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Gas and Liquid Thermal Conductivity Measurements
Published in Natan B. Vargaftik, Lev P. Filippov, Amin A. Tarzimanov, Evgenii E. Totskii, Yu. A. Gorshkov, Handbook of Thermal Conductivity of Liquids and Gases, 2020
Natan B. Vargaftik, Lev P. Filippov, Amin A. Tarzimanov, Evgenii E. Totskii, Yu. A. Gorshkov
In the material partially transparent to infrared radiation, the heat is transmitted not solely due to conduction (i.e. molecular conductivity) but, to a certain extent due to photon diffusion (i.e. radiation). Each volume element dV absorbs part of the incident radiation and reradiates radiant energy. If the absorption coefficient is large enough, the photon diffusion mechanism will be similar to the pure conduction case, and the radiative heat flux will thus obey the Fourier law, based on the radiative “thermal conductivity” coefficient. As a consequence, the effective total thermal conductivity λeff will be additrvely composed of the contributions from the molecular λm and radiative λr conductivities () λeff=λm+λr,
Diffusion Modeling of Fluorescence in Tissue
Published in Mary-Ann Mycek, Brian W. Pogue, Handbook of Biomedical Fluorescence, 2003
Thomas J. Farrell, Michael S. Patterson
In a highly scattering medium the directions of the photons are randomized after a few scattering events. Under these conditions the energy radiance is only weakly anisotropic and the radiative transport equations can be simplified to a photon diffusion equation. The derivation of the diffusion equation has been presented in detail elsewhere [7]; here we present the important steps. We start by assuming that the energy radiance is only linearly anisotropic and can be expressed as a linear combination of the energy fluence rate and the energy flux as below. (
Effects of tissue surface curvature and incident light angle on diffuse correlation spectroscopy
Published in Journal of Modern Optics, 2019
Shu Zhang, Siyu Chen, Yuxin Liu, Yuhong Liu, Zuojun Tan
For DCS measurements, the utilized light source is usually a constant intensity continuous wave laser so that becomes independent of time. This implies that the time derivative on the left-hand side of Equation (1) is zero. Then, the CDE which unnormalized electric field temporal autocorrelation function satisfied is (10,25) where μa is the absorption coefficient, μs′ is the reduced scattering coefficient, D = 1/3μs′ is the photon diffusion coefficient, k0 is the wavenumber, and is the light source distribution. represent the mean-square displacement of the moving particles at time , and its form depends on the specific flow model adopted. The diffuse model has been found to fit the experimental data over a wide range of tissues using the form . Here, DB is the effective diffusion coefficient. A factor α is added to account for the fact that not all of the particles are ‘moving’ in the tissue. So α is the ratio of ‘moving’ particles to the total number of particles. The combined term αDB is referred to as the BFI in biological tissues. The most commonly used solution for equation (1) in a semi-infinite geometry is (26,27): where ρ is the source-detector (S-D) separation as Figure 1 showed. Besides,, , , , , and .
The time step constraint in radiation hydrodynamics
Published in Geophysical & Astrophysical Fluid Dynamics, 2020
Note that enters in both terms of equation (8). In the first term, it indeed plays the role of a photon diffusion velocity, but in the second term it represents a characteristic photon crossing velocity in an optically thin medium.