Elastic vibrations of a fiber due to impact of an aerosol particle and their influence on the efficiency of fibrous filters

Abstract

The excitation of sound vibrations of a cylindrical fine fiber due to the impact of a spherical aerosol particle is investigated. The equations describing the dynamics of impact are derived for an arbitrary shooting parameter. The coefficient of restitution is calculated, and its analytical approximation is obtained. It is shown, for the case of long fibers, that the coefficient of restitution depends upon a single parameter λ(c). The parameter λ(c) depends on the particle radial velocity component near the fiber surface, the mass of the particle, the density of the fiber, the modulus of elasticity, and the geometric parameters of the fiber and the particle. The inertial deposition of submicron aerosol particles on fine fibers in a filter is considered. The efficiency of filtration is studied as a function of the gas flow velocity. The existence of a critical flow velocity U(*), below which the losses of particle energy during collision have no effect on the efficiency, is demonstrated. For velocities higher than the critical velocity, the filtration efficiency is dependent on the mechanisms of nonelastic losses of the particle's energy. Its value can be significantly lower than that estimated when particle rebound effects are neglected. After they have rebounded, some particles are not able to attain the initial high velocities in the stream, thus depositing on neighboring fibers. The dynamics of these particles is investigated. For this case, it is shown that the filtration efficiency is dependent on the velocity distribution of the rebounded particles and that it increases with the packing density of fibers. A qualitative difference between the asymptotic behavior of a fiber and that of a flat plate is found long after the initial impulse.

Special features of filtration of heavy particles with fine-fiber materials

“…As has been noted in [1,2], under standard filtration con ditions, heavy metal particles with density ρ 1 1 0 g/cm 3 can rebound from fibers, in contrast to light particles with density ρ 1 ~ 1-2 g/cm 3 . This phenome non drastically decreases the filtration performance.…”

“…This phenome non drastically decreases the filtration performance. Works [1,2] dealt with the interaction of a single par ticle with a single fiber, which is valid at an initial stage of filtration through a low density fibrous medium. As a result of particle deposition onto fibers, each subse quent particle interacts with a fiber and particles that have been previously deposited onto it.…”

“…In this work, we con sider the simultaneous interaction of a fiber with sev eral particles and the possibility of the penetration of an aerosol particle through a trap formed by several fibers. The set of equations describing the interaction of a single heavy particle with a fiber [1] can be easily generalized to the case of several particles. It is assumed that the Stokes number, which characterizes the inertial properties of particles interacting with a fiber, is large, where C 1 is the Cunningham correction for gas slip on a particle surface [3], m is the particle mass, R is the particle radius, U is the velocity of an undisturbed flow before a filter, μ is the dynamic viscosity of the gas, and r 0 is the fiber radius.…”

“…By analogy with [1], we use the following somewhat modified expression for the van der Waals forces in numerical calculations:…”

The Effect of the Coefficient of Restitution to the Particle Collection Efficiency During the Process of Magnetic Filtration - Numerical Approach

“…There are no research reports for the effect of coefficient of restitution to the collection efficiency in magnetic filtration. The scientific research for the effect of coefficient of restitution in filtration mechanisms of fibrous filters is relatively limited (Chernyakov et al, 2011).…”