Coarsening of solid-liquid mixtures in a random acceleration field

Abstract

The effects of flow induced by a random acceleration field ͑g-jitter͒ are considered in two related situations that are of interest for microgravity fluid experiments: the random motion of isolated buoyant particles, and diffusion driven coarsening of a solid-liquid mixture. We start by analyzing in detail actual accelerometer data gathered during a recent microgravity mission, and obtain the values of the parameters defining a previously introduced stochastic model of this acceleration field. The diffusive motion of a single solid particle suspended in an incompressible fluid that is subjected to such random accelerations is considered, and mean squared velocities and effective diffusion coefficients are explicitly given. We next study the flow induced by an ensemble of such particles, and show the existence of a hydrodynamically induced attraction between pairs of particles at distances large compared with their radii, and repulsion at short distances. Finally, a mean field analysis is used to estimate the effect of g-jitter on diffusion controlled coarsening of a solid-liquid mixture. Corrections to classical coarsening rates due to the induced fluid motion are calculated, and estimates are given for coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, an experiment to be conducted in microgravity in the near future.

On the variety of particle accumulation structures under the effect of g-jitters

“…Given the intrinsic nonlinear nature of the phenomena under analysis, it needs no demonstration that perturbations of velocity and temperature induced by distinct types of forcing will not just superpose linearly. For this reason, a straightforward generalization of the findings for monochromatic g-jitters to the more general "coloured" situation involving many distinct disturbances with different amplitudes, frequencies and directions, is not possible (Thomson et al, 1997). The problem is far more complex and would require its own separate exhaustive (parametric) treatment.…”

“…Other important investigations have dealt with the terminal velocity of a spherical particle in a vertically oscillating liquid (among them, it is worth mentioning Baird et al, 1967;Tunstall andHoughton, 1968 andIkeda, 1989). For the case of particles undergoing a sinusoidal motion or subjected to vibrations in an otherwise quiescent fluid, we may cite Langbein (1991), Sun et al (1994), Ellison et al (1995), Thomson et al (1997), Simic-Stefani et al (2006), Hassan et al (2006a), Hassan and Kawaji (2008). From all these works, it is known that, in general, a distinction must be introduced between the ranges of high and low frequency (the expected effects of gjitters being markedly different according to the range considered).…”

Impact of stochastic accelerations on dopant segregation in microgravity semiconductor crystal growth

“…As a final comment, it is worth stressing that the resulting segregation parameter values corresponding to the action of the accelerometric signals employed in this work, modeled from real g-jitter measurements in microgravity platforms [13], result in principle to be sufficiently small to be neglected for most practical purposes. However, as it has just been mentioned, the analysis of the system to be done in the next section will show the importance of the low frequency components of the gravity, which for real signals could differ substantially.…”

“…We should also stress that the parameters of the narrow-band noises [13], while obtained from accelerometric signals in real microgravity environments, were estimated to mainly model the principal frequency components of the accelerometric signal. The specific zero frequency components and hence the system responses are thus possibly underestimated.…”

“…[13], and stochastic modeling of g-jitters was applied to different physical processes relevant to both fundamental physics and space technology, such as in coarsening of colloidal suspensions [13], fluid-fluid interfaces [14,15] and in thermal natural convection [16]. In the present paper we pursue this approach in a realistic modelization of different prototypic setups of crystal growth in microgravity in the context of semiconductor materials.…”