Buoyancy, Soret, Dufour, and Variable Property Effects in Silicon Epitaxy

1991 ◽  
Vol 113 (3) ◽  
pp. 688-695 ◽  
Author(s):  
R. L. Mahajan ◽  
C. Wei
Keyword(s):  
Mass Transfer ◽  
Transfer Rate ◽  
Stokes Equations ◽  
A Priori ◽  
Mass Transfer Rate ◽  
Navier Stokes ◽  
Property Variation ◽  
Silicon Epitaxy ◽  
Analytical Studies ◽  
Epitaxial Deposition

In most of the previous numerical and semi-analytical studies of silicon epitaxial deposition, a common practice has been to neglect the buoyancy flow, Dufour, Soret, and property variation effects. In this paper, we take a critical look at the validity of that approach and point out some fallacies. The geometric configuration studied is a horizontal reactor for the susceptor tilt angles of 0 and 2.9 deg. The full Navier-Stokes equations coupled with those for the energy and species transfer are solved numerically for a range of parameters typical of commercial silicon epitaxial deposition systems. The effects of ignoring terms due to buoyancy, Dufour, Soret, and variable properties on the mass transfer rate are systematically evaluated. The results indicate that for typical horizontal epitaxial deposition parameters, the buoyancy and Dufour effects have negligible effect on the mass transfer rate, while the Soret and property variation have a large impact. In light of this information, it is shown that the agreement reported in the past between the experimental and numerical/analytical studies is coincidental. The implication is that these assumptions must be critically examined for a given CVD system and not ignored a priori. Finally, the effects of important parameters—reactor height, inlet velocity, inlet concentration, and susceptor temperature—on the deposition characteristics are included to provide guidelines for controlling the epitaxial layer thickness and uniformity.

The Effects of Hydrodynamics Characteristics on Mass Transfer During Droplet Formation Using Computational Approach

2006 ◽  
Author(s):  
A. Javadi ◽  
M. Taeibi-Rahni ◽  
D. Bastani ◽  
K. Javadi
Keyword(s):  
Mass Transfer ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Mass Transfer Rate ◽  
Droplet Formation ◽  
Continuous Phase ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Phases ◽  
Expansion Model

For the reason that flow expansion model (developed in our previous work) for evaluating mass transfer during droplet formation involves with manifest hydrodynamic aspects, in this research computational simulation of this phenomenon was done for characterization of hydrodynamics effects on the mass transfer during droplet formation. For this purpose, an Eulerian volume tracking computational code based on volume of fluid (VOF) method was developed to solve the transient Navier-Stokes equations for the axisymmetric free-boundary problem of a Newtonian liquid that is dripping vertically and breaking as drops into another immiscible Newtonian fluid. The effects of hydrodynamics effects on the mass transfer during droplet formation have been discussed in the three features, including: 1- The intensity of the interaction between two phases 2-The strength and positions of the main vorticities on the nozzle tip 3-The effects of local interfacial vorticities (LIV). These features are considered to explain the complexities of drop formation mass transfer between Ethyl Acetoacetate (presaturated with water) as an organic dispersed phase and water as continuous phase for two big and small nozzle sizes (0.023 and 0.047 cm, ID) which have different level of mass transfer rate particularly in first stages of formation time.

scholarly journals The effect of turbulence on mass transfer rates of small inertial particles with surface reactions

2017 ◽  
Vol 836 ◽  
pp. 932-951 ◽  
Author(s):  
Nils Erland L. Haugen ◽  
Jonas Krüger ◽  
Dhrubaditya Mitra ◽  
Terese Løvås
Keyword(s):  
Mass Transfer ◽  
Gas Phase ◽  
Transfer Rate ◽  
Relative Velocity ◽  
Surface Reactions ◽  
Mass Transfer Rate ◽  
Navier Stokes ◽  
Inertial Particles ◽  
Dense Particle ◽  
Simulation Tools

The effect of turbulence on the mass transfer between a fluid and embedded small heavy inertial particles that experience surface reactions is studied. For simplicity, the surface reaction, which takes place when a gas phase reactant is converted to a gas phase product at the external surface of the particles, is unimolar and isothermal. Two effects are identified. The first effect is due to the relative velocity between the fluid and the particles, and a model for the relative velocity is presented. The second effect is due to the clustering of particles, where the mass transfer rate is inhibited due to the rapid depletion of the consumed species inside the dense particle clusters. This last effect is relevant for large Damköhler numbers, where the Damköhler number is defined as the ratio of the turbulent and chemical time scales, and it may totally control the mass transfer rate for Damköhler numbers larger than unity. A model that describes how this effect should be incorporated into existing simulation tools that utilize the Reynolds averaged Navier–Stokes approach is presented.

Development of Mass-Conservative Phase-Change Model for Convective Boiling Simulations

2013 ◽  
Author(s):  
Yohei Sato ◽  
Sreeyuth Lal ◽  
Bojan Niceno
Keyword(s):  
Mass Transfer ◽  
Surface Tension ◽  
Phase Change ◽  
Stokes Equations ◽  
Mass Transfer Rate ◽  
Nucleate Boiling ◽  
Navier Stokes ◽  
Transfer Model ◽  
Change Model ◽  
Convective Boiling

A numerical method based on Computational Fluid Dynamics (CFD) has been developed to simulate convective nucleate boiling flows in laminar and turbulent flow regimes. A single set of Navier-Stokes equations is solved based on a staggered finite-volume algorithm on Cartesian grids using Smagorinsky model for sub-grid scale turbulence. A color function is used for the two-phase flow model with a local sharpening scheme [1] to prevent the smearing of the color function, and Brackbill’s Continuum Surface Force (CSF) model [2] is used for the surface tension and the wall adhesion force. A sharp-interface mass-conservative phase change model [3], which can capture the velocity jump accurately, is used for the mass transfer model. A micro-region model developed by Stephan [4] is used to model the mass transfer at the vapor-liquid-solid triple point, and the mass transfer rate and the surface tension force in the micro-region is introduced to the Navier-Stokes solver. The developed scheme is validated against the experiments of convective boiling flows in the horizontal and vertical flow directions [5]. The validation cases considered in this paper are based on a single nucleation site and single bubble growth, in the same approach as Li and Dhir [6], and several assumptions are used for the initial and boundary conditions to complement the limited measured data. Thus, the comparison between the simulation and the experiment may not have the true meaning of validation, but the computed bubble liftoff diameter and time show agreement with experiments under the given conditions, and the applicability of the developed method to the simulation of convective boiling flows is demonstrated.

Free Convective Mass Transfer at Isosceles Triangular Surfaces of Varying Inclination

2003 ◽  
Vol 68 (11) ◽  
pp. 2080-2092 ◽  
Author(s):  
Martin Keppert ◽  
Josef Krýsa ◽  
Anthony A. Wragg
Keyword(s):  
Mass Transfer ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Mass Transfer Process ◽  
Sulfate Solution ◽  
Convective Mass Transfer ◽  
Varying Length ◽  
Inclined Surface ◽  
Vertical Case ◽  
Limiting Diffusion Current

The limiting diffusion current technique was used for investigation of free convective mass transfer at down-pointing up-facing isosceles triangular surfaces of varying length and inclination. As the mass transfer process, copper deposition from acidified copper(II) sulfate solution was used. It was found that the mass transfer rate increases with inclination from the vertical to the horizontal position and decreases with length of inclined surface. Correlation equations for 7 angles from 0 to 90° were found. The exponent in the ShL-RaL correlation ranged from 0.247 for the vertical case, indicating laminar flow, to 0.32 for inclinations of 60 to 90°, indicating mixed or turbulent flow. The general correlation ShL = 0.358(RaL sin θ)0.30 for the RaL sin θ range from 7 × 106 to 2 × 1011 and inclination range from 15 to 90° was obtained.

Distributed mass transfer rate for modelling the leaching of porous granular materials containing soluble pollutants

2000 ◽  
Vol 55 (7) ◽  
pp. 1257-1267 ◽  
Author(s):  
Tiruta-Barna Ligia ◽  
Barna Radu ◽  
Moszkowicz Pierre ◽  
Bae Hae-Ryong
Keyword(s):  
Mass Transfer ◽  
Granular Materials ◽  
Transfer Rate ◽  
Mass Transfer Rate

Enhancement of formic acid production from CO2 in formate dehydrogenase reaction using nanoparticles

RSC Advances ◽  
2016 ◽  
Vol 6 (111) ◽  
pp. 109978-109982 ◽  
Author(s):  
Young-Kee Kim ◽  
Sung-Yeob Lee ◽  
Byung-Keun Oh
Keyword(s):  
Mass Transfer ◽  
Formic Acid ◽  
Acid Production ◽  
Transfer Rate ◽  
Formate Dehydrogenase ◽  
Mass Transfer Rate ◽  
Liquid Mass ◽  
Dehydrogenase Reaction ◽  
Liquid Mass Transfer ◽  
Mesoporous Nanoparticles

In an enzyme process using a gas substrate, the enhanced gas liquid mass transfer rate of the gas substrate by methyl-functionalized mesoporous nanoparticles could improve the productivity.

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