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Behavior of suspended particles in a turbulent fluid
Author(s) -
Friedlander S. K.
Publication year - 1957
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690030318
Subject(s) - turbulence , particle (ecology) , mean squared displacement , mechanics , brownian motion , eddy diffusion , diffusion , displacement (psychology) , thermal diffusivity , turbulent diffusion , physics , thermodynamics , chemistry , psychology , oceanography , quantum mechanics , molecular dynamics , psychotherapist , geology
Heat and mass transfer and coagulation are considered as related to the mean‐square relative velocity between particle and fluid u R 2 and eddy diffusion as described by the mean‐square particle displacement, X p 2 . The mathematical methods used are similar to those employed in the early calculations of the Brownian motion. The mean‐square relative velocity is obtained as a function of particle characteristics, intensity of turbulence, and a fluid correlation coefficient. In the limiting case of equal particle and fluid density u R 2 = 0, and for very heavy particles u R 2 → u F 2 . A general expression for the eddy diffusivity is obtained is obtained which reduces to the same form as that of the fluid for the stationary state. However, the correlation coefficient to be used in the calculations depends on u R 2 . As a first approximation, it can be assumed that at a sufficiently long time from the introduction of the particles, fluid and particle diffusivities are equal. For short times after injection, the particle spread may be much less than that of the fluid. An illustrative calculation for the initial spreading of a jet of suspended particles is offered. In all cases an effort is made to organize the available experimental data within the framework of the theory.