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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1999

Dynamics of Single Chains of Suspended Ferrofluid Particles

We present an experimental study of the dynamics of isolated chains made of super-paramagnetic particles under the influence of a magnetic field. The motivation of this work is to understand if the chain fluctuations exist and, if it does, how does the fluctuation affect chain aggregation. We find that single chains strongly fluctuate and that the characteristic frequency of their fluctuations is inversely proportional to the magnetic field strength. The higher the field the lower the characteristic frequency of the chain fluctuations. In the high magnetic field limit, chains behave like rigid rods without any internal motions. In this work, we used ferrofluid particles suspended in water. These particles do not have any intrinsic magnetization. Once a magnetic field is applied, a dipole moment is induced in each particle, proportional to the magnetic field. A dipolar magnetic interaction then occurs between particles. If dipole-dipole magnetic energy is higher than the thermal energy, the result is a structure change inside the dipolar fluid. The ratio of these two energies is expressed by a coupling constant lambda as: lambda = (pi(a(exp 3))(chi(exp 2))(mu(sub 0))(H(sub 0))(exp 2))/18kT Where a is the particle radius, mu(sub 0) is the vacuum magnetic permeability, H(sub 0) the applied magnetic field, k the Boltzmann constant and T the absolute temperature. If lambda > 1, magnetic particles form chains along the field direction. The lateral coalescence of several chains may form bigger aggregates especially if the particle volume fraction is high. While many studies and applications deal with the rheological properties and the structural changes of these dipolar fluids, this work focuses on the understanding of the chain dynamics. In order to probe the chain dynamics, we used dynamic light scattering (DLS) in self-beating mode as our experimental technique. The experimental geometry is such that the scattering plane is perpendicular to the magnetic field. Therefore, only motions in this plane are probed. A very dilute sample of a ferrofluid emulsion with a particle volume fraction of 10(exp -5) is used in this experiment. We chose such a low volume fraction to avoid multiple light scattering as well as lateral chain-chain aggregation. DLS measures the dynamic structure factor S(q,t) of the sample (q is the scattering wave vector, t is the time). In the absence of the magnetic field, identical particles of ferrofluid droplets are randomly distributed and S(q,t) reduces to exp(-q(exp 2)2D(sub 0)t). D(sub 0)=(kT/(6(pi)(eta)(a)) is the diffusion coefficient of Brownian particles (where Xi = (6(pi)(eta)(a)) is the Stokes frictional coefficient of a spherical particle in a fluid of viscosity eta). If interactions or polydispersity can not be ignored, an effective diffusion coefficient is introduced. Formally, D(sub eff) is defined as: D(sub eff) = - q(exp -2) partial derivative of (ln(S(q,t)) with respect to time, as t goes to 0. D(sub eff) reduces to D(sub 0) if no interactions and only a few particles size are present. Therefore, we can use DLS to measure particle size. The particle radius was found to be a=0.23 mu m with 7% of polydispersity. In this case, if we vary the scattering angle theta (and so q) we do not have any change in the measured diffusion coefficient: it is q-independent. When a magnetic field is applied, particles aggregate into chains if lambda > 1. We first studied the kinetics of the chain formation when lambda = 406. At a fixed scattering angle, we measured diffusion coefficient D(sub eff) as a function of time. Experimentally, we find that D(sub eff) decreases monotonously with time. Physically, this means that chains are becoming longer and longer. Since we are only sensitive to motions in the scattering plane and since chains have their main axis perpendicular to this plane, the measured diffusion coefficient is the trans-verse diffusion coefficient. We can relate D(sub eff) to the mean number of particles per chain N(t) at a given time and to the diffusion coefficient of an isolated particle D(sub 0) as D(sub eff)=f(N(t))D(sub 0). Since f(N) is known from other recent work, N can be expressed as a function of the time. We found a square root dependency: N(t) proportional to the square root of t. As expected for very low volume fraction, this behavior is characteristic of a diffusion-limited aggregation as suggested by several authors and by our previous work. In this study, we focus on the dependence of the effective diffusion coefficient on the scattering angle and the magnetic field strength. After the magnetic field is applied (lambda = 406) for a long time, typically 6 hours, kinetics of chain formation becomes very slow. Chain size does not vary much over the next hour period. Thus, we can perform different interesting experiments. First, at a fixed magnetic field, we measure the effective diffusion coefficient as a function of the scattering angle (from 5 to 130 deg). Our results show that the measured diffusion coefficient increases linearly with the scattering angle: D(sub eff) proportional to q. If we do the same experiment for different lambda values, D(sub eff) depends on lambda as D(sub eff) proportional to lambda(exp -1/2). We also find for different lambda values that the same asymptotic D(sub eff) value is obtained when q approaches zero. The angle dependency of D(sub eff) suggests that an additional motion exists besides chain drifting. Chain size is constant during experiment, which was verified by measuring the same diffusion coefficient at the beginning and at the end of the angle switching. If chains are rigid, D(sub eff) is independent of q. Therefore, we found that D(sub eff) not only measures the motion of the entire chain but also its internal fluctuations. These internal motions are the fluctuations of the particles in the chain. To understand the q dependency of D(sub eff), let us look at the probing length used. In our study, the characteristic length scale probed is l=2pi/q which is in the range of 0.9<l/a<20. When l is much larger than the particle radius (l/a going to infinity) we are mainly sensitive to the center of mass diffusion of the chain. D(sub eff) is then the diffusion of the entire chain and depends only on N but not on q and lambda. The value D(sub eff) allows us to obtain the number of particles per chain N. In the opposite limit (i.e. l/a < 1), we are sensitive to motions on the size of individual particles. The main contributions to the measured diffusion coefficient come from internal motions of the chains (i.e. particles' fluctuations inside the chain). We investigated also the effect of the chain size on D(sub eff). For the same value of the magnetic interaction lambda and different chain sizes, we found that the slope of D(sub eff) versus q decreases when N increases as a power law D(sub eff) proportional to N(exp -0.7). This is an important behavior because this means that the longer the chain the slower its internal fluctuations besides the whole chain motion.

Cutillas, S.↗
NASA NTRS2003

Evolution of Local Microstructures: Spatial and Temporal Correlation in Clusters Undergoing 2-Dimensional Diffusion

Diffusion-limited, capillarity-driven, coarsening of precipitates is an important and intensively studied phenomenon. Coarsening can occur among several microstructural constituents ranging from the primary phases to widely dispersed precipitates. Moreover, coarsening of three-dimensional (3-D) phase domains, occurring via mass transport through a two-dimensional (2-D) diffusion field (called mixed-dimensional phase coarsening) is a cooperative phenomenon that is of practical importance, especially in thin film technologies and catalysis. A primary objective of our current work is to focus on the details of evolving microstructures through a study of 'island' formation in heteroepitaxial film/substrate systems. Whereas this work has been designed for space-based coarsening studies, which require long-duration quality microgravity to observe 3-D Ostwald ripening, a significant amount of work has been performed during ground-based studies to observe diffusional coarsening in a liquid-liquid two-phase system. We have performed the experiment at an isopycnic point to maximize exclusion of gravity-based system disturbance. This has allowed observations of 3-D droplets, immobilized by container wall contact, undergoing coarsening by 2-D diffusion for the required long times (approximately 4 months) using a holographic imaging technique. Although such systems may not be as reliant on long-duration microgravity processing as 3-D systems are, they are of direct relevance to so-called mixed-dimensional coarsening and to the study of heterostructures grown by thin-film technique

Curreri, Peter A.↗
NASA NTRS2003

Evolution of Local Microstructures: Spatial Instabilities in Coarsening Clusters

Diffusion-limited capillarity-driven coarsening of precipitates is an important and intensively studied phenomenon. The classic coarsening theory developed by Lifshitz and Syozov and Wagner (LSW theory) is limited to infinitesimally small volume fractions, V(sub nu), therefore neglects all direct interparticle interactions. This work uses modeling and holographic imaging to compare coarsening rates in "high" volume fraction versus low volume fraction microstructures by observing mixed-dimensional droplets (spherical caps on a surface coarsening by two-dimensional diffusion) during ground-based investigations. The method involves filling a cell with selected homogeneous parent phase, and cooling below the consolute temperature to the isopycnic temperature in the two-phase region of a monotectic system. A microgravity holographic experiment is required for three-dimensional observations to minimize sedimentation during long-term coarsening. Determination of sizes and positions of the many droplets in the holographic images requires automation. We have developed software for automated data analysis, and demonstrated good agreement between regenerated maps and scaled photographs of the original holograms for mixed dimensional coarsening. The results of these experiments were presented in a formal microgravity Science Concept Review (SCR) on December 18, 2000.

Source record↗
NASA NTRS1971

Mechanism of the oxidation of titanium disilicide.

Study of the oxidation of TiSi2 at temperatures of 300 to 1300 C. Wafers prepared using the techniques of powder metallurgy had densities of 95 to 98% of the theoretical value. On oxidation at temperatures up to 600 C, the polished wafers formed a protective, titania-silica glass. The rate data indicate a complex surface and diffusion-limited mechanism. Above 600 deg C, the oxide consisted of an amorphous SiO2 film with crystalline islands of TiO2 (rutile). From 1000 to 1300 C, parabolic kinetics with an activation energy of 21.3 kcal/mole were observed. These data are consistent with a model in which the rate-determining step is the diffusion of oxygen through the silica film with the simultaneous diffusion of titanium from the substrate to the islands of rutile growing on top of the amorphous silica.

Schwettmann, F. N.↗
NASA NTRS1996

Non-linear resonance of fluids in a crystal growth cavity

In the microgravity environment, the effect of gravity on fluid motion is much reduced. Hence, secondary effects such as vibrations, jitters, surface tension, capillary effects, and electromagnetic forces become the dominant mechanism of fluid convection. Numerous studies have been conducted to investigate fluid behavior in microgravity with the ultimate goal of developing processes with minimal influence from convection. Industrial applications such as crystal growth from solidification of melt and protein growth for pharmatheutical application are just a few examples of the vast potential benefit that can be reaped from material processing in space. However, a space laboratory is not immune from all undesirable disturbances and it is imperative that such disturbances be well understood, quantifiable, and controlled. Non-uniform and transient accelerations such as vibrations, jitters, and impulsive accelerations exist as a result of crew activities, space vehicle maneuvering, and the operations of on-board equipment. Measurements conducted on-board a U.S. Spacelab showed the existence of vibrations in the frequency range of 1 to 100 Hz with a dominant mode of 17 Hz and harmonics of 54 Hz. The observed vibration is not limited to any coordinate plane but exists in all directions. Similar situation exists on-board the Russian MIR space station. Due to the large structure of its design, the future International Space Station will have its own characteristic vibration spectrum. It is well known that vibration can exert substantial influence on heat and mass transfer processes, thus hindering any attempts to achieve a diffusion-limited process. Experiments on vibration convection for a liquid-filled enclosure under one-g environment showed the existence of different flow regimes as vibration frequency and intensity changes. Results showed the existence of a resonant frequency, near which the enhancement is the strongest, and the existence of a high frequency asymptote. Numerical simulations of vibration convection have been conducted by Yurkov, Fu and Shieh, and by Wang. These analyses considered a two-dimensional air-filled cell under weightlessness condition and showed results similar to those of the experiments. It is not yet known whether resonance convection can be triggered by jitter alone or whether it requires the interaction of jitter with other convective forces in low gravity. An order of magnitude analysis, however, can be used to show the dependence of the resonance frequency on the fluid Prandtl number. Even though the onset of resonance convection may depend on other factors, results indicates that fluids with low Prandtl numbers are more susceptible to resonance than those with high Prandtl numbers. The current study is aimed at gaining additional insights to this problem using germanium as working fluid. Germanium was chosen for this analysis because of its common usage in solidification process and its relatively low Prandtl number (Pr = 0.02).

Wang, Francis C.↗
NASA NTRS1976

Theoretical study of reactive and nonreactive turbulent coaxial jets

The hydrodynamic properties and the reaction kinetics of axisymmetric coaxial turbulent jets having steady mean quantities are investigated. From the analysis, limited to free turbulent boundary layer mixing of such jets, it is found that the two-equation model of turbulence is adequate for most nonreactive flows. For the reactive flows, where an allowance must be made for second order correlations of concentration fluctuations in the finite rate chemistry for initially inhomogeneous mixture, an equation similar to the concentration fluctuation equation of a related model is suggested. For diffusion limited reactions, the eddy breakup model based on concentration fluctuations is found satisfactory and simple to use. The theoretical results obtained from these various models are compared with some of the available experimental data.

Gupta, R. N.↗
NASA NTRS1999

Control of Meridional Flow in Circular Cylinders by a Travelling Axial Magnetic Field

Convective flow in a Bridgman or float zone configuration significantly affects the interface shape and segregation phenomena. While the primary causative factor for this flow is buoyancy induced convection in an enclosed Bridgman melt, the presence of a free surface gives rise to surface tension driven flows in the floating zone processing of melts. It is of interest to curtail these flows in order to realize near quiescent growth conditions that have shown to result in crystals with good longitudinal and radial homogeneity and thereby of better overall quality. While buoyancy effects can be reduced by careful processing in a low gravity (space) environment, the reduction of Marangoni flows due to surface tension variations is not that straight forward. Attempts have been made with some limited success with the use of external fields to affect the melt thermo-fluid behavior. The use of a static magnetic field that reduces convective contamination through the effects of a non-intrusively induced, dissipative Lorentz force in an electrically conducting melt is one such approach. Experiments have shown that axial fields of the order of 5 Tesla can significantly eliminate convection and yield close to diffusion limited crystal growth conditions. The generation and use of such high magnetic fields require substantial hardware and incur significant costs for its operation. Lately, the use of rotating magnetic fields has been tested in semiconductor crystal growth. The method is fairly well known and commonly used in metal processing but its adaptation to crystal growth of semiconductors is fairly recent. The elegance of the technique rests in its low power requirement (typically 10-20 milli-Tesla at 50-400 Hz) and its efficacy in curtailing deleterious temperature fluctuations in the melt. A rotating magnetic field imposes a rotational force and thereby induces a circulation within the melt that tends to dominate other sporadic convective effects. Thus a known low level of convective flow is introduced into the system. A new novel variation of the Lorentz force mechanism is proposed and investigated in this study. Since one of the desired process conditions in melt crystal growth is the minimization of convective effects, this investigation examines the use of an external field of magnetic origin to counteract existing convective flow within the melt. This is accomplished by utilizing a running or traveling axial magnetic wave in the system. The concept is similar to the use of vibrational means in order to induce streaming flows that oppose buoyant or surface tension driven convection in the system. The rotation direction as well as the magnitude (strength) of this circulation can be easily controlled by external inputs thus affording a direct means of controlling the developing shape of the crystallizing front (interface). The theoretical model of this technique is fully developed and presented in this paper. Results from the solution of the developed governing equations and boundary conditions are also presented. An experimental demonstration of the concept is presented through the suppression of natural convective flow in a mercury column. Implications to crystal growth systems will be fully explored in the final manuscript.

Mazuruk, K.↗
NASA NTRS1986

Smoothing and the second law

The technique of obtaining second order, oscillation free, total variation diminishing (TVD), scalar difference schemes by adding a limited diffusion flux (smoothing) to a second order centered scheme is explored. It is shown that such schemes do not always converge to the correct physical answer. The approach presented here is to construct schemes that numerically satisfy the second law of thermodynamics on a cell by cell basis. Such schemes can only converge to the correct physical solution and in some cases can be shown to be TVD. An explicit scheme with this property and second order spatial accuracy was found to have an extremely restrictive time step limitation (Delta t less than Delta x squared). Switching to an implicit scheme removed the time step limitation.

Merriam, Marshal L.↗
NASA NTRS1987

Smoothing and the second law

The technique of obtaining second-order oscillation-free total -variation-diminishing (TVD), scalar difference schemes by adding a limited diffusive flux ('smoothing') to a second-order centered scheme is explored. It is shown that such schemes do not always converge to the correct physical answer. The approach presented here is to construct schemes that numerically satisfy the second law of thermodynamics on a cell-by-cell basis. Such schemes can only converge to the correct physical solution and in some cases can be shown to be TVD. An explicit scheme with this property and second-order spatial accuracy was found to have extremely restrictive time-step limitation. Switching to an implicit scheme removed the time-step limitation.

Merriam, Marshal L.↗
NASA NTRS2002

Vapor transport growth of organic solids in microgravity and unit gravity: some comparisons and results to date

Thin films of an organic nonlinear optical (NLO) material, N, N-dimethyl-p-(2,2-dicyanovinyl) aniline (DCVA), have been grown in space and on the ground by physical vapor transport in an effusive ampoule arrangement. The thin film growth technique developed on the ground is a direct result of information gleaned from experiments in microgravity. This paper covers the results of our experimental investigations for establishing "ideal" terrestrial conditions for deposition of a DCVA film. The active control during the deposition process was exercised by three deposition variables: the material source temperature, the background pressure external to the growth ampoule and the substrate temperature. Successful growth occurred when the difference in temperature between the source material and the copper substrate was 14 degrees C and the background nitrogen pressure was such that the transport was either diffusive or convective. A qualitative diffusion limited boundary was estimated to occur at a pressure of approximately 20 torr. We have probed the DCVA thin films with visible-near infrared reflection absorption spectroscopy, polarized Fourier transform infrared spectrometry, differential interference contrast optical microscopy, and stylus profilometry.

short duration↗
NASA NTRS2006

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering

The flux level of outer-zone relativistic electrons (above 1 MeV) is extremely variable during geomagnetic storms, and controlled by a competition between acceleration and loss. Precipitation of these electrons due to resonant pitch-angle scattering by electromagnetic ion cyclotron (EMIC) waves is considered one of the major loss mechanisms. This mechanism was suggested in early theoretical studies more than three decades ago. However, direct experimental evidence of the wave role in relativistic electrons precipitation is difficult to obtain because of lack of concurrent measurements of precipitating electrons at low altitudes and the waves in a magnetically conjugate equatorial region. Recently, the data from balloon-borne X-ray instruments provided indirect but strong evidence on an efficiency of the EMIC wave induced loss for the outer-zone relativistic electrons. These observations stimulated theoretical studies that, particularly, demonstrated that EMIC wave induced pitch-angle diffusion of MeV electrons can operate in the strong diffusion limit and this mechanism can compete with relativistic electron depletion caused by the Dst effect during the initial and main phases of storm. Although an effectiveness of relativistic electron scattering by EMIC waves depends strongly on the wave spectral properties, the most favorable assumptions regarding wave characteristics has been made in all previous theoretical studies. Particularly, only quasi field-aligned EMIC waves have been considered as a driver for relativistic electron loss. At the same time, there is growing experimental and theoretical evidence that these waves can be highly oblique; EMIC wave energy can occupy not only the region of generation, i.e. the region of small wave normal angles, but also the entire wave normal angle region, and even only the region near 90 degrees. The latter can dramatically change he effectiveness of relativistic electron scattering by EMIC waves. In the present study, we calculate the pitch-angle diffusion coefficients using the typical wave normal distributions obtained from our self-consistent ring current-EMIC wave model, and try to quantify the effect of EMIC wave normal angle characteristics on relativistic electron scattering.

Gamayunov, K. V.↗
NASA NTRS2017

Limits to Creation of Oxygen-Rich Atmospheres on Planets in the Outer Reaches of the Conventional Habitable Zone

Abundant free oxygen appears to be a requirement for macroflora and macrofauna. To the best of our knowledge, a general discussion of which habitable planets are conducive to oxygen has not taken place. Theories for the rise of oxygen fall into 4 categories: (i) It is governed by an intrinsic rate of biological innovation, independent of environmental factors. (ii) It is caused by mantle evolution, probably consequent to secular cooling. (iii) It is caused by hydrogen escape, which irreversibly oxidizes the Earth. (iv) It is Gaia's response to the brightening Sun, its rise prevented until reduced greenhouse gases were no longer needed to maintain a clement climate. All but the first of these make implicit astronomical predictions that can be quantified and made explicit. Here we address the third hypothesis. In this hypothesis hydrogen escape acts like an hourglass that continues until all relevant reduced mineral buffers have been oxidized (titrated, as it were) and the surface made safe for O2. The hypothesis predicts that abundant free O2 will be absent from habitable planets that have not experienced significant hydrogen escape. Where hydrogen escape is modest or insignificant, the atmosphere can be approximated as hydrostatic, which makes assessing radiative cooling by embedded molecules, atoms, and ions such as CO2 and H3+ straightforward. In particular, H2 is efficient at exciting non-LTE CO2 15 micron emission, which makes radiative cooling very effective when H2 is abundant. We can therefore map out the region of phase space in which habitable planets do not lose hydrogen, and therefore do not develop O2 atmospheres. A related matter is the power of radiative cooling by embedded molecules to enforce the diffusion limit to hydrogen escape. This matter in particular is relevant to addressing the empirical observation that rocky planets with thin or negligible atmospheres are rarely or never bigger than approx.1.6 Earth radii.

Zahnle, Kevin↗
NASA NTRS1967

Boundary-layer combustion in propulsion.

Propulsion-oriented subsonic boundary layer combustion research, discussing turbulent and diffusion-limited conditions, radiant heat transfer, chemical kinetics and transient phenomena

RADIATIVE HEAT TRANSFER↗
NASA NTRS1968

Silicon oxide films grown in microwave discharge

Silicon oxide films thicker than 1000 angstrom are produced in the dense plasma of a microwave discharge. The oxide growth is characterized by a rate limiting diffusion process modified by sputtering effects produced by the discharge. Silicon is rapidly oxidized at temperatures estimated to be 500 degrees C or lower.

Kraitchman, J.↗
NASA NTRS1968

Survey of the Relationship Between Theory and Experiment for Convective Heat Transfer From Rocket Combustion Gases

The problem of predicting the distribution of heat flux in a rocket engine is complicated by a flow field and thermodynamics so perturbed by as yet indescribable combustion effects that it continues to be necessary to utilize a simplified theoretical model against which to compare experimental results in order to gain insight. The most successful model applied to this problem is that of a compressible, turbulent, accelerating boundary layer flow with an arbitrary point of origin, and chemical reaction restricted to equilibrium recombination or diffusion-limited recombination on a catalytic wall. Analysis of this model was not possible without making several assumptions about the nature of the skin friction coefficient relationship and Reynold's analogy in an accelerating boundary layer flow. The paper summarizes the analysis of this model (together with detailed treatment of the special problems of variable properties, chemical reaction, and sources of transport properties), and describes several closed-form equations that have also been developed and applied to the problem. Described are results of several experiments with hot air flow made for the purpose of checking the validity of the assumptions in the boundary layer analysis. Most significant, however, are presentations of sample distributions of local heat flux measured in rocket engines operating with a wide range of conditions, propellants, injectors and sizes. When compared with predictions, these data show the significant range of deviation in heat flux that results from the combustion effects and which precludes a generally accurate prediction theory or correlation equation until the combustion process itself is correlated.

D R Bartz↗
NASA NTRS1970

Relativistic electron precipitation during magnetic storm main phase

Relativistic electrons can have cyclotron resonances with electromagnetic cyclotron waves. The resonant energy is generally well above 1 MeV throughout the magnetosphere, but it can fall to 1 MeV just within the plasmapause. This also corresponds to the region where ring current (10 to 50 keV) protons are expected to be strongly unstable. The resulting ion cyclotron wave amplitudes necessary to precipitate ring current protons leads to electron lifetimes near the strong diffusion limit ( 100 sec). Thus, 1 MeV electrons whose drift orbits intersect the stormtime plasmapause should rapidly be precipitated in the region 3 L 5 during the initial phase of a magnetic storm.

Thorne, R. M.↗
NASA NTRS1972

Thin film fuel cell electrodes.

Earlier work shows that fuel cell electrodes prepared by sputtering thin films of platinum on porous vycor substrates avoid diffusion limitations even at high current densities. The presented study shows that the specific activity of sputtered platinum is not unusually high. Performance limitations are found to be controlled by physical processes, even at low loadings. Catalyst activity is strongly influenced by platinum sputtering parameters, which seemingly change the surface area of the catalyst layer. The use of porous nickel as a substrate shows that pore size of the substrate is an important parameter. It is noted that electrode performance increases with increasing loading for catalyst layers up to two microns thick, thus showing the physical properties of the sputtered layer to be different from platinum foil. Electrode performance is also sensitive to changing differential pressure across the electrode. The application of sputtered catalyst layers to fuel cell matrices for the purpose of obtaining thin total cells appears feasible.

Asher, W. J.↗
NASA NTRS1972

Normal evaporation of binary alloys

In the study of normal evaporation, it is assumed that the evaporating alloy is homogeneous, that the vapor is instantly removed, and that the alloy follows Raoult's law. The differential equation of normal evaporation relating the evaporating time to the final solute concentration is given and solved for several important special cases. Uses of the derived equations are exemplified with a Ni-Al alloy and some binary iron alloys. The accuracy of the predicted results are checked by analyses of actual experimental data on Fe-Ni and Ni-Cr alloys evaporated at 1600 C, and also on the vacuum purification of beryllium. These analyses suggest that the normal evaporation equations presented here give satisfactory results that are accurate to within an order of magnitude of the correct values, even for some highly concentrated solutions. Limited diffusion and the resultant surface solute depletion or enrichment appear important in the extension of this normal evaporation approach.

Li, C. H.↗