Electrokinetics. The first mathematical description of electrophoresis balanced the electrical body force on the charge in the diffuse layer with the viscous forces in the diffuse layer that work against motion (6). Using this force balance, an equation for the velocity, U, of a particle in an electric field [Pg.178]

M. Williams, "Measurement and Mathematical Description of Separation Characteristics of Ha2ardous Organic Compounds with Reverse Osmosis Membranes," dissertation. University of Kentucky, Lexiagton, Ky., 1993. [Pg.158]

Capello and Bielsld, Kinetic Systems Mathematical Description of Kinetics in Solution, Wiley, 1972. [Pg.683]

Quantum mechanics (QM) is the correct mathematical description of the behavior of electrons and thus of chemistry. In theory, QM can predict any property of an individual atom or molecule exactly. In practice, the QM equations have only been solved exactly for one electron systems. A myriad collection of methods has been developed for approximating the solution for multiple electron systems. These approximations can be very useful, but this requires an amount of sophistication on the part of the researcher to know when each approximation is valid and how accurate the results are likely to be. A significant portion of this book addresses these questions. [Pg.10]

EquatitHis (8.4)-(8.8) represent a complete mathematical description of the chemical equilibrium between a rich phase and the y th MSA. The simultaneous solution [Pg.194]

Thermodynamics is one of the most well-developed mathematical descriptions of chemistry. It is the held of thermodynamics that dehnes many of the concepts of energy, free energy and entropy. This is covered in physical chemistry text books. [Pg.9]

The term theoretical chemistry may be defined as the mathematical description of chemistry. The term computational chemistry is generally used when a mathematical method is sufficiently well developed that it can be automated for implementation on a computer. Note that the words exact and perfect do not appear in these definitions. Very few aspects of chemistry can be computed exactly, but almost every aspect of chemistry has been described in a qualitative or approximately quantitative computational scheme. The biggest mistake a computational chemist can make is to assume that any computed number is exact. However, just as not all spectra are perfectly resolved, often a qualitative or approximate computation can give useful insight into chemistry if the researcher understands what it does and does not predict. [Pg.1]

Linear elastic fracture mechanics (LEFM) is based on a mathematical description of the near crack tip stress field developed by Irwin [23]. Consider a crack in an infinite plate with crack length 2a and a remotely applied tensile stress acting perpendicular to the crack plane (mode I). Irwin expressed the near crack tip stress field as a series solution [Pg.491]

Modeling the pore size in terms of a probability distribution function enables a mathematical description of the pore characteristics. The narrower the pore size distribution, the more likely the absoluteness of retention. The particle-size distribution represented by the rectangular block is the more securely retained, by sieve capture, the narrower the pore-size distribution. [Pg.63]

A combination of dimensional similitude and the mathematical modeling technique can be useful when the reactor system and the processes make the mathematical description of the system impossible. This combined method enables some of the critical parameters for scale-up to be specified, and it may be possible to characterize the underlying rate of processes quantitatively. [Pg.1046]

O. S. Heavens. Optical Properties of Thin Solid Films. Buttcrworths, 1955. Chapter 4 presents a detailed mathematical description of the Fresnel fringing phenomenon for the transmission of light through thin films. [Pg.427]

A. V. Sokolov. Optical Properties ofMetaL. Elsevier, New York, 1967, Chapters 10 and 11. A very detailed, mathematical description of solutions to the wave equations, with a nice historical perspective. [Pg.735]

Approximations are another construct that is often encountered in chemistry. Even though a theory may give a rigorous mathematical description of chemical phenomena, the mathematical difficulties might be so great that it is [Pg.2]

Tubular reactors have empty spaces only between the catalyst particles. This eliminates one big disadvantage of CSTRs. On the other hand, the mathematical description and analysis of the data become more complicated. For chemical reaction studies it is still useful to detect major changes or differences in reaction mechanism. [Pg.154]

The crystals are assumed to be circular disks. This geometry is consistent with previous thermodynamic derivations. It has the advantage of easy mathematical description. [Pg.220]

Due to the combining effects of hydrodynamic and physicochemical factors, the study of cake structure and resistance is extremely complex, and any mathematical description based on theoretical considerations is at best only descriptive. [Pg.76]

Until now we have restricted ourselves to consideration of simple tensile deformation of the elastomer sample. This deformation is easy to visualize and leads to a manageable mathematical description. This is by no means the only deformation of interest, however. We shall consider only one additional mode of deformation, namely, shear deformation. Figure 3.6 represents an elastomer sample subject to shearing forces. Deformation in the shear mode is the basis [Pg.155]

Identification of the material properties as an estimation of transfer function (TF) for the black box model. In this case the problem of identification is solving according to the results of the input (IN) and output (OUT) actions. There is a transfer of notion of mathematical description of TF on characterization of the material. This logical substitution gives us an opportunity to formalize testing procedure and describe the material as a set of formulae, which can be used for quantitative and qualitative characterization of the materials. [Pg.188]

The model describing interaction between two bodies, one of which is a deformed solid and the other is a rigid one, we call a contact problem. After the deformation, the rigid body (called also punch or obstacle) remains invariable, and the solid must not penetrate into the punch. Meanwhile, it is assumed that the contact area (i.e. the set where the boundary of the deformed solid coincides with the obstacle surface) is unknown a priori. This condition is physically acceptable and is called a nonpenetration condition. We intend to give a mathematical description of nonpenetration conditions to diversified models of solids for contact and crack problems. Indeed, as one will see, the nonpenetration of crack surfaces is similar to contact problems. In this subsection, the contact problems for two-dimensional problems characterizing constraints imposed inside a domain are considered. [Pg.13]

See also in sourсe #XX -- [ Pg.13 ]

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