Description of the Phenomenon

As we have seen in chapter 2, invasion of the tube by the liquid proceeds if the surface energy of the wall decreases with wetting sl Iso)- The force F that causes the liquid to move in the tube is [equation (2.34)] 

Prom the point of view of dynamics, two forces oppose the movement of the fluid. They are its inertia and the force of viscous friction, respectively. Thus, the equation of motion can be written as 

FIGURE 5.12. Capillary rise. The meniscus has a height z (less than Jurin s height) and progresses at a velocity V, 

The viscous friction force in a tube is given by Poiseuille s law. The velocity gradients in the tube are of order V/R, which means that the viscous stress is of order t]V/R. In a tube invaded over a length 2 (hence over a surface 27tR2 ), we conclude that the force increases as r]Vz. The numerical coefficient in this law is Therefore, the force can 

Note that equation (5.40) neglects the viscous dissipation associated with the displacement of the contact line—a topic to be discussed in chapter 6. We will see then that this simplification assumes 2 to be rather large [Z lOR/0e)  

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In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

An instability of the impulse MTS method for At slightly less than half the period of a normal mode is confirmed by an analytical study of a linear model problem [7]. For another analysis, see [2]. A special case of this model problem, which gives a more transparent description of the phenomenon, is as follows Consider a two-degree-of-freedom system with Hamiltonian p + 5P2 + + 4( 2 This models a system of two springs con-... 

Finally, the phenomenon of shock-induced polarization represents perhaps the most distinctive phenomenon exhibited by shock-compressed matter. The phenomenon has no counterpart under other environments. The delineation of the details of the phenomenon provides an unusual insight into shock-deformation processes in shock-loading fronts. Description of the phenomenon appears to require overt attention to a catastrophic description of shock-compressed matter. In the author s opinion, a study of shock-induced polarization represents perhaps the most intriguing phenomenon observed in the field. In polymers, the author has characterized the effect as an electrical-to-chemical investigation [82G02]. 

All these developments need precise values of the electrochemical systems. Springer Verlag and the editor are very grateful to the author R. Holze who collects and presents all relevant data together with a precise description of the phenomenons in this volume. The data are divided in five ehapters ... 

Oosawa (1971) developed a simple mathematical model, using an approximate treatment, to describe the distribution of counterions. We shall use it here as it offers a clear qualitative description of the phenomenon, uncluttered by heavy mathematics associated with the Poisson-Boltzmann equation. Oosawa assumed that there were two phases, one occupied by the polyions, and the other external to them. He also assumed that each contained a uniform distribution of counterions. This is an approximation to the situation where distribution is governed by the Poisson distribution (Atkins, 1978). If the proportion of site-bound ions is negligible, the distribution of counterions between these phases is then given by the Boltzmann distribution, which relates the population ratio of two groups of atoms or ions to the energy difference between them. Thus, for monovalent counterions... 

In fact, electron transfer occurs at the microscopic level where quantum mechanics provides the necessary description of the phenomenon (5-13). In the quantum mechanical solution, associated with the potential curves in Figure 1 are quantized energy levels, Ej = (vj + 1/2) 100., where Vj and 2ttvj are the vibrational... 

The book is organized in nine chapters and eleven appendices. Chapters 1 and 2 introduce the fundamental concepts and definitions. Chapters 3 to 7 treat binding systems of increasing complexity. The central chapter is Chapter 4, where all possible sources of cooperativity in binding systems are discussed. Chapter 8 deals with regulatory enzymes. Although the phenomenon of cooperativity here is manifested in the kinetics of enzymatic reactions, one can translate the description of the phenomenon into equilibrium terms. Chapter 9 deals with some aspects of solvation effects on cooperativity. Here, we only outline the methods one should use to study solvation effects for any specific system. 

An increasing number of studies on lipid metabolism in human skeletal muscle using localized MR proton spectroscopy have been performed since the first description of the phenomenon that proton NMR spectroscopy allows the differentiation of two distinct lipid compartments and the experimental confirmation that one of these compartments is attributed to the IMCL pool. The non-invasiveness and the high sensitivity even to low lipid concentrations under physiological conditions denote the uniqueness of this modality and allow examinations of large numbers of healthy volunteers and follow-up metabolic intervention studies. 

A detailed analysis of the dynamics of polyatomic photodissociation presents a formidable problem. For this reason a number of simplified models have been introduced. Based on these models, one can obtain a qualitative description of the phenomenon, and of some of the important aspects. 

L. Pasteur, J. Tyndall, E. T. Chapman, P. Miquel, W. Spring, F. Schulz, etc. Air may be freed from dust particles, etc., in suspension by filtration through biscuit earthenware, asbestos, or cotton wool. When a beam of sunlight is passed through unfiltered air, it reveals a multitude of motes constantly in motion. Lucretius, in his Be natura remm (2.113, 60 b.c.), has given a very vivid description of the phenomenon. With filtered air, there is no such eflect, and J. Tyndall said that such air is optically empty. F. O. Rice showed that in a number of reactions— e.g. the oxidation of soln. of sodium arsenite or sulphite, the decomposition of hydrogen dioxide, etc.—the suspended dust in air acts as a catalytic agent. 

This qualitative description of the phenomenon of predissociation is adequate in many ways but it is insufficient for a quantitative calculation of lifetimes and dissociation probabilities33. 

Figure 4.1 shows the concentration gradients that form on either side of a dialysis membrane. However, dialysis differs from most membrane processes in that the volume flow across the membrane is usually small. In processes such as reverse osmosis, ultrafiltration, and gas separation, the volume flow through the membrane from the feed to the permeate side is significant. As a result the permeate concentration is typically determined by the ratio of the fluxes of the components that permeate the membrane. In these processes concentration polarization gradients form only on the feed side of the membrane, as shown in Figure 4.3. This simplifies the description of the phenomenon. The few membrane processes in which a fluid is used to sweep the permeate side of the membrane,...

Let an object or process be described by model 41 =f(au..., ), where parameters at reflect the quantitative, functional, and structural sections of the phenomenon under study. The multitude of possible types of function / can be determined on the basis of expert estimation with consideration of a priori information and a heuristic set of partial descriptions of the phenomenon. The training sequence f is constructed which serves the basis for multi-row selection of the model of optimal complexity and acceptable accuracy. The first level of selection consists in calculating row ys, where ys = g(ai l,ai) (s = 1,..., L = C2n i = 1.n). The second level of selection gives row zp, where zp = g yj, yj)... 

The second virial coefficient of the macromolecular coil B(T) depends not only on temperature but on the nature of the solvent. If one can find a solvent such that B(T) = 0 at a given temperature, then the solvent is called the 0-solvent. In such solvents, roughly speaking, the dimensions of the macromolecular coil are equal to those of an ideal macromolecular coil, that is the coil without particle interactions, so that relations of Sections 1.1—1.4 can be applied to this case, as a simplified description of the phenomenon. 

Several interesting parameter-control models or systems have been reported in recent years. These are a five-state mathematical model for temperature control by Bailey and Nicholson [106], a mathematical-model description of the phenomenon of light absorption of Coffea arabica suspension cell cultures in a photo-culture vessel by Kurata and Furusaki [107], and a bioreactor control system for controlling dissolved concentrations of both 02 and C02 simultaneously by Smith et al. [108]. 

In terms of atomistic description of the phenomenon of catalysis, the border between these two approaches is determined by the rate of attenuation of the electron perturbation in a solid with the distance from an adsorbed molecule as well as by the degree of similarity between electron structures of the whole surface of a solid and of a fragment considered as a model of the adsorption or of an active site. For a long time this problem lacked an unambiguous solution. Therefore both approaches were equally widely used to describe catalytic phenomena, often without proper regard to specific features of the systems considered. Thus, active sites on metal catalyst surfaces were frequently modeled by individual metal atoms. On the contrary, catalysis on insulator oxide surfaces was sometimes discussed in terms of their cooperative electron properties. 

An expression for the line broadening resulting from rapid radiationless transitions has been derived by introducing a number of simplifying assumptions into the physical description of the phenomenon. 

We will follow a structural approach to describe ionic hydration, since, at variance with a pure thermodynamic description of the phenomenon which detects the overall level of association, it gives information on the way water molecules are arranged around the ion. 

The emission of tropospheric sulphur oxide, and that of NO emission, is now of great concern, known colloquially, but inaccurately as acid rain . Acid deposition would be a better description of the phenomenon. 

The study of such complex phenomena may be roughly separated into three phases. During the first, in which a body of descriptive data is amassed, the problem is outlined in a qualitative way. Phase two, where attention focuses on possible mechanisms, leads to a quantitative description of the phenomenon and to an appreciation of the relative significance of the controlling parameters. In the final phase, a model of the phenomenon is developed, and predictions may be made and tested. 

Let us first ask the question how can a species exist in clusters of molecules at equilibrium with its own monomers We necessarily must consider the fluctuation of any system about its equilibrium. Under normally liquid conditions, the density fluctuations are small in extent (localized) and persist for short times. A microscopic description of the phenomenon may be that of temporary formation of weak bonds, which are then quickly dissipated. If, however, these fluctuations lead to clusters that have a nontransient existence, then... 

We must realize at this point that the calorimetric technique entirely builds upon the establishment of equilibrium conditions enabling the use and help from equilibrium thermodynamics. Many facets of supramolecular chemistry, however, do not comply with this prerequisite. Molecular recognition, for instance, in particular as a crucial property of all living matter, which exists because of nonequilibrium conditions, must be considered a process that relies on kinetic selechvity and thus per se is not open to an all-encompassing description of the phenomenon using this technique [12]. Similar arguments limit the utility of calorimetry in other vectorial processes like membrane transport, signaling, catalysis or locomotion. Never-... 

An adsorption isotherm is a necessary but not sufficient way of describing the thermodynamics of ionic surfactant adsorption because a full description of the phenomenon requires knowledge of mutual interactions between all the components of the system. Such opportunity is offered by flow and batch liquid adsorption microcalorimetry [25-30]. 

In classical mechanics, positions and momenta are treated on an equal footing in the Hamiltonian picture. In quantum mechanics, they become operators, but it is true that the position r and momentum p of a particle are appropriate conjugate variables that can entirely equivalently describe a state of a system under the commutation relation [r, p] = i (Dirac, 1958). This equivalence is usually demonstrated by the example of the onedimensional harmonic oscillator. The choice of the most appropriate representation depends on convenient description of the phenomenon considered. Generally, the position representation is useful for most bound-state problems such as atomic and molecular electronic structures as well as for many scattering problems. The momentum-space treatment... 

About one century later, Lord Kelvin studied the charging between water dripping from two different liquid nozzles, which leads to electrospray phenomena at the nozzles themselves (Smith, 2000). In the last century, a series of systematic studies on electrospray were carried out by Zeleny (Zeleny, 1917) and Taylor (Taylor, 1964a and b) allowing a detailed description of the phenomenon. In the middle of the century, electrospray started to be used on the industrial scale, in the application of paints and coatings to metal surfaces. The fine spray results in very smooth even films, with the paint actually attracted to... 

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