Hydrodynamic dispersion on self-similar structures : a Laplace space renormalization group approachReport as inadecuate

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Abstract : A general method for calculating the properties of the Residence Time Distribution RTD of a fluid flowing though a self-similar network, with or without stagnation trapping effects, in the high Péclet number limit is developed. The renormalization procedure adopted yields the Laplace transform of the Residence Time Distribution and allows one to calculate its time moments. The incidence of the connectivity of the medium on dispersion is discussed. The fractal dimension does not appear explicitly in the dispersion properties of the network. Geometrical dispersion is shown to result from the difference of pathlengths offered to the fluid in the generating pattern of the network. The dispersion front is strongly non-Gaussian and presents several maxima short circuits in some extreme cases. An approximate expression for the dispersion front is derived when the distribution of pathlengths in naroow. In the latter situation, a dispersion coefficient can be defined, and it is characterised by two parametres, γ and 1-ftm, which represent respectively the intensity of the disorder or the ability to mixing related to geometric dispersion, and the characteristic hold-up time of a tracer particle in the stagnation phase supposed to occupy a fraction 1-f of the volume and to be uniformly distributed in the medium. We also discuss the conditions of moments convergence and the long time aymptotic form of the RTD.

Author: Emmanuel Villermaux Daniel Schweich

Source: https://hal.archives-ouvertes.fr/


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