Gravity field

According to Newton s law, the gravity field g (r) of a three-dimensional distribution of masses with a density p (r), satisfies the equations (Zhdanov, 1988) 

It follows from formula (1.7) that, outside masses, the gravity field is of Laplace form, i.e. it satisfies the Laplace equation  

It is well known that the solution of the Poisson equation can be presented in the form of a volume integral (Zhdanov, 1988)  

In particular, for the vertical component of a gravity field, we write  

the forward problem for an anomalous gravity field consists in computing the integral (112) over the domain D filled with anomalous mass, i.e. 

---

A single particle settling in a gravity field is subjected primarily to drag force, gravity force, Ta-g-, and buoyancy, which have to be in... 

Cyclones work by using centrifugal force to increase the gravity field experienced by the solids. They then settle to the wall under the influence of their increased weight. Settling is improved as the path the solids traverse under centrifugal flow is increased. This pam is... 

For the same case of n = 1200 rpm and r = 0.5, we obtain u,/Ug = 800, whereas for the turbulent regime the ratio was only 28. This example demonstrates that the centrifugal process is more effective in the separation of small particles than of large ones. Note that after the radial velocity u, is determined, it is necessary to check whether the laminar condition. Re < 2, is fulfilled. For the transition regime, 2 < Re < 500, the sedimentation velocity in the gravity field is ... 

Trent, D. (2004) Chemical processing in high-gravity fields, in Re-Engineering the Chemical Processing Plant Process Intensification (eds A. Stankiewicz and J.A. Moulijn), Marcel Dekker Inc., New York, pp. 33-67. 

The presence of a lithosphere with a thickness up to 100 km above the plume head obscures observations that could be made in terms of heat flow, gravity field or seismic structure. Establishing the temperature and flow fields beneath a hotspot thus becomes a difficult exercise. Several key parameters (Fig. 2) are poorly constrained and mostly result from theoretical fluid dynamics model, which underlines their large uncertainty. The temperature anomaly within the hotspot region is generally estimated to be approximately 200 100°C with large uncertainties (Shilling 1991 Sleep 1990). These temperature anomalies will induce smaller densities in the plume and the flux of the density anomalies is called buoyancy flux as defined in (Sleep 1990) ... 

Pomerantz, M. L., 1964, Film Boiling on a Horizontal Tube in Increased Gravity Fields, Trans. ASME. J. Heat Transfer 6 213-219. (2)... 

Bacteria Circular DNA Satellite DNA (RNA) External gradients of food Magnetic and gravity fields (Oxygen, CO, NO) Internal flows of substrates, NTP, Fe and Mg... 

Physical separation methods can be based on equilibrium considerations, but the majority are not. Ordinary filtration is an example of a non-equilibrium, physical method and so is ordinary centrifugation— e.g.—the separation of a precipitate from the suspending liquid using an artificial gravity field. There are separation methods, which are called filtration which are not such as gel filtration. Ultracentrifugation in a salt gradient is a physical equilibrium method. 

Since only gravity fields will be considered here, the negative derivatives of S2 are merely equal to the components of g in the respective directions. 

In the second paper (5) Ya.B. obtained the now classical similarity laws of ascending convective flow development (for both laminar and turbulent flows). These laws are now widely used by geophysicists in studies of atmospheric and oceanic convection. In 1953-1954 A. S. Monin and A. M. Obukhov independently used the same fruitful ideas for other conditions and obtained similarity laws for shear flow in a density stratified medium in a gravity field. 

Bpyum A. (1968) A one-stage procedure for isolation of granulocytes and lymphocytes from human blood. General sedimentation properties of white blood cells in a lg gravity field. Scand. J. Clin. Lab. Invest. 97, 51-76. 

Reactive crystallization, or precipitation, has been investigated by numerous research groups. Processes of industrial relevance include liquid-phase oxidation of para-xylene to terephthalic acid, the acidic hydrolysis of sodium salicylate to salicylic acid, and the absorption of ammonia in aqueous sulfuric acid to form ammonium sulfate (60). A very special type of reactive crystallization is diastereomeric crystallization, widely applied in the pharmaceutical industry for the resolution of enantiomers (61). Another fine example of reactive precipitation is the earlier-described production of nano-size particles of CaC03 in high-gravity fields (46). 

Before exploring the wide range of applications, a brief review of the history of development, a discussion of the process fundamentals, and an introduction to mechanical design issues will help to set the boundaries for use of high-gravity fields in chemical processing. 

Heat transfer involving non-Newtonian fluids has not been studied in rotating devices. Models have been developed for gravity-driven heat transfer for power-law fluids (46). These models may be useful as a starting point to evaluate performance in higher-gravity fields. 

---