Transient effects on diffusion measurements

Abstract

In this paper the transient effects of convective disturbances on self-diffusivity measurements are evaluated. In these experiments convection arises due to buoyancy caused by the interaction of temperature gradients with either gravity (terrestrial experiments) or residual acceleration (microgravity experiments). The type of experiment system under consideration is a “Codastefano-type” experiment where continuous realtime measurements of the concentration of the diffusing species are made at two discrete locations using a radioactive tracer. For comparative purposes, we also consider the kffect of disturbances to the concentration profile during diffusion experiments in shear-cell type configurations. The sensitivity parameter for the systems under consideration is defined as the difference between the measured diffusivity, D’ , and the actual diffusivity, D , expressed as a percentage of D . In particular, for small deviations of the sample from ideal isothermal conditions, we examine the response of the system to residual microgravity acceleration disturbances. We also investigate the consequences of heating and cooling “temperature ramps,” for both microgravity and terrestrial conditions. The problem is approached using a combination of %caling arguments and numerical simulation. The important parameters that influence the sensitivity of the system are the frequency, amplitude and orientation of the residuals acceleration vector and ’ Staff Scientist; National’Center for Microgravity Research on Fluids and Combustion; Case Western Reserve University t Associate Professor, Department of Mechanical and Aerospace Engineerg CopyriJInc. the magnitude of heating or cooling rates. In addition, we show that it is equally important to consider the degree of isothermality that can be attained at the elevated operating temperatures of the actual experiment. Introduction Benchmark experiments to elucidate the temperature dependence of the self-diffusion coefficients in metals are planned for the International Space Station. As part of the design of the experimental facilities and for experiment planning purposes, the effects of the time-dependerit environmental factors that can lead to undesirable disturbances of the experiments need to be assessed. The desired outcome of the present experiments is to obtain diffusivity values within 1% of D. The potential contamination of diffusivity measurements due to convection caused by spacecraft residual acceleration or g-jitter is of obvious concern. Temperature ramping (necessary to efficiently examine the temperature dependence of the diffusivity) inevitably leads to transient temperature gradients that induce buoyancy flows. Such flows could result in significant contributions to the transport of the tracer and, thus affect the measured value of the diffusivity. Even after the temperature has been ramped to the new operating point, at the elevated operating temperature for liquid metals, truly isothermal conditions maybe impossible to achieve. Neither self-diffusion in liquid elements or binary diffusion in molten alloys is X;,,: ., .i. .,;_, .,’ (c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. D(T) predicted by different theories are often less than the differences in D(T) data sets measured in the same system. It is generally accepted that the variations in experimental data can be attributed to convective contamination. That is, for many systems, convection is unavoidable under terrestrial conditions [7]. However, it appears that the low-gravity environment of a low-earth orbit space-laboratory could provide suitable conditions for self-diffusivity measurements in high-temperature liquid metals in that convection is practically absent. The technique to be employed in the flight experiments is outlined below and the sensitivity of the experiment to residual and g-jitter acceleration is assessed. Several papers have demonstrated the reliability of numerical models for the analysis of the gsensitivity of directional solidification experiments (see for example, [S-12] and references therein). A similar approach was adopted to obtain the results described here. The effect of steady acceleration on diffusivity measurements under terrestrial conditions was examined in a previous paper [4]. Transient disturbances to the evolving concentration profile can affect the value of the measured diffusivity. The sources of the disturbances are time-dependent g-jitter and temperature ramping necessary for the efficient measurement of the diffusivity’s temperature dependence.