Ideal Liquid Research Articles

Mathematical model of the flotation complex particle–bubble within the framework of Lagrangian formalism

A model of the interaction of a spherical gas bubble and a rigid particle is derived as a coupled system of second-order differential equations using Lagrangian mechanics. The model takes into account oscillations of the bubble surface and the attached to it solid cylindrical particle in infinite volume of ideal incompressible liquid. The capillary force holding the particle on the bubble is due to the shape of the meniscus surface, which determines the wetting edge angle. The series with respect Legendre polynomials is used to present small axisymmetric oscillations of the particle-bubble system. Potential and kinetic energies are expressed through coefficients of this series. Particle adhesion condition to bubble surface is implemented through Lagrange multipliers. The dependence of the particle size and its density is demonstrated as a result of the numerical integration of the resulting dynamic system of differential equations.

Effect of Radiation Force on a Flexible Spherical Particle at the Free Liquid Surface*

The effect of the radiation force on a spherical drop of an ideal liquid in the vicinity of the free boundary of the liquid when an acoustic wave is normally incident on the liquid surface is studied. As a result, the liquid sphere is located in the field of standing acoustic wave of pressure with the node at the free liquid surface. The measure of interaction is the radiation force: the time-average integral over the pressure in the external fluid caused by the acoustic wave over the surface of the sphere. The approach assuming the use of the velocity field potential obtained by solving the linear diffraction problem when determining the pressure in the liquid is used. It is established that there are frequencies of the incident wave at which the radiation force does not act on the spherical drops, which, therefore, will be stationary.

Research of adhesive dosing possibility of glued laminated lumber technology

Since the glue is not an ideal liquid for which the laws of its expiration are generally known, the purpose of our work was to determine the duration and speed of the resin outflow from the container, depending on 2 factors - the height of the container with the resin above the surface on which the resin is applied, and the conditional viscosity of the resin within its working value. As a result of the conducted research, it was found that it is possible to dose the glue in the glued beam technology, when using low-viscosity resins, by lifting the container with the resin (glue) above the level of the surface on which it is applied. Moreover, for low viscosity fluids with a viscosity up to 80 °C (on the examples of water and resin low viscosity) observed increase in flow rate from the container increasing the height of the rise of liquids over the surface to which it is applied. As the resin viscosity increases from 80 to 131s the absolute value of the resin flow rate from the container decreases.

On Investigation of Liquid Sloshing in Cylindrical Tanks With Single and Multiply Connected Domains Using Isogeometric Boundary Element Method

Abstract This paper explores an isogeometric boundary element method (IGA-BEM) for sloshing problems in cylindrical tanks with single and multiply connected domains. Instead of the Lagrange basis functions used in the standard BEM, the nonuniform rational B-splines (NURBS) basis functions are introduced to approximate the geometries of the problem boundaries and the unknown variables. Compared with the Lagrange basis functions, NURBS basis functions can accurately reconstruct the geometric boundary of analysis domain with almost no error, and all the data information for NURBS basis functions can be directly obtained from the computer-aided design (cad) or computer-aided engineering (cae) commercial software, which implies the modeling process of IGA-BEM is more simple than that of the standard BEM. NURBS makes it possible for the IGA-BEM to realize the seamless connection between cad and cae software with relative higher calculation accuracy than the standard BEM. Based on the weighted residual method as well as the divergence theorem, the IGA-BEM is developed for the single and multiply connected domains, whose boundaries are separately defined in the parameter space by different knot vectors. The natural sloshing frequencies of the liquid sloshing in a circular cylindrical tank with a coaxial or an off-center circular pipe, an elliptical cylindrical tank with an elliptical pipe, a circular cylindrical tank with multiple pipes are estimated with the introduced method by assuming an ideal (inviscid and incompressible) liquid, irrotational small-amplitude sloshing, and the linear free-surface condition. The comparison between the results obtained by the proposed method and those in the existing literatures shows very good agreements, which verifies the proposed model well. Meanwhile, the effects of radius ratio, liquid depth, number, and location of internal pipe (pipes) on the natural sloshing frequency and sloshing mode are analyzed carefully, and some conclusions are outlined finally.

Magnetization plateau observed by ultrahigh-field Faraday rotation in the kagome antiferromagnet herbertsmithite

To capture the high-field magnetization process of herbertsmithite (ZnCu3(OH)6Cl2), Faraday rotation (FR) measurements were carried out on a single crystal in magnetic fields of up to 190 T. The magnetization data evaluated from the FR angle exhibited a saturation behavior above 150 T at low temperatures, which was attributed to the 1/3 magnetization plateau. The overall behavior of the magnetization process was reproduced by theoretical models based on the nearest-neighbor Heisenberg model. This suggests that herbertsmithite is a proximate kagome antiferromagnet hosting an ideal quantum spin liquid in the ground state. A distinguishing feature is the superlinear magnetization increase, which is in contrast to the Brillouin function-type increase observed by conventional magnetization measurements and indicates a reduced contribution from free spins located at the Zn sites to the FR signal.

Relaxation phenomena in electron plasma of semiconductors

The hydrodynamics of the electron subsystems of semiconductors is studied in the approximations of the ideal and real liquid, taking into account processes of relaxation of temperatures and macroscopic velocities of electrons and phonons without assuming the local equilibrium of the system. A set of integral equations for the electron distribution function of the first order in gradients is obtained, which determines the sources in the hydrodynamic equations of the ideal liquid approximation and the dissipative flows of energy and momentum of electrons. The steady states of the system in the ideal liquid approximation are investigated. The exact formulas for the electron mobility of the semiconductor and its conductivity are derived and kinetic coefficients that determine current in a spatially inhomogeneous state are calculated. In the presence of an electric field, the phenomenon of difference of temperatures of the electron and phonon subsystems is predicted. The obtained expressions are specified for the case of temperatures much higher the Debye temperature.

Design and prediction for highly efficient SO2 capture from flue gas by imidazolium ionic liquids

An efficient method for prediction in the capture of SO2 from flue gas by imidazolium ionic liquids was reported, where the concentration of SO2 is 2000 ppm. On the basis of quantitative calculations through a combination of Langmuir simulation, theoretical calculation and quantum chemical method, SO2 absorption and desorption performance from flue gas by twelve kinds of imidazolium ionic liquids with different anions were designed and predicted. Then, among them, five kinds of imidazolium ionic liquids were chosen and prepared to investigate their behavior of SO2 absorption capacity, desorption residue, and available absorption capacity. The results indicated that the experimental values were in good agreement with the predicted values. Thus, an ideal ionic liquid [Emim][Tetz] was obtained through the predictive method for the capture of SO2 of 2000 ppm, which showed high available absorption capacity of 0.24 g SO2 per g ionic liquid and excellent reversibility.

Explosive instability of the surface of a liquid dielectric in a vertical electric field in confined geometry

Nonlinear dynamics of the free boundary of an ideal dielectric liquid in a vertical electric field is studied in a confined axisymmetric geometry. We derive an amplitude equation which describes the behavior of a fluid surface in the weakly nonlinear approximation. It is demonstrated that, due to the effect of quadratic nonlinearities, the regime of excitation of the surface electrohydrodynamic instability is always hard. It is also shown that cubic nonlinearities suppress the instability development for liquids with relatively small permittivity. On the contrary, the nonlinearity begins to play a destabilizing role for high values of dielectric constant. As a consequence, the instability development takes an explosive character: the amplitude of boundary perturbations grows unlimitedly over a finite time. Using an analogy with the motion of an effective Newtonian particle in a certain potential, we formulate conditions for explosive buildup of perturbations. Differences in the behavior between axisymmetric perturbations of the free surface and the cases of hexagonal, square, and planar symmetries are discussed.

Quantum paraelectricity in the Kitaev quantum spin liquid candidates H3LiIr2O6 and D3LiIr2O6

H3LiIr2O6 is the first honeycomb-lattice system without any signs of long-range magnetic order down to the lowest temperatures, raising the hope for the realization of an ideal Kitaev quantum spin liquid. Its honeycomb layers are coupled by interlayer hydrogen bonds. Static or dynamic disorder of these hydrogen bonds was proposed to strongly affect the magnetic exchange and to make Kitaev-type interactions dominant. Using dielectric spectroscopy, here we provide experimental evidence for dipolar relaxations in H3LiIr2O6 and deuterated D3LiIr2O6, which mirror the dynamics of protons and deuterons within the double-well potentials of the hydrogen bonds. The detected hydrogen dynamics reveals glassy freezing, characterized by a strong slowing down under cooling, with a crossover from thermally-activated hopping to quantum-mechanical tunneling towards low temperatures. Thus, besides being Kitaev quantum-spin-liquid candidates, these materials also are quantum paraelectrics. However, the small relaxation rates in the mHz range, found at low temperatures, practically realize quasi-static hydrogen disorder, as assumed in recent theoretical works to explain the quantum-spin-liquid ground state of both compounds.

Eigenfrequencies of the Oscillating Surface of a Free-Falling Compound Drop of an Ideal Liquid

The surface oscillations of a two-layer drop of an ideal liquid are analyzed. It is shown that two different oscillation frequencies of the taken mode can exist. The effect of the main parameters of the liquids that compose the drop on the mode oscillation eigenfrequencies is analyzed. It is found that a relative decrease in the outer liquid layer thickness leads to a decrease in the eigenfrequencies of both in-phase and out-of-phase oscillations. An increase in the difference between the surface tension coefficients leads to an increase in the eigenfrequencies. Relative increase in the inner liquid density increases the eigenfrequencies of the in-phase mode and affects only slightly the eigenfrequencies of the out-of-phase mode. Simplified expressions for the dependences of the eigenfrequencies of oscillating free surface of a compound drop on parameters are obtained.

The Movement of a Rectangular Cylinder in a Liquid at Short Times after Impact with Formation of a Cavity

Under consideration is some dynamical mixed problem concerning some separated impact and subsequent motion with constant velocity of a rectangular cylinder in an ideal incompressible heavy liquid. The specificity of this problem is that an attached cavity forms after impact and a new internal free boundary of the liquid appears. The shape of the cavity and the configuration of the outer free surface are unknown in advance and are to be determined during solution of the problem. Studying the problem is carried out at short times with consideration of the dynamics of the points of separation of the internal free boundary of the liquid. Location of the separation points at every time is defined from the Kutta–Zhukovsky condition. The influence is studied of the physical and geometric parameters of the problem on the shape of free boundaries of the liquid at short times. The asymptotic analysis is carried out of the internal free boundary of liquid near the separation points.

Influence of transient liquid phase bonding followed by homogenization on the fatigue lifetimes of inconel 738 at elevated temperature

An ideal transient liquid phase (TLP) joint is achievable with the complete isothermal solidification and homogenization of the Diffusion Affected Zone (DAZ), in which case, a joint with a similar microstructure to the Base Metal (BM) is obtained. In this study, Inconel 738 (IN-738) was joined by TLP bonding using a BNi-2 filler alloy at 1120 °C for different hold times followed by a Standard Heat Treatment (SHT) for the homogenization of the joint. After a microstructural study of the joints, the BM and the homogenized TLP joint were fatigue tested at 850 °C under similar conditions. A comparison of the fatigue test results (SN curve) was indicative of the reduced fatigue lifetime of IN-738 as a result of TLP bonding which can be attributed to the shorter elongation of the joint, γ grain growth during the bonding, and the larger number of fatigue crack initiation sites at the homogenized joint compared with the BM. In addition, several grain boundary cracks were observed across the fracture of the homogenized joint that may have been due to the reduced cohesive strength of the material at the boundaries or the increased density of carbides at grain boundaries. Eventually, Basquin’s equation was presented to estimate the fatigue life of the joint and the fatigue strength coefficient and fatigue strength constant of the joint were calculated -0.049 and 325.65, respectively.

Определение поля смещений в неоднородном покрытии упругой пластины при прохождении через неё плоской звуковой волны

В статье рассматривается краевая задача для системы линейных обыкновенных дифференциальных уравнений второго порядка, построенная для определения поля смещений в непрерывно-неоднородном упругом покрытии пластины при прохождении через неё плоской звуковой волны.Полагается, что однородная изотропная упругая пластина с неоднородным по толщине упругим покрытием граничит с идеальными жидкостями.Методом степенных рядов получено приближенное аналитическое решение краевой задачи. Краевая задача сведена к задачам с начальными условиями. Решение краевой задачи представлено в виде линейной комбинации фундаментальных решений. Найденное аналитическое решение краевой задачи справедливо для широкого класса законов неоднородности материала покрытия.Проведены численные расчеты зависимостей компонентов вектора смещения на границах покрытия от угла падения плоской волны.

Transient Simulation of Underground Pumped Storage Hydropower Plants Operating in Pumping Mode

The increasing penetration of variable renewable energies (VRE) in the European electricity mix requires flexible energy storage systems (ESS), such as pumped storage hydropower (PSH). Disused mining voids from deep closed mines may be used as subsurface reservoirs of underground pumped-storage hydropower (UPSH) plants. Unlike conventional PSH plants, the air pressure in UPSH plants is variable and it differs from the atmospheric conditions. In this paper, the hydraulic transient process of an UPSH plant operating in pumping mode was investigated and a preliminary thermodynamic analysis of the closed surge tank was carried out. Analytical and CFD three-dimensional numerical simulations based on the volume of fluid (VOF) model with two-phase flow have been performed for analyzing the transient process. In the transient simulation, air and water are considered as ideal gas and compressible liquid, respectively. Different guide vanes closing schemes have been simulated. The obtained results show that the dimensioning of underground reservoir, surge tank, and air ducts is essential for ensuring the hydraulic performance and optimizing the operation of UPSH plants. The static pressure in the air duct, surge tank and lower reservoir reaches −1.6, 112.8 and −4 kPa, respectively, while a heat flux of −80 W was obtained through the surge tank walls.

Алгоритм движения точечных вихрей в ограниченной области

The problem of calculating the paths of motion of a set of point vortices in an ideal incompressible liquid in a limited area is considered. The area is supposed to be piecewise smooth. The stream function at any given time is presented as a sum: the stream functions of point vortices and the potential of a simple layer, the density of which - the density of vortexes on the border - is required to determine. Regardless of time, the stream function harmoniously extends into the exterior of the area and is identically equal to a constant at the boundary, and, therefore, is a Roben potential. Briefly, the paper describes an algorithm for calculating the Roben potential. The unknown density of vortices is sought in the form of a linear combination of a complete system of potentials, and the coefficients are determined by the values of the Roben potential, as a solution to the inverse problem; determination of the coefficients reduces to solving a system of linear equations with a Gram matrix for a linearly independent system of functions. By the function of stream by tangents determine the trajectories of movements of vortices. The results of computational experiments of the motion of several point vortices in a square are presented. A computer analysis of the movement was carried out: two, four and eight point vortices, calculated the trajectories of their movement and found stationary and periodic, stable and unstable configurations.

High performence of sloshing problem in cylindrical tank with various barrels by isogeometric boundary element method

The NURBS basis is introduced into the boundary element method (BEM) for solving the liquid sloshing problem in the multiply connected domain. An ideal liquid assumed to be inviscid, incompressible is used to study the sloshing characteristics in the cylindrical tanks with barrels of the arbitrary shapes, dimensions and number. Considering the boundary conditions at the free surface and the tank bottom as well as the constant section of the tank, the Laplace equation for potential flow problem can be decoupled into 2D Helmholtz and modified Helmholtz equations. The NURBS widely used in the CAD industry is adopted in this paper to approximate both the boundary geometry and the field variables. The proposed model is verified against the available results from some existing literatures. Meanwhile, the effects of geometric parameters, number and arrangement of internal barrels on liquid sloshing characteristics (such as the sloshing force, surface elevation and natural frequencies) in cylindrical tanks are also investigated in detail. This paper is expected to provide useful guidance for design of cylindrical tanks equipped with several internal tubular structures (such as the fast reactor with pumps and heat exchangers).

Vibrations of Two-Layer Ideal Liquid in a Rigid Cylindrical Vessel with Elastic Bases

We analyze the frequency equation of natural vibrations of a heavy ideal two-layer incompressible liquid placed in a rigid circular cylindrical vessel with elastic bases in the form of fixed thin circular plates. We consider the cases of axially symmetric (longitudinal) and asymmetric (transverse) vibrations of the liquid and plates and different limiting cases (degeneration of the plates into membranes, absolutely rigid plates, and the absence of the top plate). It is shown that the frequency spectrum of coupled asymmetric vibrations of the elastic bases and two-layer ideal liquid consists of three sets of frequencies corresponding to the vibrations of the top and bottom elastic bases and to the vibrations of the inner interface of liquids. The frequency spectrum of coupled axially symmetric vibrations consists of the same three sets as for the asymmetric vibrations and an additional frequency of vibration of the liquid column as a single whole. As an example, we perform the analytic and numerical investigations of the frequency spectrum of a homogeneous liquid with free surface and elastic bottom in the form of a membrane.

Impulsive Motion Inside a Cylindrical Cavity

Experimental studies of supercavitating models moving at speeds in the range from 400 m/s to 1000 m/s revealed a regime of bouncing motion, in which the rear part of an axisymmetric body periodically bounces against the free boundaries of the supercavity. The impulsive force generated by the impacts is the main concern in this paper. The analysis is performed in the approximation of two-dimensional potential flow of an ideal and incompressible liquid with negligible surface tension effects. The primary interest of the study is to determine the added mass taking into account the shape of the cavity. The theoretical study is based on the integral hodograph method, which makes it possible to obtain analytic expressions for the flow potential and for the complex velocity in an auxiliary parameter plane and obtain a parametric solution to the problem. The problem is reduced to a system of two integro-differential equations in two unknowns: the velocity magnitude on the cavity boundary and the slope of the velocity angle to the body. The equations are solved numerically using the method of successive approximations. The obtained results show that the added mass of an arc impacting a cylindrical cavity depends heavily on the arc angle. As the angle tends to zero or the radius of the cavity tends to infinity, the obtained solution predicts the added mass corresponding to a plate impacting a flat free surface.

Comparative investigation on copper leaching efficiency from waste mobile phones using various types of ionic liquids

Recovery of valuable materials from waste mobile phones is significantly important with the rapid development of telecommunication industry. In this work, the comparative study was conducted on the copper leaching behaviors from waste mobile phones using various types of ionic liquids of [Bmim]Cl, [Emim]Cl, [Bmin][BF4], and [Bmim][PF6]. Effects of various operational factors, including ionic liquid type, additive agent, oxidizing agent, leaching time and temperature, on the copper leaching efficiency were investigated in detail. The results indicated that the copper leaching efficiency was improved with the addition of H2O2. Both considering leaching time and temperature, [Emim]Cl and [Bmim][BF6] were the ideal ionic liquids for high copper leaching rates under suitable operational conditions. The kinetics of copper leaching using the ionic liquids of [Emim]Cl and [Bmim][BF6] were clarified to determine the controlling model of copper leaching reaction. The results proved that the copper leaching reaction mainly depended on the controlling of solid membranes diffusion. The efficiencies of copper recovery by slurry electrolysis using various ionic liquid solutions were compared. The optimal copper recovery of 92.65% was obtained with the maximal current efficiency of 79.99% in the ionic liquid solution of CuSO4–NaCl–H2SO4-[Bmim][PF6]. The morphology analysis of copper deposit layer after slurry electrolysis proved better copper recovery performance using [Bmim][PF6] as ionic liquid.

Oscillations of a Stratified Liquid Partially Covered with Ice (General Case)

We study the problem of small motions of an ideal stratified liquid whose free surface consists of three regions: liquid surface without ice, a region of elastic ice, and a region of crumbled ice. The elastic ice is modeled by an elastic plate. The crumbled ice is understood as weighty particles of some matter floating on the free surface. Using the method of orthogonal projection of boundary conditions on a moving surface and the introduction of auxiliary problems, we reduce the original initial boundary value problem to an equivalent Cauchy problem for a second-order differential equation in a Hilbert space. We obtain conditions under which there exists a strong (with respect to time) solution of the initial boundary value problem describing the evolution of the hydrodynamic system under consideration.