Effective medium model for two-dimensional periodic arrays of carbon nanotubes

2010 ◽  
Author(s):  
Igor S. Nefedov ◽  
Sergei A. Tretyakov ◽  
Dmitry N. Chigrin
Keyword(s):  
Carbon Nanotubes ◽  
Effective Medium ◽  
Two Dimensional ◽  
Periodic Arrays ◽  
Effective Medium Model ◽  
Medium Model

Microscopic Effective Medium Model for Thermal Conductivity of Two Dimensional Nano-Porous and Micro-Porous Media

2005 ◽  
Author(s):  
Ravi Prasher ◽  
David Song
Keyword(s):  
Thermal Conductivity ◽  
Heat Flow ◽  
Porous Materials ◽  
Diffusion Approximation ◽  
Three Dimensional ◽  
Effective Medium ◽  
Two Dimensional ◽  
Effective Medium Model ◽  
Medium Model ◽  
Cylindrical Pores

Two-dimensional Nano-porous (NP) and micro-porous (MP) materials are currently used in a variety of applications which require the knowledge of the thermal conductivity (k). In NP and MP materials, two pertinent length scales determine the phonon thermal conductivity: 1) the ratio of inter-pore distance, δ, and the mean free path (m.f.p.) of phonons, 1, 2) the ratio of the pore diameter, d, and the m.f.p. of phonons. This is schematically shown in Fig. 1. In the traditional diffusion-approximation (macroscopic models) based models (1 ≪ d, δ) for the thermal conductivity of porous materials, the effective thermal conductivity, keff, of the porous material for a given shape of the pores and direction of the heat flow is only a function of the volume fraction (φ) of the pores. Therefore, in the diffusion approximation, keff can be written as keff=kmf(φ)(1) where km is the thermal conductivity of the host medium. Our focus is on cylindrical pores. We only consider the heat flow in the transverse direction as shown in Fig. 1a. For example, if φ <40%, Maxwell-Garnett effective medium model (MG EMM) can be used. f(φ) for MG EMM is given by f(φ)=1−φ1+φ(2) Experimental data on two-dimensional micro-porous silicon made of cylindrical pores have shown that the macroscopic model given by Eq. (1) grossly over predicts keff of the porous materials. In MP and NP materials, the phonon transport is ballistic in nature because of the dominant scattering of phonons from the pore boundaries. Ballistic transport becomes dominant when m.f.p is comparable to or larger than d and δ. In this regime, the Boltzmann Transport Equation (BTE) must be solved without invoking the diffusion approximation. Solving the BTE for such a complex network of pores is a challenging task, and a few previous works exist where BTE was solved numerically under various simplifying assumptions regarding the geometry and the arrangement of the pores. Both of these investigations assumed rectangular pores for two-dimensional composite or cubical pores for three-dimensional composites; however, in reality, these pores are never so simple in their geometry. Typically, these pores are cylindrical in shape for two-dimensional composites and nearly spherical in shape for three-dimensional composites. The solution of BTE for the multitude of non-planar pores, although achievable, will be a very tedious task.

An effective medium model for elastic waves in microcrack damaged media

2008 ◽  
Vol 75 (14) ◽  
pp. 4104-4116 ◽  
Author(s):  
Dan Su ◽  
Michael H. Santare ◽  
George A. Gazonas
Keyword(s):  
Elastic Waves ◽  
Effective Medium ◽  
Effective Medium Model ◽  
Medium Model

Rock Physics Diagnostics and Effective Medium Model of Boonsville Field

ICIPEG 2014 ◽  
2015 ◽  
pp. 313-321
Author(s):  
Ida Ayu Purnamasari ◽  
Wan Ismail Wan Yusoff ◽  
Chow Weng Sum
Keyword(s):  
Rock Physics ◽  
Effective Medium ◽  
Effective Medium Model ◽  
Medium Model

scholarly journals Quantification of gas hydrate saturation and morphology based on a generalized effective medium model

2020 ◽  
Vol 113 ◽  
pp. 104166
Author(s):  
Haojie Pan ◽  
Hongbing Li ◽  
Jingyi Chen ◽  
Michael Riedel ◽  
Melanie Holland ◽  
...  
Keyword(s):  
Gas Hydrate ◽  
Effective Medium ◽  
Effective Medium Model ◽  
Medium Model ◽  
Hydrate Saturation
Sign in / Sign up

Export Citation Format

Share Document