Abstract
This paper investigates the effective energy reflectance of materials comprised of a continuous matrix embedded with fine-scale particles of different electric permittivity and magnetic permeability. The specific objective is to determine under what conditions will increasing the particulate volume fraction initially increase (or decrease) the overall reflectance from a pure-matrix base state and, with further increase in volume fraction, reverse the trend, i.e. decrease (or increase) the effective reflectance. The importance of this condition is that it indicates when the correlation of a specific level of reflectance to a specific volume fraction of particles may not be unique, even when the properties of the particles and matrix are fixed.
Similar content being viewed by others
References
Bale-Glickman, J., Selby, K., Saloner, D. and Savas, O. 2003. Physiological flow studies in exact-replica atherosclerotic carotid bifurcation. Proceedings of IMECE’03,2003 ASME International Mechanical Engineering Congress and Exposition. Washington, D.C. 16-21.
Bale-Glickman J., Selby K., Saloner D., Savas O. (2003). Experimental flow studies in exact-replica phantoms of atherosclerotic carotid bifurcations under steady Input conditions. J. Biomech. Eng 125: 38-48
Beckwith, S., Henning, T. & Nakagawa, Y. 2000. Dust Particles in Protoplanetary Disks. Protostars & Planets IVs, Mannings, V. & Boss, A.P. & Russell, S.S., editors, University of Arizona Press, Tuscon
Benz W. (2000). From dust to planets. Spatium 6: 3-14
Blum J., Wurm G. (2000). Impact simulations on sticking, restructuring, & fragmentation of preplanetary dust aggregates. Icarus 143: 138-146
Born, M. & Wolf, E. 2003. Principles of optics. 7th edition. Cambridge University Press.
Chan R.C., Chau A.H., Karl W.C., Nadkarni S., Khalil A.S., Shishkov M., Tearney G.J., Kaazempur-Mofrad M.R., Bouma B.E. (2004). OCT-based Arterial Elastography: Robust Estimation exploiting Tissue Biomechanics. Optics Express 12(19):4558-4572
Chau A.H., Chan R.C., Shishkov M., MacNeill B., Iftima N., Tearney G.J., Kamm R.D., Bouma B., Kaazempur-Mofrad M.R. (2004). Mechanical Analysis of Atherosclerotic Plaques based on Optical Coherence Tomography. Annals of Biomedical Engineering 32(11): 1492-1501
Chokshi A., Tielens A.G.G.M., Hollenbach D. (1993). Dust Coagulation. The Astrophysical Journal. 407: 806-819
Chung J., Grigoropoulos C., Greif R. (1999). Infrared thermal velocimetry in MEMS-based fluid devices. Journal of Microelectromechanical Systems 12(3): 365-371
Cuzzi C.N., Dobrovolskis A.R., Champney J.M. (1993). Particle-gas dynamics in the midplane of a protoplanetary nebula. Icarus 106: 102-134
Dominik C., Tielens A.G.G.M. (1997). The physics of dust coagulation & the structure of dust aggregates in space. The Astrophysical Journal 480: 647-673
Khalil A.S., Chan R.C., Chau A.H., Bouma B.E., Kaazempur-Mofrad M.R. (2005). Tissue Elasticity Estimation with Optical Coherence Elastography: Toward Mechanical Characterization of In Vivo Soft Tissue. Annals of Biomedical Engineering 33(11):1631-1639
Luo L., Dornfeld D.A. (2001). Material removal mechanism in chemical mechanical polishing: theory and modeling. IEEE Transaction: Semiconductor Manufacturing 14(2): 112- 133
Luo L., Dornfeld D.A. (2003). Effects of abrasive size distribution in chemical-mechanical planarization: modeling and verification. IEEE Transaction: Semiconductor Manufacturing 16: 469-476
Luo L., Dornfeld D.A. (2003). Material removal regions in chemical mechanical planarization for sub-micron integration for sub-micron integrated circuit fabrication: coupling effects of slurry chemicals, abrasive size distribution, and wafer-pad contact area. IEEE Transaction: Semiconductor Manufacturing 16: 45-56
Luo, L. and Dornfeld, D. A. 2004. Integrated modeling of chemical mechanical planarization of sub-micron IC fabrication. Springer-Verlag.
Zohdi T.I. (2004). A computational framework for agglomeration in thermo-chemically reacting granular flows. Proceedings of the Royal Society 460: 3421-3445
Zohdi T.I. (2006a). On the optical thickness of disordered particulate media. Mechanics of Materials 38: 969-981
Zohdi, T. I. 2006b. Computation of the coupled thermo-optical scattering properties of random particulate systems. Computer Methods in Applied Mechanics & Engineering. Available at: http://www.sciencedirect.com/science/journal/00457825
Zohdi T.I., Kuypers F.A. (2006). Modeling and rapid simulation of multiple red blood cell light scattering. Proceedings of the Royal Society Interface 3(11): 823-831
Zohdi, T. I. 2007. Introduction to the modeling and simulation of particulate flows. SIAM (Society for Industrial and Applied Mathematics).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dirksen, F., Zohdi, T.I. On Effective Energy Reflectance of Particulate Materials. Int J Fract 145, 341–347 (2007). https://doi.org/10.1007/s10704-007-9137-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-007-9137-7