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Kinetic theory of gases. hide. The temperature of the ideal gas is proportional to the average kinetic energy of its particles. The size of helium atoms relative to their spacing is shown to scale under 1,950 atmospheres of pressure. The atoms have an average speed relative to their size slowed down here two trillion fold from that at room ...
The Vicsek model is a mathematical model used to describe active matter. One motivation of the study of active matter by physicists is the rich phenomenology associated to this field. Collective motion and swarming are among the most studied phenomena. Within the huge number of models that have been developed to catch such behavior from a ...
The atoms (or particles) that might stop a beam particle are shown in red. The magnitude of the mean free path depends on the characteristics of the system. Assuming that all the target particles are at rest but only the beam particle is moving, that gives an expression for the mean free path: ℓ=(σn)−1,{\displaystyle \ell =(\sigma n)^{-1},}
In physics (specifically, the kinetic theory of gases), the Einstein relation is a previously unexpected [clarification needed] connection revealed independently by William Sutherland in 1904, [ 1 ][ 2 ][ 3 ] Albert Einstein in 1905, [ 4 ] and by Marian Smoluchowski in 1906 [ 5 ] in their works on Brownian motion.
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
Viscosity depends strongly on temperature. In liquids it usually decreases with increasing temperature, whereas, in most gases, viscosity increases with increasing temperature. This article discusses several models of this dependence, ranging from rigorous first-principles calculations for monatomic gases, to empirical correlations for liquids.
An important prediction of Chapman–Enskog theory is that viscosity, , is independent of density (this can be seen for each molecular model in table 1, but is actually model-independent). This counterintuitive result traces back to James Clerk Maxwell , who inferred it in 1860 on the basis of more elementary kinetic arguments. [ 11 ]
Equation. The distribution of particle size changes in time according to the interrelation of all particles of the system. Therefore, the Smoluchowski coagulation equation is an integrodifferential equation of the particle-size distribution. In the case when the sizes of the coagulated particles are continuous variables, the equation involves ...