Shock wave structure in dense gases

The internal structure of a shock wave front in a gas is studied by molecular dynamics (MD) simulation. A new approach to MD shock simulation is used, which enables one to consider a stationary shock front at rest and radically improves the quality of simulation. The profiles of flow variables and their fluctuations are calculated. The evolution of the velocity distribution function across the shock layer is calculated and compared with the bimodal distribution. The pair distribution function in the shock layer is determined. The surface tension associated with the shock wave is estimated. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 2, 91–96 (25 July 1997)     

Shock compression of simple liquids: Implications for deuterium

Abstract

This report summarizes research on shock-compressed liquids: argon, xenon, nitrogen, and hydrogen. The purpose is to illustrate the common thread that connects all of these studies with the recent work on deuterium.     

Shock wave structure in a two-components gas mixture

Summary The nonlinear differential equations describing the problem of shock wave structure in a two-component gas mixture are reduced to a system of two coupled nonlinear differential equations. This system is solved numerically using the finite-difference method. It is found that the relative shock wave thickness of the mixture increases with the increase of the ratio between the viscosity coefficients when the ratio between the mass fractions is constant. It is also shown that the relative shock wave thickness of the mixture decreases with the increase of the ratio between the mass fractions when the ratio between the viscosity coefficients is constant.

---

Riassunto Si riducono le equazioni differenziali non lineari che descrivono il problema della struttura dell’ onda d’urto in una miscela di gas a 2 componenti a un sistema di due equazioni differenziali accoppiate non lineari. Questo sistema si risolve numericamente usando il metodo delle differenze finite. Si trova che il relativo spessore dell’onda d’urto della miscela aumenta con l’aumento del rapporto tra i coefficienti di viscosità, quando il rapporto tra le frazioni di massa è costante. Si mostra anche che lo spessore relativo dell’onda d’urto della miscela diminuisce con l’aumento del rapporto tra le frazioni della massa, quando il rapporto tra i coefficienti di viscosità è costante.

---

Резюме Нелинейные дифференциальные уравнения, описывающие проблему структуры ударной в двух-компоентной газовой смеси, сводятся к системе двух связанных нелинейыых дифференциальных уравнений. Получается, что относительная толщина ударной волны в смеси увеличвается с увеличением отношения между коэффиыентами вязкоти, когда отнощение между массовыми доями остается постоянным. Также показывается. что относительная толщина ударной волны уменьшается с увеличением отношения между массовыми долями. когда отношение между коэффициентами вязкости остается постоянным.

     

Three-particle correlations in simple liquids

We use videomicroscopy to follow the phase-space trajectory of a two-dimensional colloidal model liquid and calculate three-point correlation functions from the measured particle configurations. Approaching the fluid-solid transition by increasing the strength of the pair-interaction potential, one observes the gradual formation of a crystal-like local order due to triplet correlations, while being still deep inside the fluid phase. Furthermore, we show that in a strongly interacting system the Born-Green equation can be satisfied only with the full triplet correlation function but not with three-body distribution functions obtained from superposing pair correlations (Kirkwood superposition approximation).     

Shock wave chemistry

Abstract

Shock wave chemistry, a new scientific trend, deals with investigations of chemical aspects of the substance state under this new type of effect. Indeed, shock wave effect is not a greater imposition than pressure and temperature actions. Characteristic features of the effect are the tremendous rates of substance loading and subsequent unloading. The effects result in a substance in a strongly non- equilibrium state. The lifetime of the state is governed by the relaxation process of those phenomena which are provoked by shock waves in the substance. For instance, in the case of substance consisting of complex molecules with a large number of internal degrees of freedom, differing strongly in excitation times, all kinetic parts of the shock energy are at first absorbed by the translational degrees of freedom inside the shock wave front. Then, the energy is redistributed to the vibrational degrees of freedom. The non-equilibrium state time is not longer than the excitation time of the most slowly excited vibrational degrees of freedom (10¹⁰-10^?9 s). The same order of magnitude is the relaxation time of liquid substance polarization caused by dipolar molecules mechanically turning under the shock discontinuity zone effect. In polymers the zone turns some separate groups of polymer molecule atoms. In such a case the relaxation period, on the contrary, may last as long as it can. As far as “hot are concerned, their lifetime is determined by thermal relaxation regularities and it depends on their size. The hot spots in solids appear during the shock compression process at the sites of an imperfect substance structure. In liquids the hot spots can orighate when a shock wave front passes through negative density fluctuations. It transforms the fluctuations of very small size and of high probability into some positive temperature regions of large size and extremely low probability at equilibrium state behind the wave front. The hot spots in perfect solids (possibly in liquids too) appear due to the effect of shear stresses in shock front. Pointed and lengthy defects of solid structure occur under the effect. The lengthy defects appear in the shock wave front due to the transition from one-dimensional to volume compression. The transition takes place if the wave intensity is larger than the dynamic elastic limit of the solid under investigation. In brittle materials the transition results in their grinding into fragments and in the relative displacement of the fragments. Some liquid melted layers of substance appear between the fragments in the process of displacement. Their lifetime is also determined by the thermal relaxation regularities and probably is small. Nevertheless, the layers obviously govern the spall strength of brittle solids and promote solid-phase shock reactions. The defects created in solids by the shock effect can exist for a very long time if the solid substance residual temperature is lower than its recrystallization temperature. Therefore, solid substance treatment by shocks of proper intensity can increase their chemical reactivity.     

Translational light scattering in simple liquids

Summary A short review of translational light scattering of simple liquids is reported. The microscopic cross-section is compared with the equivalent expression for neutron scattering experiments (Van Hove, 1954). A survey of the fundamental experiments is reported and the possible application to the study of the dynamics of simple dense systems is analysed. The relevant approximations are critically discussed and the limits of the technique are established. The review mainly deals with classical or almost classical liquids, but also some extensions to quantum systems are considered. paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May 1989.     

Dynamical current correlations in simple liquids

Expressions for the longitudinal and transverse current correlation functions of simple liquids are obtained using Mori's formalism. These involve unknown damping functions. The use of damping functions for a free gas gives results which are in complete disagreement with experiments. The results obtained on the basis of a renormalized free particle memory function in which the collisional damping of collective excitations is incorporated show remarkable improvement over earlier results and are in reasonable agreement with the molecular dynamics data of Rahman. Therefore, the choice of the memory function is as important as the satisfaction of lower order moments.     

Equilibrium theories of simple liquids

In this article, the theory of equilibrium properties of simple classical fluids is reviewed. The various relationships between the pair potential φ(r) and the pair correlation function g(r) are explored, from the usual integral equations and the perturbation theories to the generalized random phase approximation proposed recently. Particular attention is devoted to the extraction of the intermolecular forces from a given experimental data on the structure and thermodynamics of fluids. In particular, the propagation of errors in these calculations arising due to uncertainties in the input data is discussed. Finally, the recent use of BGY integral equation and the vacancy-cell model in the study of solid-liquid transition and melting is discussed.     

Limits of structure stability of simple liquids revealed by study of relative fluctuations

We analyse the inverse reduced fluctuations (inverse ratio of relative volume fluctuation to its value in the hypothetical case where the substance acts as an ideal gas for the same temperature-volume parameters) for simple liquids from experimental acoustic and thermophysical data along a coexistence line for both liquid and vapour phases. It has been determined that this quantity has a universal exponential character within the region close to the melting point. This behaviour satisfies the predictions of the mean-field (grand canonical ensemble) lattice fluid model and relates to the constant average structure of a fluid, i.e. redistribution of the free volume complementary to a number of vapour particles. The interconnection between experiment-based fluctuational parameters and self-diffusion characteristics is discussed. These results may suggest experimental methods for determination of self-diffusion and structural properties of real substances.     

NMR studies on simple liquids in confinement

NMR studies on liquids in various types of confinements are reviewed. The discussion includes results for the size, the morphology, and the filling of pores. Moreover, it deals with the phase behaviors, the local structures, and in particular, the local dynamics of confined liquids. Findings for soft and hard confinements of various sizes are considered. The main focus is on the time scales of and the mechanisms for dynamics of simple liquids in simple confinements. From the methodical point of view, the review is restricted to NMR work in homogeneous magnetic fields, i.e, field-gradient approaches are not included.     

Theory of collective excitations in simple liquids

We present a parameter-free theory of the collective excitations in simple liquids such as liquid metals or rare gases. The theory is based on the mode-coupling theory (MCT), which has been previously applied successfully for explaining the liquid-to glass transition. The only input is the liquid structure factor. We achieve good agreement both for the liquid dispersion (maximum of the longitudinal current spectrum) and width (damping) with experimental findings. The time-dependent memory function predicted by MCT has a two-step exponential decay as previously found in computer simulations. Furthermore MCT predicts a scaling of the liquid dispersion with the effective hard-sphere diameter of the materials. This scaling is obeyed by the available experimental data.     

Shock compression of simple molecules

A simple approach is developed to calculate shock compression of simple molecules. This approach is based upon an accurate analytic representation of the Lennard-Jones fluids in conjunction with the Enskog theory, which is used to calculate the molecular diameter as a function of temperature along the Hugoniot. The model permits rapid, yet reliable calculations. It is applied to N₂, O₂, H₂, D₂, CH₄, CO, and CO₂. The results are tested by the comparison with experimental data and with other calculations. The computed Hugoniots agree reasonably with experimental results for many (but not all) simple molecules and are comparable to those of more complicated models.     

Cavitation-induced shock wave behaviour in different liquids

This paper follows our earlier work where a strong high frequency pressure peak has been observed as a consequence of the formation of shock waves due to the collapse of cavitation bubbles in water, excited by an ultrasonic source at 24 kHz. We study here the effects of liquid physical properties on the shock wave characteristics by replacing water as the medium successively with ethanol, glycerol and finally a 1:1 ethanol–water solution. The pressure frequency spectra obtained in our experiments (from more than 1.5 million cavitation collapsing events) show that the expected prominent shockwave pressure peak was barely detected for ethanol and glycerol, particularly at low input powers, but was consistently observed for the 1:1 ethanol–water solution as well as in water, with a slight shift in peak frequency for the solution. We also report two distinct features of shock waves in raising the frequency peak at MHz (inherent) and contributing to the raising of sub-harmonics (periodic). Empirically constructed acoustic pressure maps revealed significantly higher overall pressure amplitudes for the ethanol–water solution than for other liquids. Furthermore, a qualitative analysis revealed that mist-like patterns are developed in ethanol–water solution leading to higher pressures.     

Equilibrium theory of two-dimensional simple liquids

Using the Wigner-Kirkwood expansion and bare Lennard-Jones (LJ) (12-6) potential, an effectiveLJ potential is derived, which includes the quantum effects through the expressions of the effective diameter∂(T, λ) and well-depth (T, λ). We use theWCA perturbation theory to calculate the free energy and pressure for theLJ and effectiveLJ potentials. Simple analytic expressions are given for the reference system and the first order correction calculated. The results are quite good at high density. The quantum effects on the free energy and pressure are also discussed.     

Shock wave formation in hot nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.     

High-harmonic generation of mid-IR pulses in simple liquids

j as expected. The analysis of the frequency dependence indicates the strong influence of vibrational resonances, which were found here for the first time. Near the fundamental resonance the jth harmonic generation has to be described as a (j+3) wave mixing experiment due to the necessary inclusion of the population of the corresponding vibrational state. Received: 2 April 1997/Revised version: 18 June 1997     

On the memory functions in simple classical liquids

The relation between the two memory function formalisms for correlation functions in classical liquids is discussed. It is found that the kinetic equation formalism of Duderstadt and Akcasu with a simple exponential memory function can account for the double Gaussian form of the memory function in the generalized-hydrodynamics approach. The former therefore gives reasonably good results for the coherent scattering function S(k, ), as is shown for the case of liquid Rb at 315 K in the range 1.25 k 5.5 Å^–.     

Shock wave working of high-TC superconductors

Abstract

The results of investigating the processes of explosive compaction of Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O powdered ceramic high temperature superconducting materials and the shock-induced variation of their properties are presented. The possibility for obtaining metal-ceramic cylinder and spiral-shaped articles is illustrated. The shock wave loading of sintered ceramics is shown to result in degrading its superconducting properties up on R(T), which are subsequently restored by low-temperature annealing. The loss of superconducting properties is demonstrated to correlate with the X-ray lines width. In case of Bi-4334 ceramic, we have observed the improving SP-properties on susceptibility just after shocking it. The effect of the compaction pressure, initial particle size, atmosphere (air, O₂, N₂), initial temperature on material properties is studied.