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The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
Though initially thought to be a constant, recent work has shown that the entrainment coefficient varies with the local Richardson number. [9] Typical values for the entrainment coefficient are of about 0.08 for vertical jets and 0.12 for vertical, buoyant plumes while for bent-over plumes, the entrainment coefficient is about 0.6.
However, observations of the structure of real chemical detonations show a complex three-dimensional structure, with parts of the wave traveling faster than average, and others slower. Indeed, such waves are quenched as their structure is destroyed. [8] [9] The Wood–Kirkwood detonation theory can correct for some of these limitations. [10]
The simplest theory to predict the behaviour of detonations in gases is known as the Chapman–Jouguet (CJ) condition, developed around the turn of the 20th century. This theory, described by a relatively simple set of algebraic equations, models the detonation as a propagating shock wave accompanied by exothermic heat release.
Conduction heat flux q k for ideal gas is derived with the gas kinetic theory or the Boltzmann transport equations, and the thermal conductivity is =, -, where u f 2 1/2 is the RMS (root mean square) thermal velocity (3k B T/m from the MB distribution function, m: atomic mass) and τ f-f is the relaxation time (or intercollision time period ...
The cation transport number of the leading solution is then calculated as t + = z + c L A F I Δ t {\displaystyle t_{+}={\frac {z_{+}cLAF}{I\Delta t}}} where z + {\displaystyle z_{+}} is the cation charge, c the concentration, L the distance moved by the boundary in time Δ t , A the cross-sectional area, F the Faraday constant , and I the ...
Characterization of transport properties requires fabricating a device and measuring its current-voltage characteristics. Devices for transport studies are typically fabricated by thin film deposition or break junctions. The dominant transport mechanism in a measured device can be determined by differential conductance analysis.
Radiative transfer (also called radiation transport) is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission, and scattering processes. The equation of radiative transfer describes these interactions mathematically. Equations of ...