Fundamental characteristic times

Although the concept of mean residence time is easily visualized in terms of the average time necessary to cover the distance between reactor inlet and outlet, it is not the most fundamental characteristic time parameter for purposes of reactor design. A more useful concept is that of the reactor space time. For continuous flow reactors the space time (t) is defined as the ratio of the reactor volume (VR) to a characteristic volumetric flow rate of fluid (Y). 

Regardless of the reference time, all usual physical and chemical phenomena can be described by a fundamental characteristic time, which is peculiar to it From a general point of view, a characteristic time can be defined as the time required for a physical/ chemical system governed by this phenomenon to evolve from a non-equilibrium state to its equilibrium. In practice, they can often be considered as the ratio of a quantity of extensity to the exchanged flux or the transformation rate of this extensity. For example, a reaction time relates a mole quantity to the molar transformation rate and can be simplified as the ratio of the concentration [molm ] to the reaction rate [molm s ]. Similar relations can be developed for the heat-transfer time and mass-transfer time, where the extensities considered are the heat and the mass, respectively. 

Whereas the fundamental characteristic times are scale dependent, the structure of the couplings between these phenomena does not change with the geometric scale. However, changing the hierarchy of these phenomena enables one to control the dominating phenomenon and control the global efficiency of the system. 

Dielectric dryers have not as yet found a wide field of application. Their fundamental characteristic of generating heat within the solid indicates potentialities for diying massive geometrical objects such as wood, sponge-rubber shapes, and ceramics. Power costs may range to 10 times the fuel costs of conventional methods. 

The effects of carcinogens on tissues appear irreversible. Exposure to small doses of a carcinogen over a period of time results in a summation or potentiation of effects. The fundamental characteristic which distinguishes the carcinogenic effect from other toxic effects is that the tissues affected do not seem... 

A more complicated situation emerges in motion along nonintersecting surfaces with variable curvatures. If the distance between these surfaces remains finite everywhere, then the field lines do not expand infinitely in the directions normal to the surfaces. In the absence of dissipation this means that there is no unbounded growth of the normal field component. However, introduction of the finite conductivity yields an equation for the normal component which is not decoupled it contains the contribution of the Laplacian of the remaining components. At the same time, it is possible for all other components to increase exponentially with an increment which depends on the conductivity and vanishes for infinite conductivity. The authors called this mechanism of field amplification a slow dynamo, in contrast to the fast dynamo feasible in the three-dimensional case, i.e., the mechanism related only to infinite expansion of the field lines as, for example, in motion with magnetic field loop doubling. In a fast dynamo the characteristic time of the field increase must be of the same order as the characteristic period of the motion s fundamental scale. 

The thermal characteristics of a reaction, including its heat production rate, the necessary cooling power, and the reactant accumulation, are fundamental for safe reactor operation and process design. A successful scale-up is achieved, only when the different characteristic time constants of the process, such as reaction kinetics, thermal dynamics of the reactor, and its mixing characteristics are in good agreement [9]. If we focus on the reaction kinetics and thermal dynamics, that is, we consider that the reaction rate is slow compared to the mixing rate, in principle, there are two ways to predict the behavior of the industrial reactors ... 

Because Teflon is not soluble, it cannot be wet- or dry-spun, and because it is thermally unstable at its melting point of about 400°C, this combination would seem to pose an impossible problem for the production of fibers. Research into the fundamental characteristics of the polymer, however, revealed that the submicroscopic particles precipitated from the polymerization reaction were about 100 times as long as they were thick. 

The measurements cover a wide range of characteristic times 1 psec for neutron scattering, 1 nsec for NMR relaxation, and 100 nsec for Mossbauer spectroscopy the heat capacity is a time-average quantity. The observation of similar responses for measurements of widely varied character suggests that understanding the 200-K transition is fundamental to understanding the dynamics of proteins. 

A fundamental characteristic of the so-called thermorheologically simple systems is that consecutive isotherms have similar habits, so they overlie each other when they are shifted horizontally along the log t axis. In other words, the time-temperature correspondence principle holds. This property in creep experiments can be expressed by the relation (2,3)... 

As described in the earlier sections, the DV method is entirely numerical, and thus all variables are defined in the three-dimensional grid. The fundamental characteristic of the architecture of the DVM system of codes is that procedures are executed in the memory for a block of grid points at a time. The blocks of points are created and stored in temporary disk space, from where they are recalled. All variables are calculated and stored in disk for the same blocks. In the current version, blocks of 600 points are used. For the larger calculations, typically 1.0- 1.5Gb of temporary disk space must be reserved for this purpose. 

Various different sets of criteria are used to interpret the quality of a food product. The term "acceptability" is a practical approach when comparing it to the "quality limit". Below this limit a product is then rejected. The acceptance limit is mainly defined by economic and physiological factors, whereas the quality of a product is basically defined by its fundamental characteristics. For food products such as fruits and vegetables, properties such as color, firmness, and taste will change over time. Shelf life is calculated as the time before the product qualities drop below the acceptance limit under standardized storage conditions (Tijskens, 2000 Rico et al., 2007). 

In the formulation of the transport equations, several characteristic time scales are defined. In this framework these time scales are considered fundamental in the classification and the understanding of the dominant mechanisms in the suspension flow. The particle relaxation time Tgp was already defined in (10.98). The particle-particle collision time t, is defined by ... 

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