Centrifugal force field potential

Another significant nonconstant-gravity application is the motion of a body in a centrifugal force field, as in a centrifuge. In such a device the change in potential energy of a body is given by... 

We have observed that countercurrent separation devices achieve considerable separation under driving forces such as chemical potential gradient and the external force of a centrifugal force field. As illustrated in equations (3.1.44) and (3.1.50), there is another type of force, the thermal diffusion force. The separation achieved thereby in a closed two-bulb cell has been illustrated in Section 4.2.5.I. We have already illustrated conceptually how thermal diffusion can achieve separation in a countercurrent column via Figures 8.1.1(a)-(h). For UF isotope separation, however, the radial separation factor in a two-bulb cell is much smaller than for other isotope separation processes. In a countercurrent column, this value is reduced by about 50%. As a result, thermal diffusion columns are not used at all for any practical/large-scale separation. More details on thermal diffusion columns are available in Pratt (1967, chap, viii) and Benedict et al. (1981, pp. 906-915), where one can find information on the primary references. 

Ef r) Potential energy of molecule at position r in a centrifugal force field... 

Thus, all particles are in centrifugal forces (of inertia). Such a field is not uniform. Nevertheless one can use the concept of potential energy caused by the presence of forces of inertia. Therefore, the relation between centrifugal force and potential energy can be used (see eq. (1.4.32)) ... 

Here Uq is the value of the potential on the surface. It is proper to notice that potentials of the attraction field and the centrifugal force usually vary on the level surface of the gravitational field. Changing the value of the constant, Uq, we obtain different level surfaces, including one which coincides in the ocean with the free undisturbed surface of the water and, as was pointed out earlier, this is called the geoid. As follows from Equation (2.73) the projection of the field g on any direction / is related to the potential U by... 

In accordance with Equation (2.338) the determination of the figure of fiuid equilibrium is reduced to the following problem we have to find such a surface of the fluid, S(x,y,z), that its partial derivatives should be proportional to the corresponding components of the acting force. As we pointed out, when a fluid rotates uniformly around the same axis the total force can be represented as a sum of the attraction and centrifugal forces, and the former depends on the shape of the fluid mass in a rather complicated way. Besides, in the case of an inhomogeneous fluid the potential of the attraction field depends on the distribution of a density of a fiuid and for this reason this problem becomes even more complicated. 

Quadratic and cubic potential constants have been obtained from IR frequencies, isotopic shifts, inertial defects, Coriolis constants and centrifugal distortion, assuming the geometry from microwave data. The quadratic force field is characterized by four symmetry force constants F which are related to the inner force constants by the following equations... 

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... 

Electrosynthesis Under Ultrasound and Centrifugal potential scanning at various centrifugal acceleration Fields, Fig. 4 Cyclic voltammograms in the course of forces, (a) At 315 g on electrode A. (b) At 290 g on... 

All of the methods described earlier can be classified as static, because all of the measurements are conducted under conditions of stable equilibrium. This condition corresponds to the minimum in potential energy, which in turn corresponds to the balance between the total surface energy and the energy in a field of gravitational or centrifugal force. There are also methods in which the measurements of surface tension are conducted under conditions of metastable equilibrium, corresponding to the maximum of the free energy of the system. Such methods can be classified as semistatic. 

Figure 11.2. (A) The Lorentz force, F, causes the ion to undergo a circular orbit in the presence of a magnetic field, B. The Lorentz force is opposed by the centrifugal force of the orbiting ion, Fc- This ion orbits with a cyclotron frequency, 0), and with a radius, r. (B) The trapping potential produces a radially repulsive force, Fe, which, along with the centrifugal force, Fc, opposes the Lorentz force, Fe (Adapted ftom Ref. 161.)...

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