M. Fichman

A MODEL FOR TURBULENT DEPOSITION OF AEROSOLS

A model is developed for particle deposition to smooth surfaces in turbulent flow. The model is based on the calculation of particle trajectories in the wall region, using a detailed description of the flow in this region. The particle trajectories are derived from the equations of motion, including the lift force induced by the shear flow. This lift force, as is shown, is very important for particles with τ+ > 1, and clarifies the mechanism of deposition for these particles. The calculated particle flux compares favorably with the experimental data of various authors reported in the literature.

Adhesion moment model for estimating particle detachment from a surface

Abstract In this paper particle detachment from a surface by a hydrodynamic moment is analyzed. The detachment occurs when this moment exceeds the moment exerted on the particle by surface forces. An expression for the moment of surface forces is derived from the existing adhesion models. This moment is a product of the force acting on the particle and the variable contact radius, which decreases when the applied force increases. Accordingly, a condition for particle detachment from a smooth surface is obtained. In addition, particle detachment from a rough surface is considered. We show that a single asperity contact is similar to the contact of a particle with a smooth surface, but the detaching moment is reduced, because of the lower adhesion force and smaller contact radius. We also consider a particle in contact with two and three asperities, and obtain a condition for particle detachment from a rough surface. It is also shown that the hydrodynamic moment can cause particle detachment, while the hydrodynamic lift force is smaller than the adhesion force by several orders of magnitude. On the other hand, the lift force exceeds the weight of the particle. Hence, the detached particle is eventually removed from the surface by this force.

Particle behavior on surfaces subjected to external excitations

Abstract Oscillatory motion of a particle on a surface may be caused by mechanical vibrations of the surface, acoustic oscillations and shock waves in the surrounding fluid, and also by turbulent flow near the surface. Whatever the source of the excitation, it causes particle oscillations. The character of these oscillations depends on the direction and frequency of the external force, as well as on the stiffness of the bond. Several linear and nonlinear oscillation models are introduced and analyzed in order to show whether particle removal is possible for soft and hard particles on smooth and rough surfaces under various conditions. Application to existing methods of surface cleaning is discussed.

Mechanics of collisional motion of granular materials. Part 2. Wave propagation through vibrofluidized granular layers

According to numerous experimental observations and theoretical models vibrated layers composed of large granules behave like a solid plastic body. In contrast, in this study experimental data are presented that reveal that, for constant vibration amplitudes A ≥ 1 cm with the frequency ω increasing from zero, all layers pass through three vibrational states, with the respective behaviours being as of (i) a solid plastic body, (ii) a liquid, (iii) a gas. In the liquid-like vibrational state transverse waves propagating along the layer width were observed. These waves were shown to be gravitational resonance waves, with the corresponding frequencies well correlated by the known formula for incompressible liquids. In the gas-like vibrational state compression (shock) and expansion waves propagating across the layer height, were observed. A theoretical model for time-periodic collisional vibrational regimes was developed on the basis of the Euler-like equations of a granular gas composed of inelastic spheres. The model shows that the vibrational granular state (bed porosity, shock wave speed, granular pressure and kinetic energy) is inter alia governed by the dimensionless parameter V = ( A ω)/( h m g ) 1/2 , with g, h m being the gravitational acceleration and the height of the resting layer, respectively. This is in contrast with the previous studies, where the behaviour of vibrated granular layers was interpreted in terms of the dimensionless acceleration Δ = ( A ω 2 )/ g . The proposed model was tested by processing the data obtained from photographs of the particle distribution within vibrated layers. Theoretical predictions of the particle average concentration compared favourably with the experimental data. Other phenomena observed in vibrated granular layers include the formation of caverns, circulatory motion of granules and synchronized periodic motion of two adjacent vibrated layers of different widths. The importance of the observed phenomena in relation to various technological processes involving bulk materials (vibromixing, vibroseparation, etc.) is discussed.

Motion of spheroidal particles in vertical shear flows

The motion of non-neutrally buoyant prolate spheroidal particles in vertical shear flows is investigated. Using the generalized Faxen law, we calculate the hydrodynamic forces and moments acting on such inertial and inertialess particles, and their trajectories. The calculations are done for (i) freely rotating particles, and (ii) particles with orientations fixed by means of an external torque exerted by a strong orienting field. Inertial particles are found to migrate across the streamlines, and their trajectories differ considerably from those calculated for inertialess particles. Neutrally buoyant spheroids, inertial or not, which either freely rotate or have fixed orientations in shear flows, translate along the streamlines. Non-neutrally buoyant inertialess spheroids freely moving in simple shear flow translate along periodic trajectories with no net lateral drift. In contrast, inertial particles under similar flow conditions drift laterally toward locations characterized by higher local velocities ...

Resonance gas oscillations in closed tubes

The problem of gas motion in a tube closed at one end and driven at the other by an oscillating poston is studied theoretically. When the piston vibrates with a finite amplitude at the first acoustic resonance frequency, periodic shock waves are generated, travelling back and forth in the tube. A perturbation method, based on a small Mach number. M and a global mass conservation condition, is employed to formulate a solution of the problem in the form of two standing waves separated by a jump (shock front). By expanding the equations of motion in a series of a small parameter e = M ½ , all hydrodynamic properties are predicted with an accuracy to second-order terms, i.e. to e 2 . It is found that the first-order solution coincides with the previous theories of Betchov (1958) and Chester (1964), while additional terms predict a non-homogeneous time-averaged pressure along the tube. This prediction compares favourably with experimental results from the literature. The importance of the phenomenon is discussed in relation to different transport processes in resonance tubes.

Motion of diffusionless particles in vertical stagnation flows—II. Deposition efficiency of elongated particles

Abstract The motion of diffusionless elongated spheroidal particles in vertical stagnation flow over a flat collector of a finite size is modelled by calculating hydrodynamic forces and torques acting on a rotating and translating particle. Far above the deposition surface, particle motion is governed by its far upstream initial orientation and geometry. In close vicinity to the surface, where a viscous boundary layer prevails, particles are shown to settle down vertically due to gravity. It is found that the deposition flux of spheroidal particles which are uniformly distributed far above the surface is equal to the flux of spheres with the same settling velocity. On the other hand, randomly oriented spheroids discharged from a point source near the stagnation centerline tend to deposit in the peripheral part of the collector surface. This is in contrast with the comparable behavior of spherical particles, which deposit in a single point on the collector surface. Effects of the particle geometry, inertial and gravitational forces, initial orientation, and flow parameters on particle deposition are studied by computing particle trajectories. An approximate method is proposed for trajectory calculation, in which particle orientation is frozen and equal to the initial orientation. It is shown that trajectories of the equivalent spheres (having equal volume, or average hydrodynamic resistance, or sedimentation velocity) considerably differ from the true trajectories of spheroidal particles. Significance of the obtained results is discussed in relation to various types of stagnation flows involving aerosol deposition processes and, in particular, to clean room applications.

Effects of shear on particle motion near a surface—application to resuspension

Abstract The objective of the present work is to describe the effects of shear on small particle motion close to a horizontal surface. These effects can then be combined with those of turbulence for a complete description of particle dynamics near a stationary wall, yielding the conditions required for particle resuspension. The equations of motion are derived from the existing analytical expressions for the hydrodynamic forces of lift and drag acting on a small particle near a wall. In particular, the present solution utilizes the recent expression for the lift force of Cherukat and McLaughlin, obtained for a particle the center of which is located less than ten diameters from the wall. The equations are linearized using asymptotic expansion and solved analytically. It is shown that the shear-induced lift near a surface may be represented by two components. The first component depends on the relative particle velocity, while the second is due to the solid surface. In order to assess the accuracy of the linearized analytical solution, the full equations of particle motion are solved numerically by the Runge–Kutta method. The results show, in general, good agreement with the simplified linearized model. The linearized analysis makes it possible to determine whether particle motion for given flow conditions is stable or not. The condition of instability is derived in terms of particle size, flow shear rate, fluid viscosity, fluid and particle densities, and the distance from the wall. Unstable particle motion means that the particle escapes very rapidly from the surface into the main flow. It is shown both analytically and numerically that unstable particle motion depends on its initial velocity and distance from the wall. This result is important for the study of particle resuspension from surfaces in turbulent flows, where the particle moves inside the viscous sublayer and is subject to both shear and turbulent effects.

Motion of diffusionless particles in vertical stagnation flows—I. General model and deposition efficiency of spheres

Abstract Stagnation flows have been used in many studies as fair approximations of the flow field toward a flat collector, suitable for calculation of particle deposition rates. In particular, several analytical solutions for stagnation flows are widely used to model the flow over workbenches in clean rooms, and for calculating particle deposition on semiconductor wafers. It is shown that these solutions inadequately describe the flow velocity field either far from the collector surface or in its vicinity. Trajectories of diffusionless particles, calculated on the basis of these solutions, yield particle deposition efficiency as a quantity dependent on the particle initial distance (height) from the surface. In this study a physically realistic analytical model for the stagnation flow field over a finite flat obstacle is proposed. The flow field is approximated by a superposition of several basic solutions of potential and viscous stagnation flows. It provides an adequate description of the air velocity both far from and in the proximity of the surface. This flow field compares favorably with experimental data for air velocities collected in clean rooms over workbenches. The proposed flow field is incorporated in a general model of motion of nonspherical particles in vertical stagnation flows over a flat finite obstacle. This model is used to simulate trajectories of diffusionless aerosol particles, to revise theoretical results on deposition efficiencies of spherical particles obtained in previous studies, and to establish their range of validity. Trajectories of spherical particles are found to possess forms, enabling definition and calculation of height-independent deposition efficiency. Calculated deposition efficiencies are compared with experimental data on particle deposition, collected in clean rooms and during sampling. Comparable calculations for elongated particles are presented in a companion paper (Part II).

Effect of lift on the motion of aerosol particles

where h is the rate of shear. This study may be used to analyze particle motion in the viscous sublayer in turbulent flows, with application to particle deposition. The results show that the lift force has a strong effect on the deposition of aerosol particles from turbulent flows onto surfaces (Fichman et al, 1988). The motion of a particle in vertical flow is subject to centrifugal forces in addition to drag and lift. These centrifugal forces modify the condition for the instability of particle motion. The analysis of vertical flow assumes locally simple shear flow, and the criterion for instability is (Pnueli et al, 1997):