Mathematization Of Kinetic Behavior

The ultimate goal of science is the formulation of laws, principles, or models, through which the behavior of a system can be deduced without the necessity of experimenting with and constructing the system. The extent to which this goal is reached is an objective measure of the scientific success achieved by the scientist or engineer. Economically, such achievement can help cut a great deal of the cost due to system construction from trial-and-error experimentation. Practically, such achievement is reflected in the predictability of the system derived from the use of the model. Several prerequisites are important in striving for predictability. The first is mathematization. This involves more than just fitting numbers into an equation. With the advent of computers, mathematical modeling has become a more powerful tool than in the past. A successful mathematization of a system, and predictability exerted by the model, depends on the understanding of the mechanistic aspect of the system involved and the identification of the pertinent variables of the system. Experimental design and statistical analysis are two powerful tools for gathering such information in the analytical approach to the system.

The mathematician in the scientist or engineer can say whether a given model is adequate or not, and if such and such conditions are met, a certain behavior will follow. However, it is the scientist or engineer in the mathematician who must judge the adequacy or appraise the predictability of the behavior. Mathematization is a necessity in forming models and making use of their predictability; sound experiments and good judgment are equally necessary in the formulation of foul proof models. Not to take any credit from the usefulness of a pure stochastic, statistical, or synthetic approach to rather unanalyzable prob lems, the subject matter in this article calls for the analytical, deterministic approach to problem solving.

Chemical kinetics is the study of rate, changes occurred per unit time, and mechanism by which one chemical species is converted to another. Mechanism is the elemental process of motion, that is, collisions among the molecules, atoms, radicals, or ions that take place simultaneously or consecutively in producing the observed overall rate. Overall rate depends on the nature of the participants and the environment surrounding them. The overall rate, in some cases, is controlled by the slowest step of the simultaneous or consecutive reactions. If the overall reaction involves a heterogeneous environment, where, for example, concentration is not uniform, the rate of the transport of the materials involved in the reaction can also control the overall rate of the reaction. In such a case, it is usually considered to be an overall rate controlled by transport (mass transfer), a physical change, not a chemical reaction. Similar arguments can be said for reaction systems with temperature variations. Overall rates can be controlled by heat-transfer rate in some situations.

The changes food materials undergo during processing, preparation, or storage are the results of complex physical changes, chemical reactions, and biological activities. Microscopically or macroscopically biological materials represent systems of heterogeneous natures in terms of the chemicals and biochemicals involved and in terms of the physical separations of these molecules into compartments in the system. Again, the overall rate of a change can be controlled either by the slowest step of a chemical reaction or by a physical change such as mass transfer of an essential substrate. Such a step is called the rate-limiting step or the rate-controlling step. The identification of the said step is necessary for the formulation of the correct mathematical model, which is useful for the design of efficient processes.

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