Centrifugal fields, effects

In pressure diffusion, a pressure gradient is estabUshed by gravity or in a centrifugal field. The lighter components tend to concentrate in the low pressure (center) portion of the fluid. Countercurrent flow and cascading extend the separation effect. 

In the hydrocyclone, or hydraulic cyclone, which is discussed extensively in the literature(29 35), separation is effected in the centrifugal field generated as a result of introducing the feed at a high tangential velocity into the separator. The hydrocyclone may be used for ... 

The flow problems considered in Volume 1 are unidirectional, with the fluid flowing along a pipe or channel, and the effect of an obstruction is discussed only in so far as it causes an alteration in the forward velocity of the fluid. In this chapter, the force exerted on a body as a result of the flow of fluid past it is considered and, as the fluid is generally diverted all round it, the resulting three-dimensional flow is more complex. The flow of fluid relative to an infinitely long cylinder, a spherical particle and a non-spherical particle is considered, followed by a discussion of the motion of particles in both gravitational and centrifugal fields. 

In this volume, we will apply the principles developed in Principles and Applications to the description of topics of interest to chemists, such as effects of surfaces and gravitational and centrifugal fields phase equilibria of pure substances (first order and continuous transitions) (vapor + liquid), (liquid 4-liquid), (solid + liquid), and (fluid -f fluid) phase equilibria of mixtures chemical equilibria and properties of both nonelectrolyte and electrolyte mixtures. But do not expect a detailed survey of these topics. This, of course, would require a volume of immense breadth and depth. Instead, representative examples are presented to develop general principles that can then be applied to a wide variety of systems. 

A better approach to produce a significant concentration gradient in a solution involves increasing the force by substituting a centrifugal field for a gravitational field, an effect that we will now consider. 

The remainder of this book applies thermodynamics to the description of a variety of systems that are of chemical interest. Chapter 12 uses thermodynamics to describe the effects of other variables such as gravitational field, centrifugal field, and surface area on the properties of the system. Most of the focus of the chapter is on surface effects. The surface properties of pure substances are described first, including the effect of curvature on the properties of the surface. For mixtures, the surface concentration is defined and its relationship to the surface properties is described. 

In all of the studies of thermodynamic equilibrium that have been presented in the previous chapters, we have neglected the effects of an external field on the equilibrium properties of a system. This has been justified because the field may be present only in specific cases, the effect of the field may be negligible, or the position of the system in the field may be unchanged. The conditions of equilibrium in the presence of a gravitational or centrifugal field, an electrostatic field, and a magnetic field are developed in this chapter. 

In the sedimentation-equilibrium method a lower centrifugal field is applied and the processes of sedimentation and diffusion are brought to equilibrium [13]. In this case the governing equation contains sedimentation equilibrium concentrations of species at different positions from the axis of rotation, but one does not need to know D. It should be pointed out that sedimentation and diffusion are more complicated when the species are electrically charged. This is because the smaller counterions sediment at a slower rate than do the colloidal-sized species. This creates an electric potential gradient that tends to speed up the counter-ions and to drag the colloidal species. The reverse effect occurs for diffusion. 

In contrast to bulk foam, in a porous medium the majority of films move separately so their rupture under certain critical pressure does not occur simultaneously, i.e. the films are not affected by the rupture of other films (there is no collective effect). On the other hand, moving films are subjected to the oscillation of thickness as well as to other mechanical effects. Hence, their critical pressure should be lower than that of the static foam and should depend also on the rate of movement due to the dynamic effects. Analogous reduction in the critical pressure is observed when a bulk foam advances [47] and when a foam is placed in a centrifugal field [183]. The influence of the dynamic effects on the critical pressure has been explained by the model of Jimenez and Radke [175]. 

In the normal mode of the SdFFF operation, a balance is reached between the external centrifugal field, driving the particles toward the accumulation wall, and the molecular diffusion in the opposite direction. In that case, the retention volume increases with particle diameter until steric effects dominate, at which transition point there is a foldback in elution order. 

These equations should be compared with Eqs. (26)-(28) to see the consequence of the absence of the gauge-field effects. It is noted that the democratic centrifugal force (DCF) arises on the gyration space as the first terms of the ... 

For ordinary molecules the rigid rotor model works quite succussfully in explaining pure rotation spectra as well as the rotational fine structure obtained in other fields of spectroscopy. The vibrational perturbations appear mostly in the change of effective rotational constants with the vibrational state and in the centrifugal distortion effects. Much useful information can be found from these perturbation effects, however5. ... 

In a sedimenting centrifuge, a continuous liquid phase moves through the rotor. To accomplish a useful separation, the discontinuous phase, either the insoluble solids or the immiscible liquid drops (or both), must move in a direction different from the flow of the continuous liquid. Stokes law is usually applied to describe this relationship. The effective force accelerating the particle in a centrifugal field is then given as ... 

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