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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
121020 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 particlesurface interaction potential
is calculated from a microscopic model based on the LennardJones 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 gascooled 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 particlesurface 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 LennardJ ones
pair potential has the advantage that the resulting sphere—particle and particleparticle 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 LennardJones 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
LennardJones 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 10581072 [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 574589
[5] Saffman P. G. 1965 J. Fluid Mech. 22 385—400 ...
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