Building Vertical Walls by Deposition of Molten Metal Droplets

2005 ◽  
Author(s):  
M. Fang ◽  
S. Chandra ◽  
C. B. Park
Keyword(s):  
Surface Layer ◽  
Analytical Solution ◽  
Substrate Temperature ◽  
Layer By Layer ◽  
Droplet Temperature ◽  
Droplet Generator ◽  
One Dimensional ◽  
Metallurgical Bonding ◽  
Experimental Parameters ◽  
Vertical Walls

Experiments were conducted to determine conditions under which good metallurgical bonding was achieved in vertical walls composed of multiple layers of droplets that were fabricated by depositing tin droplets layer by layer. Molten tin droplets (0.75 mm diameter) were deposited using a pneumatic droplet generator on an aluminum substrate. The primary parameters varied in experiments were those found to most affect bonding between droplets on different layers: droplet temperature (varied from 250°C to 325°C) and substrate temperature (varied from 100°C to 190°C). Considering the cooling rate of droplet is much faster than the deposition rate previous deposition layer cooled down too much that impinging droplets could only remelt a thin surface layer after impact. Assuming that remelting between impacting droplets and the previous deposition layer is a one-dimensional Stefan problem with phase change an analytical solution can be found and applied to predict the minimum droplet temperature and substrate temperature required for local remelting. It was experimentally confirmed that good bonding at the interface of two adjacent layers could be achieved when the experimental parameters were such that the model predicted remelting.

Experiments on Remelting and Solidification of Molten Metal Droplets Deposited in Vertical Columns

2005 ◽  
Author(s):  
M. Fang ◽  
S. Chandra ◽  
C. B. Park
Keyword(s):  
Column Height ◽  
Conductive Heat ◽  
Droplet Temperature ◽  
Droplet Generator ◽  
One Dimensional ◽  
Spherical Mass ◽  
Temperature Constant ◽  
Uniform Diameter ◽  
Surface Tension Forces ◽  
Metal Droplets

Experiments were done to determine conditions under which vertical columns could be built by metal droplets landing sequentially on top of each other. Molten tin droplets (0.6 mm diameter) were deposited using a pneumatic droplet generator on an aluminum substrate. The primary parameters varied in experiments were those found to most affect bonding between droplets: droplet temperature (250°C to 345°C), substrate temperature (60°C to 200°C) and deposition rate (1 Hz to 15 Hz). At lower deposition rates the substrate cooled down too much to induce remelting whereas at higher rates the tip of the column remained liquid and surface tension forces pulled it into a spherical mass. Assuming one-dimensional conductive heat transfer in a column a simple analytical model was developed to calculate the temperature at the tips of the column. It predicts that deposition frequency should be decreased as column height increases to hold the tip temperature constant. Droplet coalescence was best achieved when the tip temperature of a column was maintained at the melting point of the metal. Columns fabricated following the deposition frequency predicted by the model show good bonding between droplets and uniform diameter.

Experiments on Remelting and Solidification of Molten Metal Droplets Deposited in Vertical Columns

2006 ◽  
Vol 129 (2) ◽  
pp. 311-318 ◽  
Author(s):  
M. Fang ◽  
S. Chandra ◽  
C. B. Park
Keyword(s):  
Column Height ◽  
Conductive Heat ◽  
Droplet Temperature ◽  
Droplet Generator ◽  
One Dimensional ◽  
Spherical Mass ◽  
Temperature Constant ◽  
Uniform Diameter ◽  
Surface Tension Forces ◽  
Metal Droplets

Experiments were done to determine conditions under which vertical columns could be built by metal droplets landing sequentially on top of each other. Molten tin droplets (0.6mm diameter) were deposited using a pneumatic droplet generator on an aluminum substrate. The primary parameters varied in experiments were those found to most affect bonding between droplets: droplet temperature (250-345°C), substrate temperature (60-200°C), and deposition rate (1-15Hz). At lower deposition rates the substrate cooled down too much to induce remelting whereas at higher rates the tip of the column remained liquid and surface tension forces pulled it into a spherical mass. Assuming one-dimensional conductive heat transfer in a column a simple analytical model was developed to calculate the temperature at the tips of the column. It predicts that deposition frequency should be decreased as column height increases to hold the tip temperature constant. Droplet coalescence was best achieved when the tip temperature of a column was maintained at the melting point of the metal. Columns fabricated following the deposition frequency predicted by the model show good bonding between droplets and uniform diameter.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

scholarly journals Analytical solution of one-dimensional Pennes’ bioheat equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1084-1092
Author(s):  
Hongyun Wang ◽  
Wesley A. Burgei ◽  
Hong Zhou
Keyword(s):  
Analytical Solution ◽  
Radiofrequency Energy ◽  
Bioheat Equation ◽  
Surface Cooling ◽  
One Dimensional ◽  
The Fourier Transform ◽  
The One ◽  
Parameter Values ◽  
Mathematical Derivation ◽  
Effect Of Surface

Abstract Pennes’ bioheat equation is the most widely used thermal model for studying heat transfer in biological systems exposed to radiofrequency energy. In their article, “Effect of Surface Cooling and Blood Flow on the Microwave Heating of Tissue,” Foster et al. published an analytical solution to the one-dimensional (1-D) problem, obtained using the Fourier transform. However, their article did not offer any details of the derivation. In this work, we revisit the 1-D problem and provide a comprehensive mathematical derivation of an analytical solution. Our result corrects an error in Foster’s solution which might be a typo in their article. Unlike Foster et al., we integrate the partial differential equation directly. The expression of solution has several apparent singularities for certain parameter values where the physical problem is not expected to be singular. We show that all these singularities are removable, and we derive alternative non-singular formulas. Finally, we extend our analysis to write out an analytical solution of the 1-D bioheat equation for the case of multiple electromagnetic heating pulses.

Formation of Cr-rich Nano-clusters and Columns in (Zn,Cr)Te Grown by MBE

2009 ◽  
Vol 1183 ◽  
Author(s):  
Yôtarõ Nishio ◽  
Kôichirô Ishikawa ◽  
Shinji Kuroda ◽  
Masanori Mitome ◽  
Yoshio Bando
Keyword(s):  
Magnetic Properties ◽  
Substrate Temperature ◽  
Crystallographic Orientation ◽  
Vertical Direction ◽  
Growth Conditions ◽  
Chemical Analyses ◽  
Mbe Growth ◽  
One Dimensional ◽  
X Ray ◽  
Cr Content

AbstractThe correlation between the Cr aggregation and magnetic properties are investigated for the series of Zn1-xCrxTe films grown by MBE with a systematic variation of growth conditions. Structural and chemical analyses using TEM and energy-dispersive X-ray spectroscopy (EDS) reveal that the crystallinity and the Cr distribution change significantly with the substrate temperature during the MBE growth. For a relatively low average Cr content x ≅ 0.05, it is found that the crystal quality is improved with the increase of the substrate temperature. For a higher average Cr content x ≅ 0.2, the shape of Cr-rich regions is transformed from isolated clusters into one-dimensional nanocolumns with the increase of the substrate temperature. The direction of the nanocolumn formation changes depending on the crystallographic orientation of the grown films. In the magnetization measurements, anisotropic magnetic properties are observed in the films in which Cr-rich nanocolumns are formed in the vertical direction, depending on the relation between the direction of the nanocolumns and the applied magnetic fields.

Diffusion-Limited Cell Dehydration: Analytical and Numerical Solutions for a Planar Model

1999 ◽  
Author(s):  
Alexander V. Kasharin ◽  
Jens O. M. Karlsson
Keyword(s):  
Analytical Solution ◽  
Numerical Solutions ◽  
Planar System ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Dimensional Diffusion ◽  
Constant Diffusivity ◽  
A Cell ◽  
Cell Dehydration ◽  
The One

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

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