Solid-liquid Boundary Research Articles

Kapitza resistance: Axiomatic acoustic mismatch theory with loss

We examine the anatomy of the quantitative properties of thermal transport across a solid-liquid boundary as it is described by acoustic mismatch theory. The single parameter, the Kapitza resistance, is a function of four loss parameters and one thermal transport parameter, the thermal diffusivity of the fluid. The loss parameters are to be determined from the dispersion relations for phonons at the peak of the thermal excitation in the material. The temperature dependence of the Kapitza resistance depends on the variation of the phonon excitation in the material with temperature, the familiar temperature-cubed factor, and the variation of the loss factors with temperature and frequency for phonons at the thermal peak, and the variation of the diffusivity with temperature. Since these parameters are undetermined and experimentally rather inaccessible, we conclude that for the present the Kapitza resistance must be viewed as a technological heat transport parameter. Some discussion is given of the part played by second sound in helium II in the surface heat transport process.

Thermodynamics of the System NaF-AlF3: Part V. Solid Solution in Cryolite

Electrical resistivity measurements have been used to demonstrate the existence of solid solutions of AlF3 in the high-temperature form of cryolite above the transition at 565°C. An expression was derived for the resistivity of single-phase mixtures as a function of composition and temperature, and it was then used to deduce the composition at the solid-solid phase boundaries. At the NaF-cryolite eutectic temperature (880°C) the boundary lies at 74.8 mole pct NaF, and at the chiolite peritectic temperature (737°C) the other boundary lies at 74.4 mole pct NaF. The variation of composition with activity of NaF is reasonably consistent with the hypothesis that solid solution leads to formation of AlF41 ions and cation vacancies. On this basis extrapolation is made for the solid-liquid boundaries, and the solid solution region is found to touch the liquidus at 74.0 mole pct NaF. On the above hypothesis the anomalous heat content of cryolite between 888°C and the melting point can be accounted for.

Fluid flow in a hemisphere induced by a distributed source of current

One of the main problems in welding is to produce consistent weld profiles. Simple heat-flow models of the weldpool, which are currently used to predict the shape of the solid-liquid boundary, do not take account of fluid motion which is observed in practice and the effect of such motion could be significant. Electromagnetic j × B forces due to the welding arc have been proposed as a major cause of the motion and we attempt here to develop existing flow models towards more practical welding situations. We consider the steady-state flow of an incompressible viscous conducting fluid in a hemispherical container due to various axisymmetric representations of the distributed current sources which can arise in arc welding. A solution is found for sufficiently small currents that inertial effects may be ignored and no singularities appear in the velocity field. We discover that varying the current distribution can lead to qualitatively different flow patterns, i.e. poloidal flows in opposite directions and breakup into two distinct counter-rotating loops.

An automatic sedimentimeter.

A sedimentation recorder including an optical tracking head controlled to track the liquid-solid separation boundary in a tube containing a sample of liquid-solid mixture is described. The tracking head is controlled by a pulse operated servomotor wh

High-Speed Impact Between Curved Liquid Surface and Rigid Flat Surface

The impact process of a cylindrical, a spherical and a conical water drop upon a rigid plane is studied with numerical methods. Time variation of drop cross-section, pressure and velocity distribution are presented. The maximum pressure remained at the center of the contact area for the cylindrical drop, but expanded outward with the edge of the contact area for the spherical and conical drops. The peak pressure for both cylindrical and conical drop reached approximately the value predicted by a one-dimensionless analysis. The pattern of pressure distribution on the liquid-solid boundary compared favorably with the existing experimental data.

Drug release from methyl acrylate-methyl methacrylate copolymer matrix III: stimultaneous release of noninteracting drug-excipient mixtures.

The simultaneous release of mixtures of noninteracting chemicals incorporated in a methyl acrylate-methyl methacrylate copolymer was studied. Different mixtures of dextrose-methapyrilene hydrochloride and sodium chloride-methapyrilene hydrochlodire in the plastic were compressed into tablets, and single-surface release was obtained in 0.N HCI at 37 degrees. The amounts of both drug and excipients released per unit surface rate constants were analysed in terms of the solubility, diffusion coefficient, concentrations of each chemical, and porosity and tortuosity of the tablets. It was concluded that for each tablet system the individual solid-liquid boundaries of the incorporated chemicals had merged together, and the release could be explained by Higuchi's square foot of time relationship.

Energy redistribution of an ultrasonic beam reflected from a solid plate in a liquid

Nonspecular reflection effects are known to occur when a Gaussian ultrasonic beam is incident at the Rayleigh angle at a liquid-solid boundary [Bertoni and Tamir, Appl. Phys. 2, 157 (1973)]. Nonspecular reflections are also present when an ultrasonic beam is incident on a solid plate of finite thickness, immersed in a liquid, provided the incidence angle corresponds to a Lamb angle. A theoretical analysis is given which shows that the reflected sound energy profiles depend on the plate thickness and the sound frequency. The results of the analysis are compared to existing experimental data.

Rayleigh and Lamb waves at liquid-solid boundaries

The equations governing Rayleigh and Lamb mode propagation are examined for free and for liquid-loaded solids. Examples are given to show under what conditions the free-solid approach yields acceptable solutions for the velocities and under what conditions the more involved liquid-loaded solid formulism must be used.

Hugoniot equation of state of the lanthanides

Shock wave studies of the lanthanide series show the existence of a very high pressure phase transition in all members of the series. The data show that this transformation is of necessity to a more incompressible phase and has been identified with melting. Thermodynamic considerations allow calculation of the solid-liquid phase boundary from these data; the results indicate that all the rare earths melt anomalously at sufficiently high pressures. This can be understood in the context of a “two-fluid” theory, in which the composition of the liquid along the phase boundary changes continuously with pressure due to the degree of pressure-induced electronic transition present in the liquid. Hence, at sufficiently high pressure, the density of the liquid becomes greater than the density of the contiguous solid and dP dT becomes negative.

Phase diagram of the two-dimensional electron liquid

The phase diagram of a two-dimensional electron liquid immersed in a uniform background of charge is analyzed. We present a qualitative argument based on energy considerations alone which yields the shape of the liquid-solid boundary. To determine absolute values of the density and temperature we utilize a microscopoic theory based on the self-consistent harmonic approximation to the phonon spectrum of a solid. This theory is a one-phase instability theory of the long-wavelength transverse mode in the solid phase alone. It yields values of ${r}_{s}\ensuremath{\approx}5$ in the quantum regime and ${\ensuremath{\Gamma}}_{0}=3$ in the classical case.

Liquid phase sintering of TiN - Co and TiN - Wc - Co systems.

1) A mutual solubility of titanium nitride and cobalt was observed in the sintering of the TiN-Co system at 1600°-1800°C.2) In the sintering of the TiN-WC-Co system, in addition to the above fact, tungsten carbide seemed to be dissolved into the other two phases, in the way that W atoms were mainly dissolved into the cobalt phase whereas C atoms were dissolved into the titanium nitride phase.3) The microstructure of TiN-10wt% WC-20wt% Co alloy was analysed by E. P. M. A. and I. M. A.. Grains were titanium nitride phase and a binder phase was cobalt phase.4) The solid skelton forming for grains during sintering for the binary systems was observed and it is indicating the incomplete wetting of tungsten carbide to this binary alloy resulted in an improvement of the wettability of titanium nitride phase to the binder phase.5) The solution-precipitation process in the sintering for the TiN-WC-Co system was controlled by the solution reaction of granular particles at solid-liquid boundaries.6) The maximum mechanical strength obtained for the TiN-WC-Co ternary alloys at any sintering conditions was essentially higher than that for the TiN-Co binary alloys.

Steady-state freezing of a liquid during laminar flow through pipes

The temperature fields of the liquid phase and of the solid phase, and the liquid-solid interphase boundary, are determined under conditions of forced flow through circular pipes.

Absolute solid-liquid and grain boundary energies of bismuth

Absolute solid-liquid and grain boundary energies of bismuth

Dielectric Losses in Solid-Liquid Insulating Systems - Part II

A comparative study has been carried out on the dielectric loss behavior of polycarbonate cable models impregnated with a standard low-viscosity mineral oil and a silicone fluid within the same viscosity range. The importance of space-charge polarization at the interfaces of the well-defined solid-liquid boundaries of such insulating systems was demonstrated; large space-charge losses were found to characterize the mineral oil-polycarbonate combination used. In contrast, a closer match between the dielectric parameters of the polycarbonate plastic and the silicone fluid resulted in a low-loss insulating system, having desirable voltage stress and temperature characteristics. Impregnant contamination was observed to lead to extremely high losses, whose magnitude exceeded appreciably that found with kraft-paper cable models under identical contamination conditions.

Studies of the europium-oxygen-fluorine and samarium-oxygen-fluorine systems

A portion of the ternary system EuEu 2O 3EuF 3 has been investigated by equilibrating EuOEuF 3 and EuOEuF 2 mixtures at 1500°C and examining the products with a polarizing microscope and by X-ray diffraction. The composition at the liquid-solid boundary was not measured directly, but has been estimated. A phase diagram is presented for that part of the system studied. No ternary compounds are formed with europium in an oxidation state lower than +3 in samples cooled from 1500°C. Several compositions of the Eu 2O 3Euf 3 and Sm 2O 3SmF 3 binary systems were examined using differential thermal analysis and X-ray powder diffraction. In these systems, at least one intermediate phase (and probably two or more) in addition to LnOF is stable. These additional phases all lie on the fluoride side of LnOF. At temperatures above 600°C, solid solutions extend from approximately LnO 0.8F 1.4 to LnO 0.6F 1.8.

Thermodynamic problems related to growth of magma

Thermodynamic equilibrium of the liquid surrounded by the solid is discussed to understand the behavior of the magma that is produced by partial melting in the interior of the earth. The equilibrium condition is shown to be different from the case in which both the liquid and the solid phases are under the same hydrostatic pressure because of the volume change of fusion, and the condition is investigated on the basis of the local-equilibrium theory of thermodynamics under nonhydrostatic stresses. It is shown that the liquid in the solid, which itself has been subjected to a stress field before the partial melting, is not able to attain to perfect equilibrium with the surrounding solid, In this case, the development of the solid-liquid boundary is estimated by numerical calculations based on the assumption that the reaction rate is proportional to the difference of the Gibbs free energy between the solid and the liquid across the interface. It is shown that the effective melting point is reduced as a result of nonhydrostatic components. It is also suggested that with the reaction the liquid part is developed to be like thin film, accompanied by local concentration of nonhydrostatic stress. The shear melting hypothesis by D. Griggs can be supplemented in its initial process by the present discussion, and an explanation is proposed concerning the connection between earthquake and volcanic activity.

Dynamic Viscosity of Water at Temperatures below 0°C

The probable behaviour of the viscosity of compressed liquid water in the vicinity of the solid-liquid boundary has been derived by extrapolation of an existing equation.

Properties of the core-mantle boundary and observations ofPcP

Study of PcP phases from eight explosions and three earthquakes shows that the initial direction of motion of PcP reverses at an epicentral distance of about 32° and that PcP amplitudes pass through a minimum at this distance. The effects are caused by properties of the core-mantle boundary. Calculations of reflection coefficients at a plane solid-liquid boundary show that a model with P and S velocities at the bottom of the mantle of 13.64 km/sec and 7.30 km/sec, respectively; with a P velocity at the top of the core of 7.5 km/sec; and with a ratio of core density to mantle density of 1.0 will satisfy the observations of amplitude and change of initial phase of PcP. A range of similar models with velocities at the top of the core down to 7.2 km/sec and density ratios as high as 1.05 will also satisfy the observations. Amplitude observations of PKKP phases also satisfy the model. The new structure is in sharp contrast to the structure of conventional models that have a core velocity of about 8.1 km/sec and a density ratio of about 1.7, but such models will not satisfy the new data. One way to reconcile the new structure near the core-mantle boundary with other relevant information is to assume a model in which the lowermost mantle is inhomogeneous. The inhomogeneity is caused by an increase in iron or other heavy metal content with depth, which increases the mean atomic weight and the density with little change in P velocity. The drop in P velocity across the core-mantle boundary may then be explained by a step increase in mean atomic weight with little change in density. The Adams-Williamson equation will not be valid in the regions in which the changes in density and mean atomic weight are postulated. The incompressibility is not continuous across the core-mantle boundary. PcP travel-time observations do not permit resolution of irregularities at the core-mantle boundary of less than about 5° in slope and about ±5 km in height. The scatter of the observed travel times from a least-squares fit does not indicate slopes of over 6° or elevation differences much over 5 km on the core-mantle boundary.

A study of wetting of diamond and graphite by fused metals and alloys VII. The effect of vanadium, niobium, manganese, molybdenum, and tungsten on wetting of graphite by copper-based alloys

1. The interaction between a graphite or diamond surface and the investigated transition metals is due to formation of strong chemical bonds at the interface. Spreading of these metals or alloys containing them on the graphite or diamond surface is due to a chemical reaction at the solid-liquid boundary (formation of carbides or solution). 2. For the investigated transition metals, the authors established that the interphase activities at the boundary with graphite decrease with decreasing defect in their d-electron zones as we go along the periods of the periodic table.

Corrected Pressure-Temperature Trajectories of Some Solid-Solid and Solid-Liquid Phase Boundaries Below 500°C

Article Corrected Pressure-Temperature Trajectories of Some Solid-Solid and Solid-Liquid Phase Boundaries Below 500°C was published on May 1, 1968 in the journal Zeitschrift für Physikalische Chemie (volume 59, issue 1_4).