3–5 m2/s for “best confinement” examples; this is a factor of three lower than crude “bulk” estimates commonly used. (3) The transport compared to the Bohm rate shows a great deal of scatter (40% scatter/mean ratio), i.e., “Bohm” is not a useful representation for transport scaling.

Mechanical Characteristics Calculation of 2-DOF Spherical Traveling-wave Type Ultrasonic Motor

The mechanical characteristics calculation of traveling-wave ultrasonic motor with two degrees of freedom is investigated theoretically and experimentally. The space structure relations of traveling-wave ultrasonic motor with two degrees of freedom and the friction force on the contact surface of stator and rotor are analyzed. By using space position relations, the friction driving force and friction resistance at an arbitrary point on the contact surface of traveling-wave and spherical rotor are obtained through computation. Then the analytical expression of mechanical characteristics calculation is deduced on the basis of the axial force balance relation of traveling-wave stator when the motion is stable. The validity and veracity of the model is verified by theoretical and experimental analysis of the developed motor, and the influence of motor parameters on the output mechanical characteristics is analyzed. The maximum brake torque of developed motor reaches 0.10 N·m, the idle speed is 90 r/min. This research work lays a theoretical foundation for the next design, optimization and control of spherical traveling type ultrasonic motors.

Collision-dominated dust sheaths andvoids - observations in micro-gravity experiments and numericalinvestigation of the force balance relations

Numerical solutions of stationary force balance equations areused to investigate the possible dust configurations (duststructures) in complex plasmas between two floating potentialplane electrodes. The distance between electrodes is assumed tobe larger than the ion-neutral mean free path and thehydrodynamic description is used. It includes the known forcesoperating in this limit, the ionization source and the dustcharge variations. The stationary balance equations are solvedboth in the case of the presence of one-size dust grains and for thecase of a mixture of grains with two different sizes. Recentmicro-gravity experiments with single-size dust grains and two-different-size dust grains show the formation of a system ofdust sheaths and dust voids between the two plane electrodes. The observed configurations of dust structures depend strongly onthe gas pressure and the degree of ionization used. Thenumerical investigations are able to show the necessaryconditions for the types of structure to be created and givetheir size. The size of the structures observed is larger thanthe ion-neutral mean free path and is of the order of magnitudeof that obtained numerically. The numerical investigations givedetails of the spatial distributions, the dust particles,the electron/ion densities, the ion drift velocity and dustcharges inside and outside different dust structures. Thesedetails have not yet been investigated experimentally and can indicatedirections for further experimental work to be performed.The single-dust-sheath structure with single-size dust particlessurrounded by dust free regions (dust wall-voids) and floatingpotential electrodes is computed. Such a structure was observedrecently and the computational results are in agreement withobservations. It is shown that more often a dust void in thecentre is observed. It is found that a dust void in the centreregion between two electrodes is formed if the ionization rateis larger than the critical ionization rate and that in the presence ofthe floating potential walls the central void should besurrounded by two dust sheaths. The necessary condition forthis dust structure to be formed is found to be that betweenthe sheaths and the walls there are formed two other wall-voidregions. The size of the central void and the distributions of thestructure parameters in the two sheaths and in the three voidsare computed. The qualitative features of the structure obtainedin the numerical computations correspond to those observed. Thedistributions of the structure parameters in the case of the twodust sheaths are quite different from that for the case of asingle central sheath. The possible structures between theelectrodes for the case of the presence of dust particles of twodifferent sizes are analysed numerically. It is shown that dust particles with different sizes cannot coexist inequilibrium at the same position and that the regions withdifferent size dust particles must be separated in space. Thisconclusion is in agreement with most observations performed sofar. It is illustrated numerically that for the case where thecentral void is present the dust particles of larger size form aseparate dust sheath which should be located at larger distancesfrom the centre than that for the smaller dust particles. Thisresult also coincides qualitatively with the observations.Computations for the distributions of the parameters in thelarger size dust sheath were performed both in the case wherethe central part is occupied by a dust sheath with smaller sizedust particles and for the case where in the central part there existsa dust void surrounded by dust sheaths with smaller size dustparticles. The size of the dust void between the sheaths withdifferent size dust particles is calculated and shown to besmall as compared to the sheath thickness. In the sheath withlarger size dust particles the distribution of dust and plasmaparameters differs qualitatively from that of the first dustsheath with smaller size dust particles. The stability of thestationary structures both with respect to excitation of dustconvection cells and with respect to oscillations of dust voidsize is discussed.