Coefficients of mutual influence

Note that some new engineering constants have been used. The new constants are called coefficients of mutual influence by Lekhnitskii [2-5] and are defined as... 

Lekhnitskii defines the coefficients of mutual influence and the Poisson s ratios with subscripts that are reversed from the present notation. The coefficients of mutual influence are not named very effectively because the Poisson s ratios could also be called coefficients of mutual influence. Instead, the rijjj and ri y are more appropriately called by the functional name shear-exitension coupling coefficients. 

Extension-extension coupling coefficients (Poisson s ratios) Shear-extension coupling coefficients (coefficients of mutual influence) Shear-shear coupling coefficients (Chentsov coefficients)... 

Laminate stiffness analysis predicts the constitutive behaviour of a laminate, based on classical lamination theory (CLT). The result is often given in the form of stiffness and compliance matrices. Engineering constants, i.e. the in-plane and flexural moduli, Poisson s ratios and coefficients of mutual influence, are further derived from the elements of the compliance matrix. Analyses are continuously needed in structural design since it is essential to know the constitutive behaviour of laminates forming the structure. The results are also the necessary input data for all other macromechanical analyses. A computer code for the stiffness analysis is a valuable tool on account of the extensive calculations related to the analysis. 

In contrast to consecutive reactions, with parallel competitive reactions it is possible to measure not only the initial rate of isolated reactions, but also the initial rate of reactions in a coupled system. This makes it possible to obtain not only the form of the rate equations and the values of the adsorption coefficients, but also the values of the rate constants in two independent ways. For this reason, the study of mutual influencing of the reactions of this type is centered on the analysis of initial rate data of the single and coupled reactions, rather than on the confrontation of data on single reactions with intergal curves, as is usual with consecutive reactions. 

A non-ideal function of the rate coefficient k c not representing the real effect of mutual influence of components... 

The development of mixture sorption kinetics becomes increasingly Important since a number of purification and separation processes involves sorption at the condition of thermodynamic non-equilibrium. For their optimization, the kinetics of multicomponent sorption are to be modelled and the rate parameters have to be identified. Especially, in microporous sorbents, due to the high density of the sorption phase and, therefore, the mutual Influences of sorbing species, a knowledge of the matrix of diffusion coefficients is needed [6]. The complexity of the phenomena demands combined experimental and theoretical research. Actual directions of the development in this field are as follows ... 

The mutual influence of the particles leads to their shielding within the coil and the overall coefficient of the resistance of the coil proves to be smaller than that for a free-draining coil. The requirement of covariance in relation to successive subdivisions of the macromolecule into subchains gives rise, according to formula (2.14), to the following power dependence for large values... 

This last condition is fulfilled when the ionic concentrations are very low, as they are in fact in dilute solutions of weak electrolytes. The dissociation constants of substances such as weak organic acids can be determined by a combination of the formulae of Ostwald and Arrhenius, but the procedure is quite inadmissible for salts. Here the degree of dissociation is large. In fact the value of a is often indistinguishable from unity, and the mutual influences of the ions are considerable. They are calculable in principle by methods due to Debye and Hiickel, and operate differently on different properties. The procedure outlined on p. 276 allows the calculation of the activity coefiicients. In general the thermodynamic properties of the salt in solution correspond to those of a system with apparently incomplete dissociation, not because the concentrations of the ions are reduced by molecule formation but because the activity coefficients are lowered by mutual ionic influences. 

DLS is certainly the foremost method to obtain the diffusion coefficient D of colloidal particles in the dilute regime. Since the measurements are performed at high dilution, a possible influence of mutual interaction of the particles can be safely dismissed. Hence, the diffusion coefficient D may directly be converted into the hydrodynamic radius Rh by the well-known Stokes-Einstein relation ... 

T = 0.67, < = 5 = 0.62. Despite visual indication of violent wave motion in the experiments, neither flow rate apparently influenced the mass transfer coefficient of the other phase. On the other hand, Bergelin, et al, (8), in the horizontal apparatus mentioned above, did observe the mutual influence of flow rates on the coefficients which their flow studies would predict. 

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

In addition to temperature and concentration, diffusion in polymers can be influenced by the penetrant size, polymer molecular weight, and polymer morphology factors such as crystallinity and cross-linking density. These factors render the prediction of the penetrant diffusion coefficient a rather complex task. However, in simpler systems such as non-cross-linked amorphous polymers, theories have been developed to predict the mutual diffusion coefficient with various degrees of success [12-19], Among these, the most notable are the free volume theories [12,17], In the following subsection, these free volume based theories are introduced to illustrate the principles involved. 

The physicochemical reason why two regimes occur is as follows. In the free molecule region, the effective diffusion coefficient is determined by collisions of the molecules with the catalyst pore walls. Hence, the gas composition will not influence the effective diffusion coefficient. However, in the continuum region mutual collisions between the molecules are determining and the dependence of the effective diffusion coefficient on the concentration becomes most pronounced. 

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