Aerosol and Fluid Motion

In our discussion so far, we have assumed that the aerosol particles are suspended in a stagnant fluid. In most atmospheric applications, the air is in motion and one needs to describe simultaneously the air and particle motion. Equation (9.36) will be the starting point of our analysis. 

Actually (9.36) is a simplified form of the lull equation of motion, which is (Hinze 1959) 

Neglecting the gravitational force and particle inertia leads to the zero-order approximation that v u that is, the particle follows the streamlines of the airflow. This approximation is often sufficient for most atmospheric applications, such as turbulent 

FIGURE 9.12 Schematic diagram of particles and fluid motion around a cylinder. Streamlines are shown as solid lines, while the dashed lines are aerosol paths. 

A detailed treatment of particle flow around objects, in channels of various geometries, and so on, is beyond the scope of this book. Treatments are provided by Fuchs (1964), Hinds (1999), and Flagan and Seinfeld (1988). We will focus our analysis on a few simple examples demonstrating the important concepts. 

The trajectory of the particle is governed by (8.37). Neglecting gravity, the jc and y components of the equation of motion are after the turning point 

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It should be noted that throughout this chapter, the words model and simulation are used to mean a procedure that solves mathematical equations to represent reality. This may be a less common definition of the word model for some readers. However, since the equations governing aerosol and fluid motion are well established and represent reality exactly, such models have the ability to represent reality exactly, at least in principle. 

Thus there is a lai e discrepancy between the theoretical predictions of the collision efficiency for aerosol coagulation by differential sedimentation (taking into account inter-particie fluid motion) and experimental measurements for coagulation by turbulent shear in aqueous suspensions. We do not know whether this discrepancy is due to the ba.sic difference in the coagulation mechanisms (differential sedimentation vs. turbulent shear), different phenomena operating in the different fluid media, or some other as yet unidentified effect. 

In contrast with two-phase bubble-containing fluids, aerosols, and emulsions, foam has a least three phases. Along with gas and the free continuous liquid phase, foam contains the so-called skeleton phase, which includes adsorption layers of surfactants and the liquid between these layers inside the capsule envelope. The volume fraction of the skeleton phase is extremely small even compared with the volume fraction of the free liquid. Nevertheless, this phase determines the foam individuality and its structure and rheological properties. It is the frame of reference with respect to which the diffusion motion of gas and the hydrodynamic motion of the free liquid can occur under the action of external forces and internal inhomogeneities. At the same time, the elements of the skeleton phase themselves can undergo strain and relative displacements as well as mass exchange with the other phases (solvent evaporation and condensation and surfactant adsorption and desorption). 

Particles as tracer of fluid motion - Particles are less than 4 Xm, their motion is representative of fluid motion. Aerosol dynamics may include Brownian motion and agglomeration. 

Chapter 5 considers the stabiUty of fluid interfaces, a subject pertinent both to the formation of emulsions and aerosols and to thdr destruction by coalescence of drops. The closely related topic of wave motion is also diseussed, along with its implications for mass transfer. In both cases, boundary eonditions applicable at an interface are derived—a significant matter because it is through boundary conditions that interfacial phenomena influence solutions to the governing equations of flow and transport in fluid systems. 

The concentration distribution of aerosol particles in a stagnant fluid in which the particles are subject to Brownian motion and in which there is a velocity v, in the -z direction is described by... 

Consider an aerosol particle in fluid flow as shown in Fig. 12. The equation of motion of a spherical aerosol particle of mass tn and diameter d is given as... 

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