Instability of a solidifying binary mixture

An analysis is performed on the stability of a solidifying binary mixture due to surface tension variation of the free liquid surface. The basic state solution is obtained numerically as a nonstationary function of time. Due to the time dependence of the basic state, the stability analysis is of the global type which utilizes a variational technique. Also due to the fact that the basic state is a complex function of both space and time, the stability analysis is performed through numerical means

Studies of convection in a solidifying binary mixture at reduced gravity

A great deal of interest was generated recently in the possibility of producing new materials in the reduced gravity environment provided during the forthcoming missions of Spacelab. The range of possibilities extend from producing large crystals of uniform properties to manufacturing materials with unique properties. Most of these processes involve the solidification of materials from the liquid state. Convective motions within the liquid during solidification can influence the local material composite and the shape of the solid-liquid interface which may result in solids with non-uniform properties and crystal defects. The microgravity environment of Spacelab is being viewed as one in which the buoyancy forces are eliminated so that convection driven by thermal gradients does occur, resulting in an improved solidification process. However, convection may occur for other reasons and whether convection is negligible or not during solidification constitutes processing in low-gravity environment. Little information exists presently on convection during solidification under such circumstances. A continuation of an analytical investigation into the nature of convective motion in a binary liquid layer due to surface tension forces during its solidification is reported. The onset of convection will be determined through a stability analysis which is described

Theoretical analyses of baroclinic flows

Completed and ongoing research activities are discussed briefly, including a three-dimensional, linear stability analysis of the baroclinic Hadley cell and a numerical model of the baroclinic flow between two rotating concentric spheres. This model simulates axisymmetric flow in the Atmospheric General Circulation Experiment configuration. A computer code designed to solve the strongly nonlinear stability problem for the Eady basic state is mentioned

Theoretical analyses of Baroclinic flows

A stability analysis of a thin horizontal rotating fluid layer which is subjected to arbitrary horizontal and vertical temperature gradients is presented. The basic state is a nonlinear Hadley cell which contains both Ekman and thermal boundary layers; it is given in closed form. The stability analysis is based on the linearized Navier-Stokes equations, and zonally symmetric perturbations in the form of waves propagating in the meridional direction are considered. Numerical methods were used for the stability problem. It was found that the instability sets in when the Richardson number is close to unity and that the critical Richardson number is a non-monotonic function of the Prandtl number. Further, it was found that the critical Richardson number decreases with increasing Ekman number until a critical value of the Ekman number is reached beyond which the fluid is stable

The eigenvalue spectrum of the Orr-Sommerfeld problem

A numerical investigation of the temporal eigenvalue spectrum of the ORR-Sommerfeld equation is presented. Two flow profiles are studied, the plane Poiseuille flow profile and the Blasius boundary layer (parallel): flow profile. In both cases a portion of the complex c-plane bounded by 0 less than or equal to CR sub r 1 and -1 less than or equal to ci sub i 0 is searched and the eigenvalues within it are identified. The spectra for the plane Poiseuille flow at alpha = 1.0 and R = 100, 1000, 6000, and 10000 are determined and compared with existing results where possible. The spectrum for the Blasius boundary layer flow at alpha = 0.308 and R = 998 was found to be infinite and discrete. Other spectra for the Blasius boundary layer at various Reynolds numbers seem to confirm this result. The eigenmodes belonging to these spectra were located and discussed

Spacecraft Dynamics as Related to Laboratory Experiments in Space

Proceedings are presented of a conference sponsored by the Physics and Chemistry Experiments in Space Working Group to discuss the scientific and engineering aspects involved in the design and performance of reduced to zero gravity experiments affected by spacecraft environments and dynamics. The dynamics of drops, geophysical fluids, and superfluid helium are considered as well as two phase flow, combustion, and heat transfer. Interactions between spacecraft motions and the atmospheric cloud physics laboratory experiments are also examined

Studies of convection in a solidifying system with surface tension at reduced gravity

The low gravity environment of Earth's orbit is being seriously considered for experimentation on the production of materials in space. Most of such materials processes inevitably involve either the solidification of melt or the melting of solids. Inherent in most fluid mechanisms with temperature gradients is convective motion. A study is presented for the onset of convection in a solidifying system in an environment which is similar to that encountered in space processing. Since the study is for a low gravity condition, the only driving mechanism considered is that due to the variation of surface tension force at the free surface of the melt layer. Two simple solidification models were considered, one in which the solidification process enters in the perturbation system and another in which the melt is solidifying at a constant rate. The results show that the solidification process will bring about convection in the melt earlier than otherwise

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

A three-dimensional, linear stability analysis of a baroclinic flow for Richardson number, Ri, of order unity is presented. The model considered is a thin horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The basic state is a Hadley cell which is a solution of the complete set of governing, nonlinear equations and contains both Ekman and thermal boundary layers adjacent to the rigid boundaries; it is given in a closed form. The stability analysis is also based on the complete set of equations; and perturbation possessing zonal, meridional, and vertical structures were considered. Numerical methods were developed for the stability problem which results in a stiff, eighth-order, ordinary differential eigenvalue problem. The previous work on three-dimensional baroclinic instability for small Ri was extended to a more realistic model involving the Prandtl number, sigma, and the Ekman number, E, and to finite growth rates and a wider range of the zonal wavenumber

An exact solution for the solidification of a liquid slab of binary mixture

The time dependent temperature and concentration profiles of a one dimensional finite slab of a binary liquid alloy is investigated during solidification. The governing equations are reduced to a set of coupled, nonlinear initial value problems using the method outlined by Meyer. Two methods will be used to solve these equations. The first method uses a Runge-Kutta-Fehlberg integrator to solve the equations numerically. The second method comprises of finding closed form solutions of the equations

Multi-parameter generalization of nonextensive statistical mechanics

We show that the stochastic interpretation of Tsallis' thermostatistics given recently by Beck [Phys. Rev. Lett {\bf 87}, 180601 (2001)] leads naturally to a multi-parameter generalization. The resulting class of distributions is able to fit experimental results which cannot be reproduced within the Boltzmann's or Tsallis' formalism.Comment: ReVTex 4.0, 4 eps figure