Franz Rosenberger

Mixed convection between horizontal plates. I: Entrance effects

Entrance effects in mixed convection between horizontal, differentially heated plates were studied in nitrogen by laser Doppler anemometry in a range 1368 < Ra < 8300 and 15 < Re < 170. Two entrance lengths were deduced from velocity profiles: one for the onset of buoyancy-driven convective instability, and one for the full development of the mixed flow. Explicit expressions for both entrance lengths are given. In addition, unsteady longitudinal convection rolls were observed. These are discussed in terms of an admixture of transverse convection rolls and/or contributions from upstream turbulence. The experimental results show that the critical Ra for the transverse convection roils increases as Re increases.

Inorganic and protein crystal growth - similarities and differences

Abstract Transport and interface kinetics concepts that have proven successful in the design and control of inorganic crystal growth experiments are outlined. Their potential usefulness and limitations in protein crystal growth are discussed. The presentation follows a selection of observations and statements that are often made by workers in the protein crystal growth field. The paper is meant to be tutorial in nature. Emphasis is placed on concepts which bear practical significance. Though the discussion is on an introductory level, additional references are given to facilitate deeper penetration of the various topics. Suggestions for the possible improvement of current protein crystal growth techniques are made.

Numerical modeling of diffusive physical vapor transport in cylindrical ampoules

Abstract Diffusion limited physical vapor transport in closed cylindrical ampoules of aspect ratio (length/radius) between 0.5 and 10 was studied numerically. The transport of a crystal forming component A through an inert component B, which undergoes zero net transport, was considered. A case in which the partial pressure of B is comparable to that of A, as well as systems with very low partial pressures of B (impurity cases) were treated. Concentrations and velocity distributions were obtained from the coupled transport equations for momentum, mass and components. It was found that the interdiffusion of components in viscous interaction with the container walls leads to (a) recirculation of component B, even in the absence of gravity; (b) concentration gradients normal to the main transport direction in the vapor space; and (c) non-uniform interfacial concentration gradients and, hence, non-uniform crystal growth rates.

Interfacial transport in crystal growth, a parametric comparison of convective effects

Abstract Most solid-state devices utilize properties of crystals obtained through the controlled introduction into the host lattice of impurities (“dopants”) or deviations from stoichiometry. This compositional adjustment is typically made during the growth of the solid from its nutrient (melt, vapor or solution). Since the yield and performance of devices depends strongly on their compositional uniformity, a detailed understanding of the fluid dynamics of nutrient phases and at solid-nutrient interfaces is important. Rigorous modeling of heat and mass transfer in multicomponent (crystal growth) fluids for realistic boundary conditions is typically unwieldy. Hence, the motivation for simplification is great. Numerous simplifying models have been used in the materials preparation literature. Though well justified for some special cases, these concepts have been indiscriminately generalized, causing much confusion. In this presentation we take the opposite route. Based on the generally valid transport equations and the appropriate dimensionless groups of fluid properties, we point out (a) limitations of the most commonly used mass transfer models, and (b) physically justifiable analogies between mass, heat and momentum transfer. From these considerations one can get valuable semi-quantitative guidance for the laboratory practice in many situations that currently defy rigorous treatment.

Diffusive-convective vapor transport across horizontal and inclined rectangular enclosures

Abstract The enhancement of vapor transport across horizontal and inclined rectangular (2D) enclosures by expansive convection is studied numerically for a range in Grashof number that extends up to boundary layer flow. Comparison is made with predictions of the simplifying model and resulting analytical treatment of Klosse and Ullersma for various aspect ratios of the enclosure. The influence of varying Schmidt and Prandtl numbers is investigated. Solutions for interfacial (growth) flux and temperature distributions are given, showing practically important non-uniformities.

Mixed convection between horizontal plates. II: Fully developed flow

Fully developed velocity profiles of longitudinal convection rolls in mixed convection between horizontal plates were measured in nitrogen by laser Doppler anemometry for a range 2472 < Ra < 8300 and 15 < Re < 150. It is shown analytically and experimentally that the transverse velocities of the longitudinal convection rolls are independent of the forced flow. The experimentally and numerically obtained w-profiles (Pr = 0.71) are in good agreement with theoretical predictions (Pr → ∞) and other experimental results (Pr = 11.1 and 930) for Rayleigh-Benard convection. A detailed study of the longitudinal velocity modulation Δu[wmax(Ra), Re] is presented. Also, asymmetric roll patterns were found in spite of the small temperature differences used between the horizontal plates.

Numerical modeling of diffusive-convective physical vapor transport in cylindrical vertical ampoules

Abstract Diffusive-convective physical vapor transport (PVT) in cylindrical, vertical ampoules of aspect ratio (length/radius) between 0.5 and 10 was modeled numerically. The transport of a crystal forming component A through an inert component B, that undergoes zero net transport, was considered. Systems were treated in which: (a) with unequal molecular weight of the components ( M A = 254, M B = 2) and with temperature gradients typically employed in PVT, convective flow arises dominantly from solutal density gradients; (b) with equal molecular weight of the components ( M A = M B = 254) convective flow can arise only from thermal expansion. Concentration and velocity distributions were obtained from the coupled transport equations for momentum, mass, components, and energy. It was found that, due to the diffusion-induced horizontal density gradients, buoyancy-driven convective flows are superimposed to the diffusive-advective fluxes without threshold. Net recirculations sets in adjacent to the growing interface, in contrast to the corresponding monocomponent situation where marginally stable convective modes fill the whole fluid space. Depending on the orientation of the main transport direction with respect to gravity, convection can either reduce or enhance the diffusion-induced radial concentration gradients. Significant enhancement of the net transport rate i.e. of component A transport, was found to occur only when the whole vapor space between source and growing crystal is filled by a convective recirculation roll. Solutal and thermal convection results are similar; yet for quantitative discussions, thermal and solutal Rayleigh numbers are not interchangeable in contrast to convective situations that lack net mass transport across the fluid space.

Congruent (diffusionless) vapor transport

Abstract Physical vapor transport in cylindrical ampoules was investigated under convectively stable conditions in the viscous flow range. Transport rates for iodine were measured. Rates obtained in closed ampoules were orders of magnitude below expectations for diffusionless (monocomponent) transport. Upon continuous removal of residual permanent gases from “semi-closed” ampoules, however, the mass transport rates were only limited by viscous interaction with the walls and by heat transfer at the interfaces. The rapid, diffusionless transport rates obtained were in good agreement with predictions based upon the Hagen-Poiseuille equation, justifying the assumption of interfacial equilibrium. Consequences for the practical design of PVT systems are discussed.

Expansive convection in vapor transport across horizontal rectangular enclosures

Abstract The enhancement of diffusive-advective vapor transport across horizontal rectangular (2D) enclosures by expansive convection is studied numerically. Most of the simplifying assumptions made in the analytical treatment of Klosse and Ullersma (KU) are relaxed. It is shown that up to moderately large Grashof numbers N Gr (i.e. when the Sherwood number N Sh ⩽ 5) KUs analytical model gives a reasonably good estimate of the convective transport enhancement in two dimensions, for both conducting and insulating enclosure walls. For higher N Gr their asymptotically converging solutions must be expected to depart considerably from (2D) reality. Beyond earlier analyses, solutions for temperature and concentration distributions are obtained showing practically important non-uniformities.

Low temperature electro-optical effects from off-axis Li+ in FA centers☆

Abstract Measurements of the electric field modulated absorption of KC1:Li F A centers (field applied perpendicular to center axis), and its spectral-, field- and temperature dependence are explained by an ‘off-axis’ center model in which the Li + ion can occupy four equivalent pocket states, displaced in 〈110〉 direction from the F A center axis.