Showing papers on "Thermal diffusivity published in 1976"
TL;DR: In this paper, it is shown that the particle flux in probability space due to Brownian motion is the same as that which would be produced by the application of a certain "thermodynamic" force to each particle.
Abstract: The classical theory of Brownian motion applies to suspensions which are so dilute that each particle is effectively alone in infinite fluid. We consider here the modifications to the theory that are needed when rigid spherical particles are close enough to interact hydrodynamically. It is first shown that Brownian motion is a diffusion process of the conventional kind provided that the particle configuration does not change significantly during a viscous relaxation time. The original argument due to Einstein, which invokes an equilibrium situation, is generalized to show that the particle flux in probability space due to Brownian motion is the same as that which would be produced by the application of a certain ‘thermodynamic’ force to each particle. We then use this prescription to deduce the Brownian diffusivities in two -different types of situation. The first concerns a dilute homogeneous suspension which is being deformed, and the relative translational diffusivity of two rigid spherical particles with a given separation is calculated from the properties of the low-Reynolds-number flow due to two spheres moving under equal and opposite forces. The second concerns a suspension in which there is a gradient of concentration of particles. The thermodynamic force on each particle in this case is shown to be equal to the gradient of the chemical potential of the particles, which brings considerations of the multi-particle excluded volume into the problem. Determination of the particle flux due to the action of this force is equivalent to determination of the sedimentation velocity of particles falling through fluid under gravity, for which a theoretical result correct to the first order in volume fraction of the particles is available, The diffusivity of the particles is found to increase slowly as the concentration rises from zero. These results are generalized to the case of a (dilute) inhomogeneous suspension of several different species of spherical particle, and expressions are obtained for the diagonal and off-diagonal elements of the diffusivity matrix. Numerical values of all the relevant hydrodynamic functions are given for the case of spheres of uniform size.
1,007 citations
12 Oct 1976-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, a simple model for rock deformation by pressure solution, assuming grain boundary diffusive mass transfer to be deformation rate controlling, is presented, which leads to a constitutive flow law which is of the same form as that for Coble creep.
Abstract: A simple model for rock deformation by pressure solution, assuming grain boundary diffusive mass transfer to be deformation rate controlling, is presented. The model leads to a constitutive flow law which is of the same form as that for Coble creep. It is argued that the presence of a fluid film in stressed grain boundaries leads to enhanced diffusivity of solute particles in the grain boundary. Some simple experiments are described, which demonstrate rapid diffusion in solutions in pores, much slower diffusion in stressed interfaces and deformation by pressure solution. By using the theoretical model, and by assuming that the pressure of the interfacial solution is equal to the applied normal stress, so that available experimental data on the effect of pressure on mineral solubility could be used, rates of deformation by pressure solution have been calculated. These are compared with rates of deformation by crystal plastic and high temperature diffusive flow processes, by using deformation mechanism maps. Predicted transition conditions between various deformation mechanisms are found to be consistent with those inferred from the study of textures of naturally deformed rocks.
677 citations
TL;DR: In this paper, a new treatment of the solute drag effect on the movement of grain boundaries and phase interfaces was developed, which was based upon the evaluation of the free-energy dissipation.
316 citations
TL;DR: In this paper, it was shown that with zero starting temperature, the model can be evaluated rigorously for two kinds of spikes, i.e., the activation energy for the process and the spike temperature at position r and time t.
Abstract: In the thermal spike model of the interaction of energetic radiation with matter, it is assumed that energy is deposited instantaneously in a very small region, producing a localized increase of temperature which spreads and dissipates according to the laws of classical heat conduction in a continuum. If an activated process (e.g. the migration of atoms, evaporation of atoms from a surface, etc.) is energized by the spike, the number of elementary steps caused by one spike can be expressed as an integral over space and time of the exponential of − Q/T(r, t), where Q is the activation energy for the process and T(r, t), is the spike temperature at position r and time t. In the past quantitative results have been obtained from this model only with the aid of further approximations and the assumption that thermal conductivity and heat capacity are independent of temperature. In this paper it is shown that, with zero starting temperature, the model can be evaluated rigorously for two kinds of spikes,...
280 citations
01 Jan 1976
TL;DR: The 3.5 and 2.5-year subsurface temperature histories at the Apollo 15 and 17 heat-flow sites have been analyzed, and the results yield significantly lower thermal conductivity determinations than the results of previous short-term experiments as mentioned in this paper.
Abstract: The 3.5- and 2-year subsurface temperature histories at the Apollo 15 and 17 heat-flow sites have been analyzed, and the results yield significantly lower thermal conductivity determinations than the results of previous short-term experiments. The thermal conductivity determined by probes at a depth of about 150 cm and 250 cm lies in the range 0.9-1.3 times 10 to the -4th W/cm K. On the basis of measurements of variations of surface thorium abundance and inferred crustal thicknesses, the average global heat flux is estimated to be about 1.8 microwatts/sq cm. This requires a uranium concentration of 46 ppb.
206 citations
TL;DR: In this article, it is shown that there is a change in the intrinsic jump frequency of the diffusing species due to the change in that portion of the motion energy due to magnetic exchange energy.
176 citations
128 citations
115 citations
TL;DR: The upward thermal diffusion cloud chamber was used to measure the supersaturations required to cause an observed rate of homogeneous nucleation of 2 to 3 drops cm−3⋅sec−1.
Abstract: The upward thermal diffusion cloud chamber was used to measure the supersaturations required to cause an observed rate of homogeneous nucleation of 2 to 3 drops cm−3⋅sec−1. Measurements were made on carbon tetrachloride, chloroform, Freon 11, and 1,1,2,2‐tetrachloroethane over as much as a 90 K range of temperatures. The results obtained were compared to the predictions of the classical theory of homogeneous nucleation and to the predictions of the Lothe‐Pound theory. The classical theory was found to be in excellent agreement with all these measurements even though measurements on chloroform and Freon 11 by another technique have been reported to agree with the Lothe–Pound theory.
83 citations
TL;DR: In this paper, an apparatus for the measurement of the thermal conductivity of non-conducting liquids under their saturation vapour pressure is described, which is based upon the transient hot wire principle.
Abstract: The paper describes an apparatus for the measurement of the thermal conductivity of non-conducting liquids under their saturation vapour pressure. The instrument, which is based upon the transient hot wire principle, has been designed so that the measuring element conforms as closely as possible to an infinite line source of heat in an infinite fluid. Under these conditions the thermal conductivity of the liquid can be determined from the slope of a plot of the temperature rise of the heating element against the logarithm of time. The measurement system has been arranged so as to provide as many as 60 points on this plot for any particular thermodynamic state of the fluid under investigation. The reproducibility of the instrument is of the order of 0.03% and the precision of the measurements is estimated as +or-0.1%. Owing to a lack of a suitable theory for the effects of radiative heat transfer, the accuracy of the thermal conductivity values cannot be defined unequivocally, but a reasoned upper bound is +or-0.3%. Preliminary results are presented for n-heptane at three temperatures in the range 20 to 30 degrees C.
TL;DR: In this paper, the effect of microcracking on the thermal diffusivity of polycrystalline Fe2TiO5 subjected to a range of annealing treatments was investigated.
Abstract: The effect of microcracking on the thermal diffusivity of polycrystalline Fe2TiO5 subjected to a range of annealing treatments was investigated. At fine grain size (∼1 μm), the thermal diffusivity exhibited the decrease with increasing temperature common for dielectrics. Extensive microcracking in the larger-grain-sized materials significantly decreased their thermal diffusivity. On heating, the microcracked materials exhibited increased thermal diffusivity at elevated temperatures which can be attributed primarily to microcrack closure and healing; on cooling, they exhibited a pronounced hysteresis, attributable to irreversible crack opening and closing. Thermal cycling closed the hysteresis curves, which suggests permanent changes in microcrack morphology. It appears that microcracking is a promising technique for tailoring ceramic materials to a combination of high thermal shock resistance and good insulating capability.
TL;DR: In this article, a simple method is proposed whereby the film transfer coefficient and coefficient of diffusion in the particles may be determined from finite bath adsorption experiments, which makes it possible to separate pore and surface diffusion.
TL;DR: In this paper, the authors considered the application of regular parameter perturbation technique to obtain approximate solutions of heat-transfer problems with temperature-dependent thermal properties, and compared the accuracy with corresponding numerical solutions, the accuracy was found to be good.
TL;DR: In this article, the thermal diffusivity of a series of copper whiskers-copper spheres dispersed in solder was measured by the flash method at room temperature, and the results showed that the concept of effective thermal diffusion is valid at least for particle-to-matrix diffusivities ratios between 1 and 3.5 and volume specific heat ratios between 0.02 to 0.52 in randomly dispersed composites containing up to 30 volume% of dispersed particles.
Abstract: The thermal diffusivity of a series of copper whiskers‐copper spheres dispersed in solder was measured by the flash method at room temperature. These diffusivity values are compared with the calculated thermal diffusivity values using effective thermal conductivity values computed with Maxwell’s dispersion equation. The results show that the concept of an effective thermal diffusivity is valid at least for particle‐to‐matrix diffusivity ratios between 1 and 3.5 and volume specific heat ratios between 0.02 to 0.52 in randomly dispersed composites containing up to 30 volume% of dispersed particles. These results were not influenced by changing the particle size or shape over fairly wide ranges (at room temperature). The conditions of heterogeneity used were far outside the limits implied by a previous mathematical derivation.
TL;DR: In this article, the transient and steady state temperature rise T of laser-irradiated metals indicate that values of the intensity (irradiance) If that cause failure change drastically under different experimental conditions, such as the degree of plasma ignition on the surface and the relative magnitudes of the laser-beam diameter, sample thickness l, lateral dimension, and thermal diffusion distance.
Abstract: Calculations of the transient and steady‐state temperature rise T of laser‐irradiated metals indicate that values of the intensity (irradiance) If that cause failure change drastically under different experimental conditions, such as the degree of plasma ignition on the surface and the relative magnitudes of the laser‐beam diameter, sample thickness l, lateral dimension, and thermal diffusion distance. The dependence of If on material parameters such as thermal conductivity and heat capacity is also quite different, depending on the experimental conditions. The results suggest that the highest of the recently measured copper‐damage thresholds of 125–750 J/cm2 for 0.6‐μsec pulses at 10.6 μm are likely to be at or at least quite near the intrinsic limit set by the simple process of melting that results from the intrinsic absorption. The theoretical intensity at which the cavity mirrors of recently developed xenon uv lasers fail is in good agreement with the experimental value. The theoretical value of T of ...
Alza1
TL;DR: By assuming that sorption occurs by both ordinary dissolution and binding of penetrant to immobile sites in the membrane, the experimental sorption isotherm can be predicted, and the disparity between steady state and time lag diffusivities can be reconciled.
Abstract: The sorption and rate of permeation of scopolamine base in human skin have been measured as a function of drug concentration in aqueous solution contacting the stratum corneum surface of the skin. The sorption isotherm is nonlinear, and the apparent penetrant diffusivity computed from steady state permeation data is greater than that estimated from unsteady state (time lag) measurements.
By assuming that sorption occurs by both ordinary dissolution and binding of penetrant to immobile sites in the membrane, the experimental sorption isotherm can be predicted, and the disparity between steady state and time lag diffusivities can be reconciled.
TL;DR: In this article, the kinetics of sorption of four representative hydrocarbons in 13X zeolite crystals have been investigated at temperatures within the range 409 to 513°K and pressures 0.1 to 100 torr.
Abstract: The kinetics of sorption of four representative hydrocarbons in 13X zeolite crystals have been investigated at temperatures within the range 409 to 513°K and pressures 0.1 to 100 torr. Extensive diffusivity data are presented showing the dependence on sorbate concentration and temperature. The form of the concentration dependence of the diffusivity for these systems is very similar to that of the small monatomic and diatomic molecules in 5A zeolite. This similarity is understandable, since the key factor which determines the diffusion behavior is the relative size of diffusing molecule and sieve window. For these hydrocarbons in the 13X sieve, as for the monatomic and diatomic gases in 5A, the critical diameters of the diffusing molecules are all appreciably smaller than the free diameter of the windows.
TL;DR: In this paper, the effect of plastic deformation on the amount of tritium absorbed, the surface concentration, and apparent diffusivity was determined by comparing elastically and plastically deformed sections of nickel tensile tubes.
Abstract: The effect of plastic deformation on the amount of tritium absorbed, the surface concentration, and the apparent diffusivity was determined by comparing elastically and plastically deformed sections of nickel tensile tubes that were filled with tritium during deformation. Plastic deformation increased the amount of tritium absorbed by the metal and adsorbed on the surface, but decreased the apparent diffusivity. These data for nickel can be explained by the trapping theory developed primarily to explain anomalous hydrogen diffusivity and solubility in iron, where the dislocations created during deformation are postulated to trap the tritium, thereby producing higher values for interior and surface tritium concentrations and lower values for tritium diffusivity.
TL;DR: In this paper, the influence of a magnetic field on the transport properties of binary mixtures of a polyatomic and a noble gas is studied theoretically using an inverse operator technique, first thermal conductivity and viscosity are treated, then diffusion and thermal diffusion are discussed in detail, with special emphasis on the composition dependence.
Abstract: The influence of a magnetic field on the transport properties of binary mixtures of a polyatomic and a noble gas is studied theoretically. Using an inverse operator technique, first thermal conductivity and viscosity are treated. Then diffusion and thermal diffusion are discussed in detail, with special emphasis on the composition dependence. A relation connecting the magnitudes of the field effects on thermal conductivity, diffusion, and thermal diffusion is derived. This relation is used to estimate the field effect on diffusion.
TL;DR: The chemical diffusivity coefficient of oxygen has been measured from 1180 to 1520 K in oxygen deficient rutile TiO 2−x, in following the electrical conductivity change after a step in the chemical potential of oxygen.
Journal Article•
TL;DR: In this paper, a simple model for rock deformation by pressure solution, assuming grain boundary diffusive mass transfer to be deformation rate controlling, is presented, which leads to a constitutive flow law which is of the same form as that for Coble creep.
Abstract: A simple model for rock deformation by pressure solution, assuming grain boundary diffusive mass transfer to be deformation rate controlling, is presented. The model leads to a constitutive flow law which is of the same form as that for Coble creep. It is argued that the presence of a fluid film in stressed grain boundaries leads to enhanced diffusivity of solute particles in the grain boundary. Some simple experiments are described, which demonstrate rapid diffusion in solutions in pores, much slower diffusion in stressed interfaces and deformation by pressure solution. By using the theoretical model, and by assuming that the pressure of the interfacial solution is equal to the applied normal stress, so that available experimental data on the effect of pressure on mineral solubility could be used, rates of deformation by pressure solution have been calculated. These are compared with rates of deformation by crystal plastic and high temperature diffusive flow processes, by using deformation mechanism maps. Predicted transition conditions between various deformation mechanisms are found to be consistent with those inferred from the study of textures of naturally deformed rocks.
IBM1
TL;DR: In this paper, the dilatational dependence of the Grueneisen parameter from data on the pressure dependence of thermal conductivity (or, equivalently, thermal diffusivity) is critically examined and applied to thermal diffusion data for sodium chloride and quartz.
Abstract: The method proposed by Mooney and Steg (1969) for obtaining the dilatational dependence of the Grueneisen parameter from data on the pressure dependence of the thermal conductivity (or, equivalently, thermal diffusivity) is critically examined and applied to thermal diffusivity data for sodium chloride and quartz. The values obtained are ..gamma../sub 0/'(identical with (d..gamma../d..delta..)parallel bar/sub ..delta.. = 0/) = 3.0 for sodium chloride and ..gamma../sub 0/' = 2.0 for quartz. Corresponding values of the parameter q(identical with ..gamma../sub 0/'/..gamma../sub 0/) are 1.9 and 2.8, in reasonable agreement with values obtained by other methods. It is suggested that this method be further investigated as a means of obtaining ..gamma../sub 0/' and q from thermal data. A model for the lattice thermal conductivity of the mantle to the core boundary is presented. The model suggests that increases in conductivity with pressure due to lattice conduction processes in the mantle are less than 2.0 percent/kbar or 0.7 percent/km. Under conditions of normal geothermal gradient in the crust and upper mantle the increase in lattice conductivity due to the pressure effect will be substantially less than the decrease due to the temperature effect. A minimum value of lattice conductivity is attained in the region ofmore » the olivine-spinel phase change, 400 km. The lattice conductivity may increase by a factor of 3 at the depth of the spinel-postspinel phase change owing to the high conductivity of the dense oxide phases. The lattice contribution to the thermal conductivity at the mantle-core boundary is approximately 0.01 cal/cm s/sup 0/K.« less
TL;DR: In this paper, simple perturbation methods are employed to analyze the horizontal absorption of moisture in unsaturated soils and the solution emerges as an explicitly determined power series in the Boltzmann variable.
Abstract: Simple perturbation methods are employed to analyze the horizontal absorption of moisture in unsaturated soils. The special case treated assumes the diffusivity to be an exponential function of the concentration and the concentration at the boundaries to be constant. The solution emerges as an explicitly determined power series in the Boltzmann variable.
The resulting profiles are compared with some others found in the existing literature. A discussion about the relevance and advantages of this type of analysis forms the concluding part of the paper.
TL;DR: In this article, double beam interferometry was used to measure the transient refractive index fields in stagnant CuSO4 solutions during galvanostatic deposition of copper, and the time-dependent concentration profiles were derived from the interferograms by correcting for optical aberrations caused by beam deflection and reflection.
TL;DR: In this article, the effects of nonuniform surface heating in the flash method of thermal diffusivity measurement are investigated theoretically and experimentally, and an expression for the temperature response with non-uniformity is presented.
Abstract: The effects of nonuniform surface heating in the flash method of thermal‐diffusivity measurement are investigated theoretically and experimentally. An expression for the temperature response with nonuniform surface heating is presented. Evaluation of this expression shows that 30% nonuniformity results in diffusivity errors of 0.1–7.4%, depending on the method of data reduction used. It is shown experimentally that corrections for nonuniform heating can be made with this expression given quantitative information about the nonuniformity, in this case reducing the error from 26% to zero.
TL;DR: In this article, it was shown that the proper formula may differ numerically by an order of magnitude from the empirical relation between an apparent diffusivity and the scale of diffusion can be used in numerical modeling for oceanic dispersion.
TL;DR: In this paper, two centrifugal techniques are proposed for determining the hydraulic conductivity of cores of natural soil, and experimental results are presented for one technique in which the change in weight of one end of the sample, previously centrifuged, is measured with a balance.
Abstract: Two centrifugal techniques are proposed for determining the hydraulic conductivity of cores of natural soil. Experimental results are presented for one technique in which the change in weight of one end of the sample, previously centrifuged, is measured with a balance. The mathematical equations describing this redistribution process were developed and fitted to the data to ascertain the soil water diffusivity D. The value of the hydraulic conductivity K was obtained from K = bD, where b is also calculated. Calculated values of K agreed with previously published values. The second technique for which a theory is presented but no experimental values are provided depends upon the measurement of the volumetric outflow of water from a soil core when the speed of centrifugation is suddenly increased.
TL;DR: In this paper, the magnitude of the surface thermal conductivity effect in dropwise condensation heat transfer is determined experimentally in a low conductivity surface (stainless steel) using deposited thin-film resistance thermometers.