Diffuse reflection continuum theories

As expected from continuum theory, the friction and diffusion coefficients are replaced In Inhomogeneous fluid by tensors whose symmetry reflects that of the Inhomogeneous media. 

Griffiths, P.R. 8t Olinger, J.M., Continuum Theories in Diffuse Reflection. In Chalmers, J.M. 8c Griffiths, P.R. (eds) Handbook of Vibrational Spectroscopy, Sampling Techniques, Volume 2 John Wiley 8t Sons Chichester, 2002 pp. 1125-1139. 

P. R. Griffiths and D. J. Dahm, Continuum and Discontinuum Theories of Diffuse Reflections, in Handbook of Near-Infrared Analysis, 3rd ed., ed. D. A. Burns and E. W. Ciurczak, Taylor and Francis, Boca Raton, FL, 2008. 

What for the case of small particles is called backward and forward scatter is, for the case of particles with large, flat surfaces, the sum of reflection and transmission. For infinitesimally small particles, continuum theories of diffuse reflection may be applied. As particles get larger, it becomes more likely that the terms for geometrical optics will be applied and discontinuum theories are more relevant. 

The temperature instability of a two-dimensional reactive fluid of N hard disks bounded by heat conducting walls has been studied by molecular dynamics simulation. The collision of two hard disks is either elastic or inelastic (exothermic reaction), depending on whether the relative kinetic energy at impact exceeds a prescribed activation barrier. Heat removal is accomplished by using a wall boundary condition involving diffuse and specular reflection of the incident particles. Critical conditions for ignition have been obtained and the observations compared with continuum theory results. Other quantities which can be studied include temperature profiles, ignition times, and the effects of local fluctuations. 

Griffiths, P.R. and Olinger, J.M. (2002) Continuum theory of diffuse reflection. In Handbook of Vibrational Spectroscopy, Vol. 2 (eds J.M. Chalmers and P.R. Griffiths), John Wiley Sons, Ltd, Chichester, pp. 1125-1139. [The paper entitled Bin Beitrag ztir Optik der Farbanstriche by Kubelka, P. and Munk, F. (1931) was published in Z. 

Considerable effort has been made during the last two decades to develop a "microscopic" description of gas diffusion in polymers, which is more detailed than the simplified continuum viewpoint of Fick s laws. It has been known for a long time that the mechanism of diffusion is very different in "rubbery" and "glassy" polymers, i.e., at temperatures above and below the glass-transition temperature, Tg, of the polymers, respectively. This is due to the fact that glassy polymers are not in a true state of thermodynamic equilibrium, cf. refs. (1,3,5,7-11). Some of the models and theories that have been proposed to describe gas diffusion in rubbery and glassy polymers are discussed below. The models selected for presentation in this review reflect only the authors present interests. 

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