An Efficient Network Model for Determining the Effective Thermal Conductivity of Particulate Thermal Interface Materials
ABSTRACT Particulate composites are commonly used in microelectronics applications. One example of such materials is thermal interface materials (TIMs) that are used to reduce the contact resistance between the chip and the heat sink. The existing analytical descriptions of thermal transport in particulate systems do not accurately account for the effect of interparticle interactions, especially in the intermediate volume fractions of 30%80%. Another crucial drawback in the existing analytical as well as the network models is the inability to model size distributions (typically bimodal) of the filler material particles that are obtained as a result of the material manufacturing process. While fullfield simulations (using, for instance, the finite element method) are possible for such systems, they are computationally expensive. In the present paper, we develop an efficient network model that captures the physics of interparticle interactions and allows for random size distributions. Twenty random microstructural arrangements each of Alumina as well as Silver particles in Silicone and Epoxy matrices were generated using an algorithm implemented using a Java language code. The microstructures were evaluated through both fullfield simulations as well as the network model. The fullfield simulations were carried out using a novel meshless analysis technique developed in the author's (GS) research [26]. In all cases, it is shown that the random network models are accurate to within 5% of the full field simulations. The random network model simulations were efficient since they required two orders of magnitude smaller computation time to complete in comparison to the full field simulation.

 "A comparison of ZehnerSchlunder model (1970) with other models (Maxwell, 1865; Rayleigh, 1892; Meredith and Tobias, 1915; Woodside, 1958) with the measurements of Kanuparthi et al. (2008) at k2 / k1 = 125 is indicated in Fig. 3. The data corresponds to aluminum particles in a silicone matrix (kl = 0.2 W/m.K). "
Article: On the Effective Thermal Conductivity of Porous Packed Beds with Uniform Spherical Particles
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ABSTRACT: Point contact models for the effective thermal conductivity of porous media with uniform spherical inclusions have been briefly reviewed. The model of Zehner and Schlunder (1970) has been further validated with recent experimental data over a broad range of conductivity ratio from 8 to 1200 and over a range of solids fraction up to about 0.8. The comparisons further confirm the validity of ZehnerSchlunder model, known to be applicable for conductivity ratios less than about 2000, above which area contact between the particles becomes significant. This validation of the ZehnerSchlunder model has implications for its use in the prediction of the effective thermal conductivity of water frost (with conductivity ratio around 100) which arises in many important areas of technology.Journal of Porous Media 01/2011; 14(10). DOI:10.1615/JPorMedia.v14.i10.70 · 0.47 Impact Factor 
 "Both parameters are set to 0.5 to best match experimentallyobtained thermal conductivity values. Note that the same values of e and v are reported for metallic filler particles within the matrix in [17] where the parameter a ) 1 (similar to the dry soil condition as the ratio between thermal conductivity of mineral and air is much greater than the unity). Fig. 6 presents the 3D random thermal conductance web and temperature distribution for Test ID P4 at the end of successive iterations . "
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ABSTRACT: This paper describes a threedimensional random network model to evaluate the thermal conductivity of particulate materials. The model is applied to numerical assemblies of polydispersed spheres generated using the discrete element method (DEM). The grain size distribution of Ottawa 20–30 sand is modeled using a logistic function in the DEM assemblies to closely reproduce the gradation of physical specimens. The packing density and interparticle contact areas controlled by confining stress are explored as variables to underscore the effects of micro and macroscales on the effective thermal conductivity in particulate materials. It is assumed that skeletal structure of 3D granular system consists of the web of particle bodies interconnected by thermal resistor at contacts. The interparticle contact condition (e.g., the degree of particle separation or overlap) and the particle radii determine the thermal conductance between adjacent particles. The Gauss–Seidel method allows evaluation of the evolution of temperature variation in the linear system. Laboratory measurements of thermal conductivity of Ottawa 20–30 sand corroborate the calculated results using the proposed network model. The model is extended to explore the evolution of thermal conduction depending on the nucleation habits of secondary solid phase as an anomalous material in the pore space. The proposed network model highlights that the coordination number, packing density and the interparticle contact condition are integrated together to dominate the heat transfer characteristics in particulate materials, and allows fundamental understanding of particlescale mechanism in macroscale manifestation.Computers and Geotechnics 11/2010; 37(7):991998. DOI:10.1016/j.compgeo.2010.08.007 · 1.65 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: A critical need in developing thermal interface materials (TIMs) is an understanding of the effect of particle/matrix conductivities, volume loading of the particles, the size distribution, and the random arrangement of the particles in the matrix on the homogenized thermal conductivity. Commonly, TIM systems contain random spatial distributions of particles of a polydisperse (usually bimodal) nature. A detailed analysis of the microstructural characteristics that influence the effective thermal conductivity of TIMs is the goal of this paper. Random microstructural arrangements consisting of lognormal sizedistributions of alumina particles in silicone matrix were generated using a dropfallshake algorithm. The generated microstructures were statistically characterized using the matrixexclusion probability function. The filler particle volume loading was varied over a range of 40%55%. For a given filler volume loading, the effect of polydispersivity in the microstructures was captured by varying the standard deviation(s) of the filler particle size distribution function. For each particle arrangement, the effective thermal conductivity of the microstructures was evaluated through numerical simulations using a network model previously developed by the authors. Counter to expectation, increased polydispersivity was observed to increase the effective conductivity up to a volume loading of 50%. However, at a volume loading of 55%, beyond a limiting standard deviation of 0.9, the effective thermal conductivity decreased with increased standard deviation suggesting that the observed effects are a tradeoff between resistance to transport through the particles versus transport through the interparticle matrix gap in a percolation chain.IEEE Transactions on Components and Packaging Technologies 07/2009; DOI:10.1109/TCAPT.2008.2010502 · 0.96 Impact Factor