Microstructure of two‐phase random media. IV. Expected surface area of a dispersion of penetrable spheres and its characteristic function

1984 ◽  
Vol 80 (2) ◽  
pp. 878-880 ◽  
Author(s):  
S. Torquato ◽  
G. Stell
Keyword(s):  
Characteristic Function ◽  
Surface Area ◽  
Random Media ◽  
Two Phase ◽  
Penetrable Spheres

scholarly journals Simulated Microstructural Evolution and Design of Porous Sintered Wicks

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
Karthik K. Bodla ◽  
Suresh V. Garimella
Keyword(s):  
Thermal Conductivity ◽  
Particle Size ◽  
Transport Properties ◽  
Effective Thermal Conductivity ◽  
Surface Area ◽  
Microstructural Evolution ◽  
Ad Hoc ◽  
Three Dimensions ◽  
Two Phase ◽  
Sintering Kinetics

Porous structures formed by sintering of powders, which involves material-bonding under the application of heat, are commonly employed as capillary wicks in two-phase heat transport devices such as heat pipes. These sintered wicks are often fabricated in an ad hoc manner, and their microstructure is not optimized for fluid and thermal performance. Understanding the role of sintering kinetics—and the resulting microstructural evolution—on wick transport properties is important for fabrication of structures with optimal performance. A cellular automaton model is developed in this work for predicting microstructural evolution during sintering. The model, which determines mass transport during sintering based on curvature gradients in digital images, is first verified against benchmark cases, such as the evolution of a square shape into an area-preserving circle. The model is then employed to predict the sintering dynamics of a side-by-side, two-particle configuration conventionally used for the study of sintering. Results from previously published studies on sintering of cylindrical wires are used for validation. Randomly packed multiparticle configurations are then considered in two and three dimensions. Sintering kinetics are described by the relative change in overall surface area of the compact compared to the initial random packing. The effect of sintering parameters, particle size, and porosity on fundamental transport properties, viz., effective thermal conductivity and permeability, is analyzed. The effective thermal conductivity increases monotonically as either the sintering time or temperature is increased. Permeability is observed to increase with particle size and porosity. As sintering progresses, the slight increase observed in the permeability of the microstructure is attributed to a reduction in the surface area.

scholarly journals Rock-soil slope stability analysis by two-phase random media and finite elements

2018 ◽  
Vol 9 (6) ◽  
pp. 1649-1655 ◽  
Author(s):  
Yong Liu ◽  
Huawen Xiao ◽  
Kai Yao ◽  
Jun Hu ◽  
Hong Wei
Keyword(s):  
Stability Analysis ◽  
Finite Elements ◽  
Slope Stability ◽  
Random Media ◽  
Slope Stability Analysis ◽  
Soil Slope ◽  
Two Phase

Necessary and sufficient conditions for the two-point phase probability function of two-phase random media

2008 ◽  
Vol 464 (2095) ◽  
pp. 1761-1779 ◽  
Author(s):  
John A Quintanilla
Keyword(s):  
Random Media ◽  
Probability Function ◽  
Recent Literature ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Condition ◽  
Two Phase ◽  
Decomposition Formula ◽  
Positive Matrices ◽  
Necessary And Sufficient

Constructing realizations of random media with a specified two-point phase probability function S 2 has attracted considerable attention in the recent literature. However, little is known about conditions under which a prescribed S 2 is realizable. The only known necessary and sufficient condition, due to McMillan, involves a class of square matrices, called corner-positive matrices, about which almost nothing is known except their definition. As a result, McMillan's theorem has gone mostly unused in the literature for over 50 years. In this paper, we present a general decomposition formula for corner-positive matrices, which allows McMillan's theorem to be written in a significantly more tractable and testable form. We also connect McMillan's theorem with many known but heretofore unrelated necessary conditions on S 2 , extending many of these conditions.

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