Particle settling phenomena

A particle falling freely in vacuum is subjected to a constant acceleration, and its velocity increases continuously. The velocity at any point depends only on the distance from the starting point, and is independent of the size and the density of the particle. Thus a heavy stone and a feather fall at exactly the same rate in an evacuated system. However, in the event of a particle falling in a fluid medium, there is resistance to this fall or movement. The resistance increases as the velocity of the particle increases, and this continues until the forces tending to accelerate the particle and the fluid resistance forces become equal. The particle is then said to have attained its terminal velocity it continues to fall, but with a uniform velocity. 

There are essentially three forces that act on a particle moving through a fluid. They are (i) the external force, gravitational or centrifugal (ii) the buoyant force, which acts parallel with the external force, but in the opposite direction and (iii) the drag force which appears 

In the general case, the direction of movement of the particle relative to the fluid may not be parallel with the direction of the external and buoyant forces, and the drag force then creates an angle with the other two. This is known as two-dimensional motion. In this situation, the drag force must be resolved into two components, which complicates the treatment of particle mechanics. This presentation considers only the one-dimensional case in which the lines of action of all forces acting on the particle are collinear. 

Thus as pointed out above, further treatment on the mechanics of particle motion remains confined only to one-dimensional motion of particle through fluid. A particle of mass m moving through a fluid under the action of an external force Fe is considered. The velocity of the particle relative to the fluid is taken to be v. The buoyant force on the particle is taken to be Fb, and the drag force be FD. Then, the resultant force on the particle is Fe - Fb - Fd, the acceleration of the particle is dv/dt, and the resulting equation of motion is given by 

The external force can be expressed as a product of mass and the acceleration ae of the particle from this force, and 

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Eq. (1) is valid for a particle settling without the interference of other particles, i.e., for diluted systems. The particle settling velocity decreases as particle concentration increases. This phenomenon is known as hindered settling. Several equations can be found in the literature to account for this phenomenon, but a simple method to calculate the hindered settling velocity is to use Eq. (1) replacing the liquid density and viscosity by the apparent density and viscosity of the suspension [24]. 

G. I. Fuks [75] directed attention to the dependence of adhesion on the period of contact between particles and surface when the particles settle out in a liquid. At the initial moment of settling, the adhesion of the particles is at a minimum with increasing contact time, we see an increase in adhesion, this rise in adhesion ending some 60-90 min after the particles first come into contact with the surface. This phenomenon has come to be known as aging. ... 

When a particle settles among other particles previously deposited on the membrane surface and partially blocks some pores or directly blocks some membrane area, the resulting model corresponds to the so-called intermediate blocking phenomenon. In this case = 1 and... 

The flow problems considered in previous chapters are concerned with homogeneous fluids, either single phases or suspensions of fine particles whose settling velocities are sufficiently low for the solids to be completely suspended in the fluid. Consideration is now given to the far more complex problem of the flow of multiphase systems in which the composition of the mixture may vary over the cross-section of the pipe or channel furthermore, the components may be moving at different velocities to give rise to the phenomenon of slip between the phases. 

Sedimentation of particles follows the principle outlined above [Eq. (1)] in which particles in the Stokes regime of flow have attained terminal settling velocity. In the airways this phenomenon occurs under the influence of gravity. The angle of inclination, t /, of the tube of radius R, on which particles might impact, must be considered in any theoretical assessment of sedimentation [14,19]. Landahl s expression for the probability, S, of deposition by sedimentation took the form ... 

Apart from the critical impeller speed for solid suspension and efficient gas dispersion, flooding is also a very important phenomenon in three-phase systems. Flooding may take place at low impeller speed or high gassing rate. Under these conditions, the gas is dispersed just around the central shaft of the tank, whereas the solids are settled at the bottom. Flooding characteristics are not affected by particles. Furthermore, high-viscosity liquids are able to handle more gas before flooding than low-viscosity liquids. 

The transport phenomenon for any spray material released In the air Is foremost a function of the particle size and size distribution of the released spray. The particle density plays a minor role, the settling rate from Stokes law for example varies as the square root of the density. Further, the density differences between liquids commonly used for pesticides Is very little, varying only slightly from water at density of 1 gm/ml. Other formulation physical factors of surface tension, viscosity and viscoelasticity play significant roles In the atomization process. These are altered by the addition of petroleum and vegetable oil as solvents and carriers as well as a host of adjuvants In varying... 

Solids suspension involves producing the required distribution of solids in the tank and is essentially a physical phenomenon. The criterion is normally a physical description of the degree of uniformity required in the suspension. A key variable for solids suspension is the settling velocity of the solids. This is usually measured by timing the fall velocity of individual solid particles in a defined depth of... 

To an extent that increases with the w/c ratio, fresh cement pastes exhibit the phenomenon of bleeding, i.e. settlement of the solid particles. The interparticle attractions are sufficiently strong that particles of all sizes settle at the same rate, typically about 2pms . Settlement also tends to increase the w/c ratio at the top and to decrease it at the bottom of the sample. It decreases with increased fineness or increased early hydration rate of the cement. In a concrete, it can produce layers of water beneath aggregate particles or reinforcing bars. 

We use here the term sorption as the retention of a compound on the surface of a solid particle that removes it from the aqueous medium. This phenomenon affects the composition of water by transferring the compound or ion from the aqueous medium to a solid (mainly a sediment in suspension or a colloid). Then, it may no longer be present in water, especially if the sediment settles. Sorption may be identified and associated with adsorption, surface precipitation, surface complexation, and/or ion exchange (or even absorption). 

The Werner and Travis methods [81,82] also operate on the layer principle but their methods have found little favor due to the basic instability of the system a dense liquid on top of a less dense liquid being responsible for a phenomenon known as streaming in which the suspension settles en masse in the form of pockets of particles which fall rapidly through the clear liquid leaving a tail of particles behind. 

Flocculation comes from the Latin word flocculate meaning loose and woolly. Flocculated systems result in rapid rate of settling because each individual unit is composed of many particles and is therefore larger. However, due to the loose packing of floes they are easily dispersible on shaking. Deflocculated systems on the other hand are made up of smaller particles whose settling rate is slower, but the settled particles tend to form an irreversible compact and are difficult to redisperse. This phenomenon is called caking. For coarse suspensions, a deflocculated suspension will have better uniformity of dose but poorer stability... 

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