Theory of Metastable State Relaxation in a Gravitational Field for Non-Critical Binary Systems with Non-Conserved Order Parameter

A new mathematical ansatz is developed for solution of the time-dependent Ginzburg-Landau nonlinear partial differential equation describing metastable state relaxation in binary (solute+solvent) non-critical solutions with non-conserved scalar order parameter in presence of a gravitational field. It has been demonstrated analytically that in such systems metastability initiates heterogeneous solute redistribution which results in the formation of a non-equilibrium singly-periodic spatial solute structure in the new solute-rich phase. The critical radius of nucleation and the induction time in these systems are gravity-dependent. It has also been proved that metastable state relaxation in vertical columns of supersaturated non-critical binary solutions leads to formation of the solute concentration gradient. Analytical expression for this concentration gradient is found and analysed. It is concluded that gravity can initiate phase separation (nucleation or spinodal decomposition)

Concentration Dependence of Solution Shear Viscosity and Solute Mass Diffusivity in Crystal Growth from Solutions

The physical properties of a supersaturated binary solution such as its density rho, shear viscosity eta, and solute mass diffusivity D are dependent on the solute concentration c: rho = rho(c), eta = eta(c), and D = D(c). The diffusion boundary layer equations related to crystal growth from solution are derived for the case of natural convection with a solution density, a shear viscosity, and a solute diffusivity that are all depen- dent on solute concentration. The solution of these equations has demonstrated the following. (1) At the vicinity of the saturation concentration c(sub s) the solution shear viscosity eta depends on rho as eta(sub s) = eta(rho(sub s))varies as square root of rho(c(sub s)). This theoretically derived result has been verified in experiments with several aqueous solutions of inorganic and organic salts. (2) The maximum solute mass transfer towards the growing crystal surface can be achieved for values of c where the ratio of d ln(D(c)/dc) to d ln(eta(c)/dc) is a maximum

A statistical understanding of nucleation

Abstract In order to study a stochastic phenomenon such as nucleation it is necessary to collect a large enough set of nucleation data to obtain nucleation statistics. This is done by performing nucleation experiments with the same solution under exactly the same conditions many times N (N&150-300). Such an experiment, based on simultaneous levitation of N&150-300 identical microdroplets (1-20 m in diameter) of supersaturated solutions in a solvent atmosphere, is possible by employing the linear quadrupole electrodynamic levitator trap (LQELT). The LQELT is supplemented with a special optical system which is based on scattering of monochromatic polarized light. This will enable fast observation of nucleation and, thus, induction times in each of the levitated microdroplets. The N different induction times, counted from the moment t at which supersaturation is established are recorded. This data provides nucleation statistics (induction time statistics). The numerical and analytical studies of nucleation statistics and parameters provide an insight into statistical properties of the underlying nucleation phenomenon