scholarly journals Evolution of a Polydisperse Ensemble of Ellipsoidal Crystals with Fluctuating Growth Rates in Supercooled Melts

2021 ◽  
Vol 2114 (1) ◽  
pp. 012003
Author(s):  
M.A. Nikishina
Keyword(s):  
Distribution Function ◽  
Growth Rates ◽  
Integral Method ◽  
Complete System ◽  
Intermediate Step ◽  
Volume Distribution ◽  
Particle Volume ◽  
System Of Integrodifferential Equations ◽  
Spherical Crystals ◽  
Kinetics Of

Abstract In this paper, an analytical solution to the model of the evolution of ellipsoidal crystals with fluctuating growth rates at the intermediate step of bulk phase transition is presented. A complete system of integrodifferential equations describing the problem was derived and analytically solved using the Laplace integral method. The kinetics of supercooling removal in melts has been found. The particle-volume distribution function represents a pike-shaped curve decreasing its maximum with time. It is demonstrated the differences in the distribution function for ellipsoidal and spherical crystals.

Kinetics of the Crystallization of Potassium Sulfate

1993 ◽  
Vol 58 (8) ◽  
pp. 1848-1854 ◽  
Author(s):  
Miroslav Karel ◽  
Jaroslav Nývlt
Keyword(s):  
Experimental Data ◽  
Crystal Growth ◽  
Growth Rates ◽  
Potassium Sulfate ◽  
Kinetics Of

The kinetics of the crystallization of potassium sulfate has been determined using the MSMPR technique. Values of the nucleation and crystal growth rates evaluated from the experimental data are compared with the corresponding literature data.

Cooling of Fruit with Arbitrary Shape: Simulation Using Galerkin-Based Integral Method

2017 ◽  
Vol 10 ◽  
pp. 1-15
Author(s):  
P. Morais Pessôa ◽  
A.G. Barbosa de Lima ◽  
R. Swarnakar ◽  
J.P. Gomes ◽  
W.M.P. Barbosa de Lima
Keyword(s):  
Integral Method ◽  
Arbitrary Shape ◽  
Heat Conduction Equation ◽  
Low Cost ◽  
Experimental Studies ◽  
Volume Ratio ◽  
Transient Heat Conduction ◽  
Cooling Time ◽  
Time Required ◽  
Kinetics Of

Cooling has been used for the preservation of fresh produce such as fruit and vegetables due to its low cost and high effectiveness in maintaining the product quality. Recently, several researchers have conducted theoretical and experimental studies for obtaining the kinetics of cooling and cooling time for fruits with different geometries. Present work, therefore, aims to simulate the cooling of fruits with particular reference to banana, orange, strawberry and Tahiti lemon. The transient heat conduction equation and its analytical solution using Galerkin based integral method are presented. It has been found that the strawberry has lower dimensionless cooling time compared with time required to cool other fruits, which is due to its higher surface area/volume ratio value. In orange and lemon the temperature distribution was found to be homogeneous in the angular direction, while in banana and strawberry it was two-dimensional due to shape of the fruits.

The kinetics of Ge lateral overgrowth on SiO2

MRS Advances ◽  
2015 ◽  
Vol 1 (23) ◽  
pp. 1703-1708 ◽  
Author(s):  
M. Yako ◽  
N. J. Kawai ◽  
Y. Mizuno ◽  
K. Wada
Keyword(s):  
Growth Kinetics ◽  
Growth Rates ◽  
Growth Process ◽  
Theoretical Calculations ◽  
Film Formation ◽  
Lateral Overgrowth ◽  
Flat Film ◽  
The Difference ◽  
Kinetics Of

ABSTRACTThe kinetics of Ge lateral overgrowth on SiO2 with line-shaped Si seeds is examined. The growth process is described by the difference between the growth rates of Ge on (100) planes (GR100) and <311> facets (GR311). The theoretical calculations well reproduce the growth kinetics. It is shown that narrowing the line-seeds helps Ge coalescence and flat film formation.

Fast Solutions for the Fiber Orientation of Concentrated Suspensions of Short-Fiber Composites Using the Exact Closure Method

2010 ◽  
Author(s):  
Stephen Montgomery-Smith ◽  
David A. Jack ◽  
Douglas Smith
Keyword(s):  
Distribution Function ◽  
Orientation Distribution Function ◽  
Fiber Orientation ◽  
Orientation Distribution ◽  
Equation Of Motion ◽  
Fiber Composites ◽  
Short Fiber ◽  
Second Order ◽  
Orientation Tensor ◽  
Kinetics Of

The kinetics of the fiber orientation during processing of short-fiber composites governs both the processing characteristics and the cured part performance. The flow kinetics of the polymer melt dictates the fiber orientation kinetics, and in turn the underlying fiber orientation dictates the bulk flow characteristics. It is beyond computational comprehension to model the equation of motion of the full fiber orientation probability distribution function. Instead, typical industrial simulations rely on the computationally efficient equation of motion of the second-order orientation tensor (also known as the second-order moment of the orientation distribution function) to model the characteristics of the fiber orientation within a polymer suspension. Unfortunately, typical implementation forms of any order orientation tensor equation of motion requires the next higher, even ordered, orientation tensor, thus necessitating a closure of the higher order expression. The recently developed Fast Exact Closure avoids the classical closure problem by solving a set of related second-order tensor equations of motion, and yields the exact solution for pure Jeffery’s motion as the diffusion goes to zero. Typical closures are obtained through a fitting process, and are often obtained by fitting for orientation states obtained from solutions of the full orientation distribution function, thus tying the closure to the flows from which it was fit. With the recent understandings of the limitations of the Folgar and Tucker (1984) model of fiber interactions during processing, it has become clear the importance of developing a closure that is independent of any choice of fitting data. The Fast Exact Closure presents an alternative in that it is constructed independent of any fitting process. Results demonstrate that when diffusion exists, the solution is not only physical, but solutions for flows experiencing Folgar-Tucker diffusion are shown to exhibit an equal to or greater accuracy than solutions relying on closures developed via a curve fitting approach.

scholarly journals Effects of nonlinear growth rates of spherical crystals and their withdrawal rate from a crystallizer on the particle-size distribution function

2019 ◽  
Vol 377 (2143) ◽  
pp. 20180210 ◽  
Author(s):  
Eugenya V. Makoveeva ◽  
Dmitri V. Alexandrov
Keyword(s):  
Distribution Function ◽  
Size Distribution ◽  
Growth Rates ◽  
Separation Of Variables ◽  
Size Distribution Function ◽  
Solid Particles ◽  
Supersaturated Solution ◽  
Metastable Liquid ◽  
Differential Model ◽  
Nonlinear Growth

In this paper, we show that the nonlinear growth rate of particles in a supersaturated solution or supercooled melt, as well as the rate of removal of crystals from the metastable liquid of a crystallizer, significantly change the size-distribution function of crystals. Taking these rates into account, we present a complete analytical solution of the integro-differential model describing the transient nucleation of solid particles and their evolution in a metastable liquid. The distribution function and metastability degree (supersaturation or supercooling) are found by means of the separation of variables and saddle-point methods. The nonlinear growth rates of crystals in supersaturated solutions and supercooled melts (single-component and binary) are summarized and compared with experimental data. This article is part of the theme issue ‘Heterogeneous materials: metastable and non-ergodic internal structures’.

Sintering Kinetics of an Yttrium Aluminosilicate Glass

2012 ◽  
Vol 1475 ◽  
Author(s):  
Miguel O. Prado ◽  
Diana Lago ◽  
Diego S. Rodriguez
Keyword(s):  
Viscous Flow ◽  
Glass Powder ◽  
Glass Particle ◽  
Aluminosilicate Glass ◽  
Powder Size ◽  
Particle Volume ◽  
Sintering Kinetics ◽  
Nucleation Sites ◽  
Yttrium Disilicate ◽  
Kinetics Of

ABSTRACTYttrium aluminosilicate (YAS) glasses have been proposed as host matrices for the immobilization of radioactive elements. In addition, yttrium has been used to simulate actinides [1]. It is well known that these glasses are resistant to water corrosion and exhibit high Tg and good mechanical properties [2]. As shown in [3], on heating, yttrium disilicate and mullite / sillimanite crystals grow from the pre-existing nucleation sites on the surface, until each glass particle volume is fully crystallized (volume-homogeneous nucleation was not observed), decreasing the glassy surface available for sintering by viscous flow. Sintering takes place simultaneously, by viscous flow but competes with surface crystallization; thus, if thermal treatment is not carefully designed a vitroceramic is obtained. In this paper we study the isothermal sintering kinetics of a YAS glass-powder-size distribution and non-isothermal sintering kinetics at 1, 3, 5, 10 and 15 K/min of two YAS glass-powder-size distributions. From the experimental evidence obtained, and crystallization data from [3], we design a sintering procedure in order to achieve a high-density glass monolith with submicrometric crystalline phases.

Distribution Function Integral Method for Modeling Ferroelectric Devices

1999 ◽  
Author(s):  
Holger Goebel ◽  
Marc Ullmann ◽  
Guenther Schindler ◽  
Marcus Kastner
Keyword(s):  
Distribution Function ◽  
Integral Method
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