Particle forces controlling motions

In gas-solid flows, flow patterns of both phases depend not only on the initial conditions and physical boundaries of the system but also on the mechanisms of momentum transfer or the interacting forces between the phases. The forces controlling the motions of particles may be classified into three groups (1) forces through the interface between fluid and particles, (2) forces due to the interactions between particles, and (3) forces imposed by external fields. Although interparticle forces and field forces do not directly change the course of the fluid motion, they may indirectly influence the motion via particle-fluid interactions. 

Molecules and their parts move incessantly and randomly at any temperature above 0 K. This chaotic movement is termed Brownian motion after another Scottish scientist, Robert Brown, who observed it in 1827 when looking at pollen particles suspended in water through a microscope. As a consequence of this phenomenon any attempt to push or pull molecules in a particular direction by the one-off application of a force (as opposed to the continuous application of a force) will be completely swamped by the random background motion of the environment. In many ways trying to control motion at the molecular level is like trying to play pool on a table on which hundreds of balls are moving constantly and randomly. As soon as we strike the cue ball it is immediately hit by others and proceeds on a random pathway irrespective of the direction that it was initially struck. 

Factors which adversely influence the separation of veiy fine particle systems are brownian motion and London forces. However, it is possible to counter these forces by the use of dispersants, temperature control, and so on. 

Cyclone Separators Cyclone separators are described in Chapter 7. Typically used to remove particulate from a gas stream, the gas enters tangentially at the top of a cylinder and is forced downward into a spiral motion. The particles exit the bottom while the gas turns upward into the vortex and leaves through the top of the unit. Pressure drops through cyclones are usually from 13 to 17 mm water gauge. Although seldom adequate by themselves, cyclone separators are often an effective first step in pollution control. 

The control of sedimentation is required to ensure a sufficient and uniform dosage. Sedimentation behavior of a disperse system depends largely on the motion of the particles which may be thermally or gravitationally induced. If a suspended particle is sufficiently small in size, the thermal forces will dominate the gravitational forces and the particle will follow a random motion owing to molecular bombardment, called Brownian motion. The distance moved or displacement, Dt, is given by ... 

The prime difficulty of modeling two-phase gas-solid flow is the interphase coupling, which deals with the effects of gas flow on the motion of solids and vice versa. Elgobashi (1991) proposed a classification for gas-solid suspensions based on the solid volume fraction es, which is shown in Fig. 2. When the solid volume fraction is very low, say es< 10-6, the presence of particles has a negligible effect on the gas flow, but their motion is influenced by the gas flow for sufficiently small inertia. This is called one-way coupling. In this case, the gas flow is treated as a pure fluid and the motion of particle phase is mainly controlled by the hydrodynamical forces (e.g., drag force, buoyancy force, and so... 

Sedimentation analyses must be carried out at concentrations which are sufficiently low for interactive effects between particles to be negligible so that their terminal falling velocities can be taken as equal to those of isolated particles. Careful temperature control (preferably to 0.1 deg K) is necessary to suppress convection currents. The lower limit of particle size is set by the increasing importance of Brownian motion for progressively smaller particles. It is possible however, to replace gravitational forces by centrifugal forces and this reduces the lower size limit to about 0.05 p,m. 

During the Langevin sections of the particle motion, the dynamics is controlled by the Langevin equation in the external force field F(x) = — (jc),... 

It is worth reviewing the forces that act and can be used for the manipulation of cells in microstructures. Random thermal (Brownian) motion becomes important for objects of cellular size and very important for smaller ones. The energy associated with this (about 2 x 10 21 J/particle, regardless of size at room temperature) provides a yardstick to which the strengths of the other forces can be compared. For instance, a perfectly controlled force of 10 15 N would be capable of holding a particle within about 2 pm of a target position. 

The characterization and control of electrostatic forces are of particular interest. Electrostatic forces depend on the electric charge and potential at the particle surfaces. When subjected to a uniform, unidirectional electric field E. charged colloidal particles accelerate until the electric body force balances the hydrodynamic drag force, so that the particles move at a constant average velocity v. This motion is known as electrophoresis, and v is the electrophoretic velocity. 

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