Volumetric region

Atomic Density The number of atoms that fits into some spatial or volumetric region is otherwise referred to as the atomic density. Only solid state densities are of interest in SIMS. 

Heyder J, Blanchard JD, Brain JD. Particle deposition in volumetric regions of the human respiratory tract. Ann Occup Hyg 1988 32 71-79. 

A volumetric technique is generally to be preferred especially when reasonable accuracy is required in the region of high relative pressure, as in... 

Figure 6-32, taken from Govier and Aziz, schematically indicates four flow pattern regions superimposed on a plot of pressure gradient vs. mixture velocity = Vl -t- V5 = Qj + ( s)/A where and Vs are the superficial liquid and solid velocities, Qi, and ( 5 are liquid and solid volumetric flow rates, and A is the pipe cross-sectional area. is the transition velocity above which a bed exists in the bottom of the pipe, part of which is stationary and part of which moves by saltation, with the upper particles tumbling and bouncing over one another, often with Formation of dunes. With a broad particle-size distribution, the finer particles may be fully suspended. Near V 4, the pressure gra-... 

Cf, C y, and Cq are the concentrations of the substance in question (which may be a colligend or a surfactant) in the feed stream, bottoms stream, and foamate (collapsed foam) respectively. G, F, and Q are the volumetric flow rates of gas, feed, and foamate respectively, is the surface excess in equilibrium with C y. S is the surface-to-volume ratio for a bubble. For a spherical bubble, S = 6/d, where d is the bubble diameter. For variation in bubble sizes, d should be taken as YLnid fLnidj, where n is the number of bubbles with diameter dj in a representative region of foam. 

We first consider strain localization as discussed in Section 6.1. The material deformation action is assumed to be confined to planes that are thin in comparison to their spacing d. Let the thickness of the deformation region be given by h then the amount of local plastic shear strain in the deformation is approximately Ji djh)y, where y is the macroscale plastic shear strain in the shock process. In a planar shock wave in materials of low strength y e, where e = 1 — Po/P is the volumetric strain. On the micromechanical scale y, is accommodated by the motion of dislocations, or y, bN v(z). The average separation of mobile dislocations is simply L = Every time a disloca-... 

Consider a system of constant volume V through which a stream of fluid is passing at a steady volumetric rate u. If t is the age of elements in the stream at a point or over a region in the system, then the element whose age is between t and t + dt is known as the t-element. The relative frequency of the appearance of t-elements at a point or over a region in the system is an age distribution at the point or over that region. 

Baranowski [680] concluded that the decomposition of nickel hydride was rate-limited by a volume diffusion process the first-order equation [eqn. (15)] was obeyed and E = 56 kJ mole-1. Later, Pielaszek [681], using volumetric and X-ray diffraction measurements, concluded from observations of the effect of copper deposited at dislocations that transportation was not restricted to imperfect zones of the crystal but also occurred by diffusion from non-defective regions. The role of nickel hydride in catalytic processes has been reviewed [663]. 

Mtllf.r and Gidaspow 82 have studied transport of 75 pm catalyst particles in a 75 mm diameter vertical pipe. The flow was characterised by a dilute rising core and a dense annular region at the walls which tended to move downwards. The fractional volumetric concentration of the solids was from 0.007 to 0.04 in the core and up to 0.25 in the annular region. 

The velocity prohle in a tube of length L is Tz(r). The normal case is for V ir) to have its maximum value at the centerline and to decline monotonically toward Tz(r) =0 dX r = R. The volumetric flow rate is Q. The fraction of that flow rate associated with the region from the centerline to radial position r is found from the following integral ... 

Variation of bubble size, bubble frequency, and the standard deviation of -APbed with variation of Ug in the conical fluidized beds with a uniform gas distributor (Fopen = 3.87 %) is shown in Fig. 7. As can be seen, the standard deviation of - APbed and the bubble size increase with increasing Ug in the fully fluidized region. However, bubble frequency remains unchanged with variation of Ug that may imply the bubble size will increase as much as the volumetric gas flow increases. As shown, the bubble size dramatically increases with increasing Ug. Also, it is confirmed that the increase of standard deviation of -APbed is closely related to bubble size. 

Conversion efficiencies of the dynamometer-aged catalysts were measured in a standard A/F sweep test on an engine dynamometer [6]. The sweep experiments were carried out at 450 and 85,000 h space velocity (volumetric basis standard conditions). The sweep ranged from 0.5 A/F lean of stoichiometry to 0.5 A/F rich of stoichiometry with imposed A/F perturbations of+.0.5 A/F at 1 Hz. After sweep evaluation, small samples of catalyst were renrroved from the front region of the brick for chemisorption and flow reactor experiments. 

The fractional flow rate, (1 - f) Lu,n> is then also the volumetric flow passing through the well-mixed region of settler phase volume, Vmix. The flows leaving the plug-flow and well-mixed regions, Xsp and Xsmn. respectively, then combine to give the actual exit concentration from the settler, X . 

Slomianka L, Rungby J. West Ml, et al. 1989. Dose-dependent bimodal effect of low-level lead exposure on the developing hippocampal region of the rat A volumetric study. Neurotoxicology 10 177-190. 

The fraction of the volumetric flow rate that takes place in the region bounded by r = 0 and r = r will be equal to F(t) where t is equal to the time necessary for a fluid element to traverse the reactor length at a given r (equation 11.1.17). Thus... 

In most commercial fluidized bed processes, the bed is much higher than the jet penetration length. There are several parameters that affect attrition in the jetting region, namely the design parameters of the distributor (i.e., orifice diameter, dor, open surface area, Aa, number of orifices, Nor) and the operating parameters (i.e., gas density, pg, volumetric flow rate, vg, superficial gas velocity, t/g, orifice velocity, uor). It holds... 

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