Lazaridis 1995 - J Aerosol Sal Vol 26 Suppl 1 pp 55795580...

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Unformatted text preview: J. Aerosol Sal, Vol. 26. Suppl 1. pp. 55795580, 1995 P Elsevier Science Ltd ergamon Printed in Great Britain 0021v8502/95 $9.50 + 0.00 Resuspension of small particles by turbulent flow Mihalis Lazaridis and Yannis Drossinos Safety Technology Institute Joint Research Centre 1-21020 Ispra (VA), Italy March 27, 1995 Abstract A resuspension model is developed and applied to the resuspension of a sparse monolayer of spherical particles from a stainless steel surface. The particle-surface interaction potential is calculated from a microscopic model based on the Lennard-Jones intermolecular potential; both the attractive and the repulsive parts of the intermolecular potential are considered. The natural frequency of vibration of a particle on a surface and the depth of the potential well are expressed in terms of microscopic material parameters. The present model is an extension of a previous developed resuspension model where the influence of the fluid flow on the adhesive potential is recognized. Surface roughness that leads to a. spread and decrease of the adhesive forces has been included in the present model. The predictions of the present model are in good agreement with available experimental data for A1203 and Cd particles. 1 Introduction Resuspension of particles due to turbulent fluid flow is an important phenomenon in the atmosphere and industrial processes. In the nuclear industry an important area is the recirculation of gas flows as found in gas-cooled nuclear reactors. During a postulated severe reactor accident in a Light Water Reactor fission product aerosols can deposit and resuspend repeatedly in the primary circuit and containment. Resuspension can have a. strong effect on the timing and magnitude of the source to the containment and the environment. In the present work we develop a microscopic model for the particle-surface adhesion forces, which is based on the Lennard—Jones intermolecular interaction. We take into account both the attractive (van der Waals interaction) and the repulsive part of the potential and from that we calculate the natural frequency of vibration of a particle attached to a surface and the depth of the adhesive potential well. These parameters are needed to calculate the resuspension rate of particles exposed an external turbulent flow because the particle is bound to the surface by a potential. The natural frequency depends on the size, composition of the particle and the flow velocity. The detachment flow velocity in this approach is much lower than the threshold velocity predicted by force balance models. In the calculations we use values for the turbulent energy spectrum based both experimental correlations and on theoretical calculations. The use of a microscopic model to calculate the adhesive potential based on the Lennard-J ones pair potential has the advantage that the resulting sphere—particle and particle-particle interaction potential may be used in a molecular dynamics or Monte Carlo simulation of resuspension. Fur- thermore, the model can be used in the development of a multilayer resuspension model, where the nearest neighbor interactions between different deposit layers are be considered. 2 Adhesive potential In the present study we make use a microscopic theory for the interaction of a particle with a surface and the well known Lennard-Jones potential is used to describe the pairwise interaction between $579 8580 M. LAZARIDIS and Y. DROSSINOS two molecules. For the interaction between two macroscopic bodies we follow the approach first introduced by Hamaker [2], in which the assumption of pairwise additivity of intermolecular inter- actions is used. In calculating the interaction potential between a macroscopic spherical particle and a surface We integrate the interactions, both attractive and repulsive, of all pairs of molecules. We use both the attractive and repulsive part of the potential in order to calculate the minimum distance of approach between the particle and the surface, the depth of the potential well, as well as the natural frequency of vibration of the particle on the surface. Therefore we can obtain infor~ mation on the adhesive parameters of the particles on a surface based on microscopic parameters, which may used to calculate the resuspension rate. The interaction energy of a sphere with radius TP and a flat surface at distance r can be expressed as [3] : V(r) = —%Cu + B05 (1) where the constant A is the well known Hamaker constant, B is a constant depending on the Lennard-Jones parameters and densities of the sphere and the surface, Ca and 0;, are functions of particle radius and distance r. The closest approach distance can be found from the first derivative of the potential and the natural frequency of vibration (up) is given by —ld2V(T)]1/2 M (2) up:[m where m is the particle mass. 3 Resuspension model The model that we used in the present model is an extension of the work done by Reeks et a1. [4]. The model is applied to the resuspension of a monolayer of particles from a surface. The attractive potential between a particle and a surface is calculated with the use of a microscopic model, from which we can obtain the natural frequency of vibration and the depth of the potential barrier. The particle is bound to the surface by the potential and the fluid flow influences the motion of the particle by transferring energy to it. The particle can be resuspended when it has received enough energy from the turbulent part of the flow to escape from the potential well. The resuspension rate J has been calculated in the case of resonant energy transfer from the fluid [4] in terms of the height of the potential Q and the average potential energy of particles < U > in the potential well, J : ‘—:—:§exp(—-———-——_2 <QU>) (3) where cup is the natural frequency of vibration of a particle on a surface. For the lift force we use two expressions, first one empirical relationship determined by Hall [1] and secondly a theoretical expression calculated by Saffman [5]. References [1] Hall D. 1994 CEGB Report RPTG/P(93)11 [2] Hamaker H. C. 1937 Physica 10 1058-1072 [3] Lazaridis M. and Y. Drossinos 1995, in preparation. [4] Reeks M. W., Reed J. and Hall D. 1988 J. Phys. D: Appl. Phys. 21 574-589 [5] Saffman P. G. 1965 J. Fluid Mech. 22 385—400 ...
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