Ideal Liquid Research Articles

Calculation of craters resulting from impact rupture of rock mass using pulse hydrodynamic problem formulation

A liquid–solid hydrodynamic model is used to determine shapes and sizes of craters generated by impact rupture of rocks. Near the impact location, rock is modeled by an ideal incompressible liquid, in the distance—by an absolute solid. The calculated data are compared with the experimental results obtained under impact treatment of marble by a wedge-shaped tool.

On the relation between Stokes drift and the Gerstner wave

We discuss the properties of two-dimensional, nonlinear, potential, and vortex waves on the surface of an ideal liquid of infinite depth. It is shown that in the quadratic order in the amplitude, the vorticity of the Gerstner wave is equal in magnitude to and different in sign from that of the Stokes drift current in a surface layer. This allows a classic Stokes wave obtained in the framework of potential theory to be interpreted as a superposition of the Gerstner wave and Stokes drift. It is proposed that the nonlinearity coefficient in the nonlinear Schrödinger equation can be physically interpreted as the Doppler frequency shift along the vertically averaged Stokes drift current.

The Ideal Ionic Liquid Salt Bridge for Direct Determination of Gibbs Energies of Transfer of Single Ions, Part II: Evaluation of the Role of Ion Solvation and Ion Mobilities.

An important intermediate goal to evaluate our concept for the assumption-free determination of single-ion Gibbs transfer energies Δtr G°(i, S1 →S2 ) is presented. We executed the crucial steps a) and b) of the methodology, described in Part I of this treatise, exemplarily for Ag+ and Cl- with S1 being water and S2 being acetonitrile. The experiments showed that virtually all parts of the liquid junction potentials (LJPs) at both ends of a salt bridge cancel, if the bridge electrolyte is an "ideal" ionic liquid, that is, one with nearly identical diffusion of anion and cation. This ideality holds for [N2225 ]+ [NTf2 ]- in the pure IL, but also in water and acetonitrile solution. Electromotive force measurements of solvation cells between S1 and S2 demonstrated Nernstian behavior for Ag+ concentration cells and constant like cell potentials for solutions with five tested Ag+ counterions.

The Ideal Ionic Liquid Salt Bridge for Direct Determination of Gibbs Energies of Transfer of Single Ions, Part II: Evaluation of the Role of Ion Solvation and Ion Mobilities

AbstractAn important intermediate goal to evaluate our concept for the assumption‐free determination of single‐ion Gibbs transfer energies ΔtrG°(i, S1→S2) is presented. We executed the crucial steps a) and b) of the methodology, described in Part I of this treatise, exemplarily for Ag+ and Cl‐ with S1 being water and S2 being acetonitrile. The experiments showed that virtually all parts of the liquid junction potentials (LJPs) at both ends of a salt bridge cancel, if the bridge electrolyte is an “ideal” ionic liquid, that is, one with nearly identical diffusion of anion and cation. This ideality holds for [N2225]+[NTf2]‐ in the pure IL, but also in water and acetonitrile solution. Electromotive force measurements of solvation cells between S1 and S2 demonstrated Nernstian behavior for Ag+ concentration cells and constant like cell potentials for solutions with five tested Ag+ counterions.

The Ideal Ionic Liquid Salt Bridge for the Direct Determination of Gibbs Energies of Transfer of Single Ions, Part I: The Concept.

Described is a procedure for the thermodynamically rigorous, experimental determination of the Gibbs energy of transfer of single ions between solvents. The method is based on potential difference measurements between two electrochemical half cells with different solvents connected by an ideal ionic liquid salt bridge (ILSB). Discussed are the specific requirements for the IL with regard to the procedure, thus ensuring that the liquid junction potentials (LJP) at both ends of the ILSB are mostly canceled. The remaining parts of the LJPs can be determined by separate electromotive force measurements. No extra-thermodynamic assumptions are necessary for this procedure. The accuracy of the measurements depends, amongst others, on the ideality of the IL used, as shown in our companion paper Part II.

The Ideal Ionic Liquid Salt Bridge for the Direct Determination of Gibbs Energies of Transfer of Single Ions, Part I: The Concept

AbstractDescribed is a procedure for the thermodynamically rigorous, experimental determination of the Gibbs energy of transfer of single ions between solvents. The method is based on potential difference measurements between two electrochemical half cells with different solvents connected by an ideal ionic liquid salt bridge (ILSB). Discussed are the specific requirements for the IL with regard to the procedure, thus ensuring that the liquid junction potentials (LJP) at both ends of the ILSB are mostly canceled. The remaining parts of the LJPs can be determined by separate electromotive force measurements. No extra‐thermodynamic assumptions are necessary for this procedure. The accuracy of the measurements depends, amongst others, on the ideality of the IL used, as shown in our companion paper Part II.

Vibrations of Elastic Shells of Revolution Partially Filled with Ideal Liquid

We propose an algorithm for the numerical analyses of vibrations of elastic shells of revolution partially filled with ideal incompressible liquids. In the solution of this problem, the wave motions of liquid on its free surface are taken into account. The solution of the problem of hydroelasticity is based on the application of the method of decomposition of the domain of integration of equations of the theory of shells with the use of the variational statement of the problem and on the approximate construction of the operator inverse to the operator of the hydrodynamic part of the problem. We construct a generalized functional of displacements of the shell for which the role of conditions of matching for the solutions in different subdomains is played by the natural boundary conditions. The obtained numerical results are compared with the existing exact solutions of the analyzed problem for a shell in the form of a straight circular cylinder.

Малые движения идеальной стратифицированной жидкости со свободной поверхностью, полностью покрытой крошеным льдом

Малые движения идеальной стратифицированной жидкости со свободной поверхностью, полностью покрытой крошеным льдом

Instability of a Charged Droplet in an Inhomogeneous Electrostatic Field of a Rod of Finite Thickness

The instability of a charged droplet of an ideal liquid in an inhomogeneous electrostatic field of a rod of finite thickness maintained at a constant electrostatic potential is investigated within the framework of analytic asymptotic calculations. It is shown that the mode amplitudes and the drop oscillation frequencies increase with the rod thickness. The critical conditions of instability of the droplet reduce by several times as compared with the critical conditions of implementation of its instability in the electrostatic field of an infinitely thin filament maintained at a constant electrostatic potential. An analytic dependence between the charge and field parameters, critical for implementation of the instability of a charged droplet in an inhomogeneous electrostatic field and dependent on the rod thickness, is found.

On the Stability of the Surface of a Short Charged Jet Moving with Respect to an External Material Medium

The problem of the stability of capillary waves on the surface of a charged jet of an ideal incompressible electroconducting liquid, which moves with respect to a material dielectric medium, is considered. There is a tangential discontinuity of the velocity field on the interface between the media. Solutions to the problem in two idealized models have been compared, i.e., when the jet has a finite and infinite length. It has been shown that the instability increments and the wave numbers of the most unstable waves, computed in both models, are linearly related, and velocity of motion of the jet acts as a coefficient of proportionality.

Dispersion Properties of Lamb Waves in an Elastic Layer–Ideal Liquid Half-Space System

The problem of the propagation of normal waves in an elastic layer interacting with a compressible ideal liquid half-space is stated and solved using the three-dimensional linear equations of classical elasticity for the solid and the three-dimensional linearized Euler equations for the compressible ideal fluid. The dispersion curves are plotted for quasi-Lamb modes over a wide frequency range. The effect of the ideal compressible fluid and the elastic layer thickness on the dispersion of the phase velocities of quasi-Lamb modes in hydroelastic waveguides is analyzed. The localization properties of these modes in hydroelastic waveguides are studied. The numerical results are presented in the form of plots and analyzed.

Gravitation according to theory of sources

The metric of spherically symmetric ball of ideal liquid is considered in $G^2$- approximation with the help of theory of sources. Using the integral equations of this theory gives the exterior metric depending upon the radius of the ball of matter in some terms proportional to $G^2$..I argue that according this metric from measurement outside the ball one can infer the value of ball radius.

Electrostatic instability of the surface of a volume charged jet of dielectric liquid moving relative to the surrounding medium

The laws of implementation of electrostatic instability of the surface of a cylindrical volume charged jet of an ideal incompressible dielectric liquid moving relative to the ideal incompressible dielectric medium and the stability of bending-deformation capillary waves developed on the surface are investigated analytically. It is found that there are thresholds for the critical conditions of implementation of the instability with respect to the jet velocity relative to the medium (Weber number) and with respect to the electric space charge (relative to the ratio of the electrostatic pressure on the jet surface to the Laplace pressure). The critical analytic dependence between these dimensionless parameters is found.

Stress State of a Partially Fixed Spherical Shell Filled with Liquid and Subjected to Impulsive Excitation

We study the stress-strain state of a closed elastic spherical shell filled with ideal compressible liquid. The energy introduced in the form of pulses in the gas cavity in the central part of the system serves as the source of its excitation. The hypotheses used for the investigations by the finite-difference method are presented and a correct mathematical statement of the problem is formulated. We obtain the data on the behavior of stresses as function of time in the cases of free shell and of the partial rigid fixing of its surface. The effect of rigid fixing on the stress-strain state of the shell is analyzed.

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.

Nanoscale liquid crystal polymer Bragg polarization gratings.

We experimentally demonstrate nearly ideal liquid crystal (LC) polymer Bragg polarization gratings (PGs) operating at a visible wavelength of 450 nm and with a sub-wavelength period of 335 nm. Bragg PGs employ the geometric (Pancharatnam-Berry) phase, and have many properties fundamentally different than their isotropic analog. However, until now Bragg PGs with nanoscale periods (e.g., < 800 nm) have not been realized. Using photo-alignment polymers and high-birefringence LC materials, we employ multiple thin sublayers to overcome the critical thickness threshold, and use chiral dopants to induce a helical twist that effectively generates a slanted grating. These LC polymer Bragg PGs manifest 85-99% first-order efficiency, 19-29° field-of-view, Q ≈ 17, 200 nm spectral bandwidth, 84° deflection angle in air (in one case), and efficient waveguide-coupling (in another case). Compared to surface-relief and volume-holographic gratings, they show high efficiency with larger angular/spectral bandwidths and potentially simpler fabrication. These nanoscale Bragg PGs manifest a 6π rad/μm phase gradient, the largest reported for a geometric-phase hologram while maintaining a first-order efficiency near 100%.

Optimal control of the motion of a helical body in a liquid using rotors

The motion controlled by the rotation of three internal rotors of a body with helical symmetry in an ideal liquid is considered. The problem is to select controls that ensure the displacement of the body with minimum effort. The optimality of particular solutions found earlier is studied.

Behavior of a semi-infinite ice cover under periodic dynamic impact

Oscillations of a semi-infinite ice cover in an ideal incompressible liquid of finite depth under local time-periodic axisymmetric load are considered. The ice cover is simulated by a thin elastic plate of constant thickness. An analytical solution of the problem is obtained using the Wiener–Hopf method. The asymptotic behavior of the amplitudes of oscillations of the plate and the liquid in the far field is studied. It is shown that the propagation of waves in the far field is uneven: in some directions, the waves propagate with a significantly greater amplitude.

Study on the effect of new type liquid accelerator on the performance of shotcrete

Shotcrete is an essential preliminary support means in New Austrian Tunneling Method (NATM) construction and plays a very important role in controlling the stability of surrounding rock. The accelerator is a necessary admixture in shotcrete and its quality can greatly affect shotcrete performance. This paper proposes a new liquid accelerator characterized by short initial and final setting time, small dosage, and good adaptability to cement. Laboratory tests and field tests are conducted to verify the influence of this liquid accelerator on performance of shotcrete. Numerical simulation is carried out to study the strength growth of shotcrete with time and interaction between the strength and stress release of surrounding rock. The results show that the initial and final setting time of this liquid accelerator is 2 minutes and 4 minutes respectively. Its dosage is just 1.5% to 4% of the cement quantity. Adding this liquid accelerator can effectively improve the early strength and reduce the later strength loss of shotcrete, and therefore enhance the supporting effects of shotcrete on surrounding rock. In the field application, it is an ideal liquid accelerator for shotcrete, characterized by little resilience, no slurry shedding, and low dust.

New Method for Highly Efficient Conversion of Biomass-Derived Levulinic Acid to γ-Valerolactone in Water without Precious Metal Catalysts

γ-Valerolactone (GVL) is receiving increasing attention because of its significant characteristics of an ideal sustainable liquid fuel. In this work, a novel and nonprecious metal catalytic method of the hydrogenation of biomass-derived levulinic acid (LA) into GVL by water splitting is first reported. Commercially available nonprecious metals of Fe, Ni, Cu, Cr, and Mo exhibited significantly catalytic activities in the hydrogenation of LA into GVL. Over 90% yield of GVL from LA can be obtained at a relatively low temperature of 180 °C, and an excellent 98% yield of GVL was achieved over the Fe catalyst at 250 °C. Catalyst Fe is stable and still keeps the high catalytic activity after recycles. The extraordinary catalytic activity of the general Fe powder is probably because of the role of hot water and also a synergistic role of the Fe and ZnO or Zn/ZnO. Also, the reactor wall of a reactor made of the stainless steel material acted as a significant catalyst, and a considerably high GVL yield of 56% can b...