Rate of accumulation

In spite of considerable development of thermodynamics and molecular theory, most of the methods used today are empirical and their operation requires knowledge of experimental values. However, the rate of accumulation of experimental data seems to be slowing down even though the need for precise values is on the rise. It is then necessary to rely on methods said to be predictive and which are only estimates. 

General Equation of Motion. Neglecting relativistic effects, the rate of accumulation of mass within a Cartesian volume element dx-dy-dz must equal the sum of the rates of inflow minus outflow. This is expressed by the equation of continuity ... 

Decay products of the principal radionuclides used in tracer technology (see Table 1) are not themselves radioactive. Therefore, the primary decomposition events of isotopes in molecules labeled with only one radionuclide / molecule result in unlabeled impurities at a rate proportional to the half-life of the isotope. Eor and H, impurities arising from the decay process are in relatively small amounts. Eor the shorter half-life isotopes the relative amounts of these impurities caused by primary decomposition are larger, but usually not problematic because they are not radioactive and do not interfere with the application of the tracer compounds. Eor multilabeled tritiated compounds the rate of accumulation of labeled impurities owing to tritium decay can be significant. This increases with the number of radioactive atoms per molecule. 

Pharmacokinetic studies are designed to measure quantitatively the rate of uptake and metaboHsm of a material and determine the absorbed dose to determine the distribution of absorbed material and its metaboHtes among body fluids and tissues, and their rate of accumulation and efflux from the tissues and body fluids to determine the routes and relative rates of excretion of test material and metaboHtes and to determine the potential for binding to macromolecular and ceUular stmctures. 

The differential equation of batch grinding is deduced from a balance on the material in the size range k. The rate of accumulation of material of size k equals the rate of production from all larger sizes minus the rate of bre age of material of size k ... 

Rate of Accumulation = Rate of Input — Rate of Output ... 

The effects of chronic sleep deprivation or cumulative minor sleep losses have been relatively under investigated. Little is known about the relationships among the size of the sleep deficit, its rate of accumulation, the amount and timing of optimum recovery sleep, and their effect on human performance and productivity. 

The rate of corrosion in any of these three modes is substantially higher than in normal circumstances. In the absence of off-load corrosion, rates of accumulation of magnetite on boiler tubes range from I to 2 m/l OCX) h. In contrast, on-Ioad corrosion rates are from 20 to 1 000 times these values. The oxide forms as a duplex layer, although both layers are not invariably present. In waterside deposits, the outer layer, nominally of magnetite, also... 

For a liquid which is flowing with a velocity u in a rectangular channel of width B, the depth of liquid is initially D. As a result of a change in conditions at the downstream end of the channel, the level there suddenly increases to some value D2. A wave therefore Lends to move upstream against the motion of the oncoming fluid. For two sections, 1 and 2, one on each side of the wave at any instant, as shown in Figure 3.22. the rate of accumulation of fluid between the two sections is given by ... 

The rate of accumulation of A (moles/unit time) is given by ... 

The turnover rate of a transmitter can be calculated from measurement of either the rate at which it is synthesised or the rate at which it is lost from the endogenous store. Transmitter synthesis can be monitored by administering [ H]- or [ " C]-labelled precursors in vivo these are eventually taken up by neurons and converted into radiolabelled product (the transmitter). The rate of accumulation of the radiolabelled transmitter can be used to estimate its synthesis rate. Obviously, the choice of precursor is determined by the rate-limiting step in the synthetic pathway for instance, when measuring catecholamine turnover, tyrosine must be used instead of /-DOPA which bypasses the rate-limiting enzyme, tyrosine hydroxylase. 

The adsorption and accumulation of various impurities from the electrolyte or surrounding atmosphere on the catalyst surface. The rate of accumulation of impurities on the catalyst surface depends on its activity for adsorption, which often is parallel to its catalytic activity. 

In closed systems (batch reactors), the instantaneous overall rate of accumulation of the reactant S is related to the reaction rate by the following expression ... 

Here the rate of accumulation term represents the rate of change in the total mass of the system, with respect to time, and at steady state this is equal to zero. Thus the steady-state mass balance is seen to be a simplification of the more general dynamic balance. 

Rate of accumulation of mass /dMj of component i within the system/ dt /... 

Rate of accumulation /Rate of production of A of reactant A / by chemical reaction J... 

Rate of accumulation /Mass flow of mass in the reactor/ rate in /... 

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