In gravitational and centrifugal fields

Voit, H. Zeppenfeld, R. Mersmann, A. Calculation of Primary Bubble Volume in Gravitational and Centrifugal Fields, Chem. Eng. Technol. 10 (1987), p. 99/103... 

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. 

In this chapter the thermal motion of dissolved macromolecules and dispersed colloidal particles will be considered, as will their motion under the influence of gravitational and centrifugal fields. Thermal motion manifests itself on the microscopic scale in the form of Brownian motion, and on the macroscopic scale in the forms of diffusion and osmosis. Gravity (or a centrifugal field) provides the driving force in sedimentation. Among the techniques for determining molecular or particle size and shape are those which involve the measurement of these simple properties. 

For analytical purposes counter-current sifting in gravitational and centrifugal force fields is normally used. The cross-current principle is also sometimes applied more often this variation is combined with counter-current sifting. The terms counter- and cross-current describe the movement of coarse particles in relation to fluid flow in the separation zone. 

In this chapter, we study the effects of uniform static electric and magnetic fields on the thermodynamic properties of material. The source of the fields may be in the surroundings or included in the system of interest. In either case, the properties of the material affect the value of the effective field at any point in the material. It is for this reason that the study of electric and magnetic fields is more complicated than the study of gravitational and centrifugal fields presented in the next chapter. 

In this chapter, we study the effects of gravitational and centrifugal fields on the thermodynamic properties of systems. We generalize many of the results obtained in previous chapters to include the effects of these fields. 

Equations (4.332), (4.333) are starting equations for deducing barometric and Sved-berg formulae or calculation of chemical equilibrium in gravitational or centrifugal fields [3, 79].23... 

The size distribution of supramolecular polymers should be sensitive not only to changes in the solvent conditions, but also to externally applied fields including electric and magnetic fields [82,83], flow fields [84-86], gravitational and centrifugal fields [87,88], confining walls [89,90], and so on. 

This chapter will present the very important kinetic properties of coUoids, and their motion under the influence of gravitational and centrifugal fields. Kinetic properties are important for many reasons, for example they provide methods for determining the molecular weight (molar mass) of colloidal particles, their size and shape - i.e. for the characterization of colloidal particles. Many of the methods we will see in this chapter have found widespread use in the study of biological and polymeric molecules. 

A further electrokinetic phenomenon is the inverse of the former according to the Le Chatelier-Brown principle if motion occurs under the influence of an electric field, then an electric field must be formed by motion (in the presence of an electrokinetic potential). During the motion of particles bearing an electrical double layer in an electrolyte solution (e.g. as a result of a gravitational or centrifugal field), a potential difference is formed between the top and the bottom of the solution, called the sedimentation potential. 

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. 

Methods of separation may exploit the differential solubility of the macromolecules in different solutions, for instance, salt solutions of different strengths, or in organic solvents (alcohol or acetone) the different stabilities of proteins to acids and alkalies the different mobilities of the proteins under gravitational and electrical fields (centrifugation and electrophoresis) and the ability of certain substances to absorb some proteins but not others (chromatography). Some of these methods are worth describing in a little detail. 

While for quite some time particles with sizes down to a few hundred micrometers have been successfully removed by conventional dust collection (mostly using gravitational and centrifugal or other field forces) and dry and wet filtration, air borne (Fig. 8.1) and suspended solid pollutants continued to be a great problem. Because of the small mass of fine and ultrafme particles they do not settle, even if high-field forces are produced, and they follow the flow lines in filter media so that impacts, which are necessary for collection (Fig. 8.2), do not take place. 

When dealing with the sedimentation of colloidal particles, it is principally necessary to regard the Brownian motion of the particles, which results in diffusive particle transport and, thus, acts against the migration in the gravitational or centrifugal field. The relevance of the Brownian motion can be roughly estimated by means of a Peclet-number ... 

Sedimentation (MICROSCOPIC PROCESS) motion of particles in viscous media due to gravitation or centrifugal fields (also settling), the term refers frequently to the state in which the field forces are counterbalanced by the drag force this state is almost instantaneously achieved in the case of colloidal suspensions the sedimentation of an individual particle depends on its size, the density contrast, the rheological fluid properties, the field strength, and the viscous interactions with other particles. 

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