Capture Brownian diffusions

The mechanism of particle capture by depth filtration is more complex than for screen filtration. Simple capture of particles by sieving at pore constructions in the interior of the membrane occurs, but adsorption of particles on the interior surface of the membrane is usually at least as important. Figure 2.34 shows four mechanisms that contribute to particle capture in depth membrane filters. The most obvious mechanism, simple sieving and capture of particles at constrictions in the membrane, is often a minor contributor to the total separation. The three other mechanisms, which capture particles by adsorption, are inertial capture, Brownian diffusion and electrostatic adsorption [53,54], In all cases, particles smaller than the diameter of the pore are captured by adsorption onto the internal surface of the membrane. 

Figure 2.34 Particle capture mechanism in filtration of liquid solutions by depth microfilters. Four capture mechanisms are shown simple sieving electrostatic adsorption inertial impaction and Brownian diffusion...

The second mechanism is capture by Brownian diffusion, which is more of a factor for smaller particles. Small particles are easily carried along by the moving fluid. However, because the particles are small, they are subject to random Brownian motion that periodically brings them into contact with the pore walls. When this happens, capture by surface adsorption occurs. 

In the case of Brownian diffusion and interception, particle capture is enhanced by London attractive forces and reduced by electrostatic double layer repulsive forces. 

Particle capture occurs through an interception mechanism. Because of the strong electrostatic forces operating in the experimental system, the contribution of Brownian diffusion to particle capture is negligible. 

For a consideration of wet deposition mechanism it is useful to make a distinction between processes transferring material to cloud droplets before they begin their descent as a raindrop, known collectively as rain-out and processes transferring material to falling raindrops known as washout, There are five mechanisms [8] by which particulate and gaseous compounds may be captured by cloud or rain drop diffusiophoresis, brownian diffusion, impact and interception, solution and oxidation of gaseous species (notably SO2 and NO2) and the cloud condensation nuclei (CCN) pathway. 

Assuming for the time being that cloud droplets are stationary, then particles are captured by Brownian diffusion. The collection of particles by a falling drop will be... 

Following Spielman and the aims of this book, our discussion is confined to the capture of particles in liquid suspension from low-speed laminar flows, where the particles are generally small compared with the collector. The two principal transport mechanisms are (a) Brownian diffusion for submicrometer-size particles, and (b) interception of micrometer-size, nondiffusing, inertia free particles with the collector as a consequence of geometrical collision due to particles following fluid streamlines. Inertial impaction, which can be important for gas-borne particles, is usually unimportant for particles in liquids, because the particle—fluid density difference is smaller and the higher viscosity of liquids resists movement relative to the fluid (Spielman 1977). In this section we shall... 

Assuming for the time being that cloud droplets are stationary, then particles are captured by Brownian diffusion. The collection of particles by a falling drop will be discussed when we consider wet deposition in Chapter 20. The collection coefficient K Dp, x) can then be estimated by (12.57). Let us estimate this collection rate assuming that the cloud has a liquid water content of 0.5 g m and that all drops have diameters of 10 /im, resulting in a number concentration of Nj = 955 cm For such a monodisperse droplet population (15.95) simplifies to... 

We assume that deposition on the sphere is ideal, that is, each collision of a particle with the sphere results in the particle being captured. The factor of Brownian diffusion Dj,r = kTwhere Oj, is the particle s radius, is much smaller than the factor of molecular diffusion, therefore the Peclet diffusion number is Peo = Ua/Dhr 1- By virtue of this inequality (see Section 6.5), the diffusion flux of particles toward the sphere can be found by solving the stationary equation of convective diffusion with a condition corresponding to a thick or thin diffusion-boundary layer. Particles may then be considered as point-like, and the diffusion equation will become ... 

Many studies indicate that aerosols tend to be more readily scavenged by rainout processes such as condensation than by the washout process, such as capture by falling droplets. Thus sulphate and nitrate aerosols are thought by some to act as cloud condensation nuclei. In addition particulate material containing sulphate and nitrate are captured by cloud droplets via impaction, interception and Brownian diffusion. 

X 10 cm/sec to 1.2 x 10 cm/sec), the contributions of other mechanisms like Brownian diffusion and particle inertia to total capture can be neglected in comparison to that of the mechanism of direct interception. 

Single-collector efficiency for monolayer filtration vreis estimated with the expression developed by Rajagopalan and Tien [128], obtained by the combination of the trajectory analysis of a spherical particle in the vicinity of a spherical collector with the contribution of the Brownian diffusion. For fine-fine capture step, filtration becomes driven by the fine-fine interaction forces yielding a multilayer deposit for which the filter coefficient no longer remains constant in time. The change of the filter coefficient as a function of the specific deposit was estimated using the correlation developed by Tien et al. [129]. Extra information about trickle-bed deep-bed filtration model is given in Iliuta and Larachi [130] and Iliuta et al. [119]. 

Diffusion effect The capture of particles due to Brownian motion. 

Fig. 9.3. Acid mist removal candle filter being installed atop a stainless steel H2SO4 making tower. It is one of many. Exiting gas passes inward through the candle fabric and out the top of the candle - then out of the tower. The acid mist is caught in the candle fabric by impact, diffusion and Brownian forces (Brink, 2005 Friedman and Friedman, 2004 Lee and Byszewski, 2005 Ziebold and Azwell, 2005). The large total area of the candles gives a low gas velocity through the fabric, which allows 99+% capture of the mist. The captured mist trickles down the fabric and drips back into the tower or into collection pipes (Outokumpu 2005).

In the model of Agarwal and Khakhar [57] the polymer molecules are taken to be bead-rod chains with the hydrodynamic forces concentrated at the beads. The chains may bend about a bead, and a spring force acts to restore the chain to is equilibrium conformation, which is a straight chain. The connecting rods are inextensible. The system is confined to a plane, and the chains diffuse due to Brownian forces resisted by hydrodynamic forces. Hydrodynamic forces resulting from an imposed shear flow deform and orient the molecules. Two chains may react and combine to form a longer chain if the chain ends approach to within the capture radius (a) and if the angle between the chains is less than the critical value (0 ). The reaction is assumed to be very fast (kfj k j ) so that every collision that satisfies the above criteria results in... 

We treat first the capture by a collector of submicrometer-size particles undergoing Brownian motion in a low-speed flow of velocity U. The collector is taken to be a sphere of radius a and is assumed to be ideal in that all of the particles that impinge on its surface stick to it (Fig. 8.3.1). Because the Brownian particle diffusivities D - kTIGiruap, where is the particle radius, are typically about a thousand times smaller than the molecular diffusivities, the diffusion Peclet number (Ua/D) is generally very large compared with unity. The diffusive flux of the particles to the surface is therefore governed by the steady, convective, diffusion boundary layer equation, with the particles treated as diffusing points. ... 

It is widely accepted that the fibres in the filter fabric capture the dust particles by one of several mechanisms, these being identified as inertial impaction, interception,diffusion (Brownian motion) and electrostatic forces (see Rg. 7.1). Inertial impaction occurs when particles are of sufficient mass and bulk as to leave the gas stream and make a direct impact on a fibre in the filter. 

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