Gravity effects, density gradient

Different grades of both of the ABS and HIPS plastics have specific gravities in the range of 1.055-1.125 g cm-1. As a result such mixtures can not be effectively separated by density gradient procedures. 

The first term on the left-hand side describes the variation of the fluid momentum in time and the second term describes the transport of the momentum in the flow (convective transport). The first term on the right-hand side describes the effect of gradients in the pressure p the second term, the transport of momentum due to the molecular viscosity p (diffusive transport) the third term, the effect of gravity g and in the last term, F lumps together all the other forces acting on the fluid. Techniques for solving the set of four equations (one continuity and three momentum equations) are discussed in a later section of this entry. When the flow is compressible, it is usually necessary to close the system of equations listed above using a thermodynamic equation of state (such as the ideal gas law) that calculates the density as a function of temperature and pressure. 

The effects of gravity on the one-component coexistence curve are severe. > > - In long vertical tubes it is to be expected that large density gradients will occur in the critical region. The effect of these gradients is to cause a flat-topped coexistence ciuve if short tubes are used for the measurements, the curves become rounded and, in fact, cubic. 

The composition gradients in CH + CF are of comparable magnitude to the density gradients in Xe, so we see that critical phenomena in binary mixtures can be quite as sensitive to gravity effects as are gas-liquid critical phenomena in pure fluids.f... 

The force of gravity has a profound influence on the processing of materials in solutioiL Thermal or concentration gradients in solution result in density gradients. This in turn leads to fluid flows effecting heat and mass tranqiort as less dense fluid rises and more dense sinks within the solutions. These flows often convolute or mask other intmesting phenomena such as diffusive processes or sur ce tension driven convection. 

In equations 5-8, the variables and symbols are defined as follows p0 is reference mass density, v is dimensional velocity field vector, p is dimensional pressure field vector, x is Newtonian viscosity of the melt, g is acceleration due to gravity, T is dimensional temperature, tT is the reference temperature, c is dimensional concentration, c0 is far-field level of concentration, e, is a unit vector in the direction of the z axis, Fb is a dimensional applied body force field, V is the gradient operator, v(x, t) is the velocity vector field, p(x, t) is the pressure field, jl is the fluid viscosity, am is the thermal diffiisivity of the melt, and D is the solute diffiisivity in the melt. The vector Fb is a body force imposed on the melt in addition to gravity. The body force caused by an imposed magnetic field B(x, t) is the Lorentz force, Fb = ac(v X v X B). The effect of this field on convection and segregation is discussed in a later section. 

The only external force on the dispersion considered so far has been the earth s gravitational field. On particles of colloidal size and especially tho.se below c. 0.5 pm diameter, and density close to the medium, the effect of gravity is completely outweighed by the thermal motion of the particles Brownian motior, leads to a structure which is close to an equilibrium state. As the particle size increases, e.g. for a suspension, then the effect of external fields has to be considered since under the influence of gravity particles tend to senle. Another importani external field occurs when the system is stirred or sheared. The easiest case to consider is the application of a simple shear gradient The flux J (velocity x... 

Due to composition and enthalpy variations when reaction occurs, the density can vary significantly. Using the one-point joint velocity-composition PDF transport equation (12.4.2-2), the terms related to convection, gravity, and the mean pressure gradient, as well as the reaction rates, appear in closed form, irrespective of variations of the density in composition space. Some effects of the variable density on the conditional expectations (12.4.2-3) and (12.4.2-4) should be considered, however. 

Gravity forces essentially influence both velocity and mainly hydraulic gradient of capsules conveyed by liquid in inclined pipes. The difference of the values Vc/Vo and U in inclined and horizontal pipes is higher for low velocities and decreases with increasing velocity. It was a surprise that ctqtsules move even faster in inclined pipe than in horizontal one for low pipe inclination and density ratio. It could be explained by higher tendency of capsules to be lifted off the bottom in inclined pipe. If the velocity ratio approaches unity, capsules are lifted even in horizontal pipe, this phenomenon vanishes and effect of gravity prevails. 

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