Specific rate definition

In clinical chemistry and medical diagnostics the true positive rate is called sensitivity rate and the true negative rate specificity rate (O Rangers and Condon [2000]) without any relation to the general definition of the terms sensitivity and specificity and their use in analytical chemistry (see Sects. 7.2 and 7.3). 

Starting from the definitions (2-3), we can also evaluate the average of the tensor of space-specific rates of evolution. We have... 

Process intensification can be considered to be the use of measures to increase the volume-specific rates of reaction, heat transfer, and mass transfer and thus to enable the chemical system or catalyst to realize its full potential (2). Catalysis itself is an example of process intensification in its broadest sense. The use of special reaction media, such as ionic liquids or supercritical fluids, high-density energy sources, such as microwaves or ultrasonics, the exploitation of centrifugal fields, the use of microstructured reactors with very high specific surface areas, and the periodic reactor operation all fall under this definition of process intensification, and the list given is by no means exhaustive. 

Thus far, the discussion of reaction rate has been confined to homogeneous reactions taking place in a closed system of uniform composition, temperature, and pressure. However, many reactions are heterogeneous they occur at the interface between phases, for example, the interface between two fluid phases (gas-liquid, liquid-liquid), the interface between a fluid and solid phase, and the interface between two solid phases. In order to obtain a convenient, specific rate of reaction it is necessary to normalize the reaction rate by the interfacial surface area available for the reaction. The interfacial area must be of uniform composition, temperature, and pressure. Frequently, the interfacial area is not known and alternative definitions of the specific rate are useful. Some examples of these types of rates are ... 

By this definition, the specific rate of reaction is uniquely defined, and its sign is always positive. Inversely, the rate of reaction of each component or species participating in the reaction is the specific reaction rate multiplied by the species stoichiometric coefficient with the corrected sign (negative for reactants, positive for products). 

The rate of the forward reaction is RatCf = f[A] [B] the rate of the reverse reaction is RatCj. = j.[A2B]. In these expressions, and k. are the specific rate constants of the forward and reverse reactions, respectively. By definition, the two rates are equal at equilibrium (Ratef = Ratej.). So we write... 

Controlled release implies regulation of the delivery of a drug usually by a device. The control is aimed at delivering the drug at a specific rate for a definite period of time independent of the local environments. The periods of delivery are usually much longer than in case of SR and vary from days to years. Controlled release may also incorporate methods to promote localization of drug at an active site. Site-specific and targeted delivery systems are the descriptive terms used to denote this type of control. 

Therefore, an ITK experiment allows the simultaneous definition of the number of active sites on the catalyst and the specific rate of reaction over these active sites. A full description of the data analysis procedures used to interpret TTK data is beyond the scope of this article, but such details can be found in the literature (see eg [10]). 

The specific rate of oxygen transfer per unit of liquid membrane area seems to be quite reasonable. However, methods to form and utilize effectively much smaller diameter liquid membranes, perhaps similar to those used in other liquid membrane applications, would be required to obtain enough membrane area per unit blood volume for a practical blood oxygenator. The stability of the liquid membranes does not seem to be a major problem however, more definitive liquid membrane stability information would be required before the blood oxygenator application. 

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The specific rate in macroregime 2-3 is given by Equation 23.18. This equation is also valid for regime 3, but the denominator vanishes (when the value of / mp exceeds 3.0). Knowing the specific rate, we calculate A/mp from this equation. Then, from the definition of given by Equation 23.14, we calculate the microphase contribu-... 

A flux F is defined as the amount that flows through a unit area per unit of time F = Ag/qAr (q area). Flux in this definition is a vector. However, in general flux in earth system research relates to the movement of a substance between compartments. This looser usage (Chapter 2) is equivalent to a rate (change of mass per time) sometimes, the term specific rate is used in the more exact sense of time-and area-related flux. Generally, the terms rate and flux as well as velocity and speed are often not separated in the literature in such an exact physical sense, but used synonymously. 

The interfacial area entering in this definition must, of course, be of uniform composition, temperature and pressure. The rate will then be expressed for instance in g-mole/cm -sec. In particular when the locus of reaction is an interface between a solid phase and a liquid phase, if the interfacial area, as frequently happens, is not known, alternative definitions of the specific rate are useful ... 

Of course many alternative definitions of specific rates for homogeneous and heterogeneous reactions are conceivable. Many of these are in use but conversion to the standard forms (1.3.2) and (1.3.12) should be attempted in every case where enough information is available. Whatever the choice of the definition of reaction rate adapted to a particular situation, it must be proportional to the derivative with respect to time of the extent of reaction. 

These rates have dimensions of [g T" h" ] or [kJ T h ] and are intensive quantities that may be substituted directly into the mass balance equation. On the other hand, these absolute rates may take on any value and are therefore not characteristic of the system. Comparable variables, which are biologically representative, are the so-called specific rates of production or utilization, which refer to the catalytically active mass (to a first approximation, the concentration of biomass, x, is taken as the dry cell weight). With this, one has the definitions of the specific rates for bioprocesses of Equs. 2.5a-f where, in each case, the specific rate has the dimension [h ]. For growth, the specific rate is p... 

These definitions for specific rates are analogous to the definition of specific rates rf in chemical kinetics, where the mass of the active catalyst, in the case of heterogeneous catalysis, is used to define a specific rate... 

The concept of balanced growth was introduced by Campbell (1957) to describe a metabolic state of a culture in terms of the distributed concentration (xj) or total mass (X- ) of a metabolic variable. According to Campbell s definition, growth is balanced when the specific rate of change of all such variables is constant. That is. 

The maximum stress intensities acting on particles during ultrasonication are considered for energy and for force quantities. Some authors estimated the specific rate of dissipation (power density) based on caloric data, which yielded values in the range of 10 -10" kW/m (Pohl et al. 2004) to 10 kW/m (Kuntzsch 2004, p. 100). The problem here is the definition of the dispersion zone, i.e. the volume where the ultrasonic field significantly contributes to deagglomeration. This zone... 

The complexes were heterogenized from their aqueous and methanol solutions in the atmosphere of Ar, as described in [2]. The experiments were performed in a reaction vessel with a magnetic stirrer, equipped by a water jacket, reflux condenser, and sampling device [1]. We loaded 0.05 - 0.1 g of the catalyst (4.95 X 10- g-atom of Ru) and 0.025 g of NaBH4 into the reaction vessel, filled the system with Ar (or air), added 5 ml of propanol-2, stirred the reaction mixture at 82.5° for some definite time period to activate the catalyst, and then added p-BT (9.9 x 10- - 4.95 x 10- mole). The composition of the catalyzate was analyzed by gas-liquid chromatography. The activity of the catalysts was characterized by the initial specific rate of toluene formation (W, ... 

We should introduce definition of specific rate, as shown in (7.3), (7.4) and (7.5), because the reaction rate relates to the volume, mass or surface area of catalyst. 

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