Gravitational force field

The pressure drop of a two-phase flow generally consists of three components frictional loss, momentum change, and elevation pressure drop arising from the effect of the gravitational force field. The local Ap therefore is normally written as... 

Figure 31. Schematic representation of a sifter separating counter-currently in the gravitational force field (Gonell)...

In a centrifugal sifter (Figure 33) the constant gravitational force field is replaced by an adjustable and stronger centrifugal one. The separation chamber... 

Smaller components move into the faster flows farther away from the accumulation wall and therefore elute before large molecules. This normal elution mode is reverse to that observed in SEC. The separation can be performed with different force fields. In thermal FEE, the separation is based on thermal diffusion between temperature difference of top and bottom wall. In case of electric FEE, the separation is driven by charge differences and electrophoretic mobility of the molecules applying an electrical field. Another way to separate components depending on their density properties is sedimentation FEE, where a circular channel rotates and generates a gravitational force field. 

FFF technology is applicable to the characterization and separation of particulate species and macromolecules. Separations in FFF take place in an open flow channel over which a field is applied perpendicular to the flow. Among the various FFF subtechniques, depending on the kind of the applied external fields, sedimentation FFF (SdFFF) is the most versatile and accurate, as it is based on simple physical phenomena that can be accurately described mathematically. SdFFF, which uses a centrifugal gravitational force field, is a flow-modified equilibrium sedimentation-separation method. Solute layers that are poorly resolved under static equilibiium sedimentation become well separated as they are eluted by the laminar flow profile in the SdFFF channel. In normal SdFFF, where the colloidal particles under study do not interact with the channel wall, the potential energy of a spherical particle, (p(x), is related to the particle radius, a, to the density... 

The rate of hydrogenation of a-Me styrene with palladium as catalyst in the rotating beds of spherical particles and metal foam support was in the range of 30 to 40 times in a centrifugal force field of approximately 450 times the gravitational force field. A trickle bed industrial reactor of 60 m could be replaced with a rotating bed that is less than 1.5 m in volume. Industrial trickle bed reactors are bulky because of poor interfacial transport. 

Note that Equations (5.3)-(5.6) have been derived for the case of the onedimensional random walk. This is because these equations will be used later in analysis of sedimentation under gravity where motion only in one direction (one dimension) is of interest. Only motion of particles in the direction of the applied gravitational force field is of interest in sedimentation lateral motion in the other two orthogonal directions is not. In the case of the three-dimensional random walk, the analogy to Equation (5.3) would be L = V6af. 

For separation in a single-phase, the gravitational force field is rather weak compared to the strength of a centrifugal or electrical force field. Still, some amount of separation is achieved in the gravitational field. Employing the criterion (3.3.25) for equilibrium for species i, namely... 

What one observes as the particles fall toward the vessel bottom is that a clear layer of liquid, free of particles, emerges near the top of the vessel, whereas near the bottom of the vessel a sludge layer or a dense layer of particles appears (Figures 4.2.6(b), (c)). If sufficient time is allowed for equilibrium to be achieved in the gravitational force field, most of the liquid is clarified and becomes free of particles all particles accumulate at the bottom of the vessel in a sludge layer of thickness Zhs... 

This section covers separation by an electrical force field (Section 7.3.1), a centrifugal force field (Section 7.3.2), a gravitational force field (Section 7.3.3) and a magnetic force field (Section 7.3.5) Section 7.3.4 covers field flow fractionation. 

If there was no thermal movement of molecules, they would all fall to the ground under the action of gravitational force, and all the air would concentrate as a layer, several meters in thickness, on the surface of the ground. If there were no gravitational force field, the molecules would scatter throughout open space. The atmosphere is... 

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