Bulking coefficient

Where the reduction in ASE is attributable to bulking of the cell wall by the modifying agent, some workers calculate the influence of this in terms of a bulking coefficient (BC), defined as follows ... 

Similarly, the volume change (VC), or bulking coefficient (BC), can be reported as a percentage increase compared to the original volume (Equation (2.7)). 

Another concept that has been used freely and frequently in analyzing the coefficient of friction in lubricated sliding involves the dependence of the shear strength of a monomolecular film of fatty acid on the contact pressure, but no detailed model has ever been advanced to show the relation between shear strength and the molecular structure of the film. Bowers and Zisman [45] wrote the following relation for the "bulk" coefficient of friction of stearic acid ... 

Referring back to Fig. 16, we assume that the fraction of space between the globs just above the melting point is AF/F, and this is the volume available for perfect gas atoms. However, since the thickness of the inter-globular shell is assumed to maintain a constant value r, then the space is a two-dimensional gas. Since the bulk coefficient of expansion of a perfect gas at constant pressure is IjT, that of a two-dimensional gas is fT. So the bulk coefficient of thermal expansion of a liquid just above the melting point should be obtained by prorating the expansions due to the solid fraction 1 — AF/F and the gaseous fraction AF/F ... 

Fig. 5. The computed value of the change in bulk coefficient of expansion on melting using (19) plotted against the experimental differences for liquid and solid.

Highly structured, agglomerated amorphous silicates are a class of synthetically prepared pigments that are used in a variety of paper grades, where brightness, opacity, bulk, coefficient of friction and ink receptivity are considered critical properties. In many cases, precipitated silicas serve as partial or complete replacements for titanium dioxide. 

Axial expansion was plotted as a function of temperature for both the a and c param.jters. From this data, average axial thermal expansion values were determined for each composition, and used to compute the bulk coefficient of thermal expansion (CTE) values shown in Table 1. 

The use of air-bome ultrasound for the excitation and reception of surface or bulk waves introduces a number of problems. The acoustic impedance mismatch which exists at the transducer/air and the air/sample interfaces is the dominant factor to be overcome in this system. Typical values for these three media are about 35 MRayls for a piezo-ceramic (PZT) element and 45 MRayls for steel, compared with just 0.0004 MRayls for air. The transmission coefficient T for energy from a medium 1 into a medium 2 is given by... 

Here (D is the diffusion coefficient and C is the concentration in the general bulk solution. For initial rates C can be neglected in comparison to C/ so that from Eqs. IV-59 and IV-60 we have... 

It was commented that surface viscosities seem to correspond to anomalously high bulk liquid viscosities. Discuss whether the same comment applies to surface diffusion coefficients. 

The dififiision time gives the same general picture. The bulk self-diffusion coefficient of copper is 10"" cm /sec at 725°C [12] the Einstein equation... 

The state of an adsorbate is often described as mobile or localized, usually in connection with adsorption models and analyses of adsorption entropies (see Section XVII-3C). A more direct criterion is, in analogy to that of the fluidity of a bulk phase, the degree of mobility as reflected by the surface diffusion coefficient. This may be estimated from the dielectric relaxation time Resing [115] gives values of the diffusion coefficient for adsorbed water ranging from near bulk liquids values (lO cm /sec) to as low as 10 cm /sec. 

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

A quite different approach was adopted by Robinson and Stokes [8], who emphasized, as above, that if the solute dissociated into ions, and a total of h molecules of water are required to solvate these ions, then the real concentration of the ions should be corrected to reflect only the bulk solvent. Robinson and Stokes derive, with these ideas, the following expression for the activity coefficient ... 

Surface waves at an interface between two innniscible fluids involve effects due to gravity (g) and surface tension (a) forces. (In this section, o denotes surface tension and a denotes the stress tensor. The two should not be coiifiised with one another.) In a hydrodynamic approach, the interface is treated as a sharp boundary and the two bulk phases as incompressible. The Navier-Stokes equations for the two bulk phases (balance of macroscopic forces is the mgredient) along with the boundary condition at the interface (surface tension o enters here) are solved for possible hamionic oscillations of the interface of the fomi, exp [-(iu + s)t + i V-.r], where m is the frequency, is the damping coefficient, s tlie 2-d wavevector of the periodic oscillation and. ra 2-d vector parallel to the surface. For a liquid-vapour interface which we consider, away from the critical point, the vapour density is negligible compared to the liquid density and one obtains the hydrodynamic dispersion relation for surface waves + s>tf. The temi gq in the dispersion relation arises from... 

This rate coefficient can be averaged in a fifth step over a translational energy distribution P (E ) appropriate for the bulk experiment. In principle, any distribution P (E ) as applicable in tire experiment can be introduced at this point. If this distribution is a thennal Maxwell-Boltzmann distribution one obtains a partially state-selected themial rate coefficient... 

The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

Computer simulations act as a bridge between microscopic length and time scales and tlie macroscopic world of the laboratory (see figure B3.3.1. We provide a guess at the interactions between molecules, and obtain exact predictions of bulk properties. The predictions are exact in the sense that they can be made as accurate as we like, subject to the limitations imposed by our computer budget. At the same time, the hidden detail behind bulk measurements can be revealed. Examples are the link between the diffiision coefficient and... 

Therefore, in tire limiting case—tire surface concentration of tire reacting species is zero as all tire arriving ions immediately react—tire current density becomes voltage independent and depends only on diffusion, specifically, on tire widtli of tire Nerstian diffusion layer S, and of course tire diffusion coefficient and tire bulk concentration of anions (c). The limiting current density (/ ) is tlien given by... 

The most widely used descriptor for the hydrophobicity term in toxicology is the distribution coefficient between octanol and water, log Pq< - (the environmental scientists would rather call it log The bulk solvent octanol is of course a... 

Let us now turn attention to situations in which the flux equations can be replaced by simpler limiting forms. Consider first the limiting case of dilute solutions where one species, present in considerable excess, is regarded as a solvent and the remaining species as solutes. This is the simplest Limiting case, since it does not involve any examination of the relative behavior of the permeability and the bulk and Knudsen diffusion coefficients. 

The limiting cases of greatest interest correspond to conditions in which the mean free path lengths are large and small, respectively, compared with the pore diameters. Recall from the discussion in Chapter 3 that the effective Knudsen diffusion coefficients are proportional to pore diameter and independent of pressure, while the effective bulk diffusion coefficients are independent of pore diameter and inversely proportional to pressure. 

It may seem curious that Knudsen diffusion coefficients still appear in equations (5.18) and (5.19), which supposedly give the flux relations at the limit of bulk diffusion control. However, inspection reveals that only ratios of these coefficients are effectively present, and from equation (2,11) it follows that... 

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