François Drolet

Coarsening of solid-liquid mixtures in a random acceleration field

The effects of flow induced by a random acceleration field (g-jitter) 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.

Lamellae alignment by shear flow in a model of a diblock copolymer

A mesoscopic model of a diblock copolymer is used to study the stability of a lamellar structure under a uniform shear flow. We first obtain the nonlinear lamellar solutions under both steady and oscillatory shear flows. Regions of existence of these solutions are determined as a function of the parameters of the model and of the flow. Finally, we address the stability of the lamellar solution against long wavelength perturbations.

ONSET OF OSCILLATORY INSTABILITIES UNDER STOCHASTIC MODULATION

We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random component in both the control parameter of the bifurcation and in the modulation amplitude. Stability boundaries are computed by either solving the stationary Fokker-Planck equation on the center manifold of the underlying deterministic system whenever possible, or by direct numerical solution otherwise. If the modulation amplitude has a stochastic component, the primary bifurcation is always to standing waves at a value of the control parameter that depends on the intensity of the fluctuations. More precisely, and to contrast our results with the case of a deterministic periodic forcing, the onset of instability in the standing-wave regime is shifted from its deterministic location, and the region of primary bifurcation to traveling waves disappears, yielding instead standing waves at negative values of the control parameter. {copyright} {ital 1997} {ital The American Physical Society}