Particle transfer function

The particle transfer function relating the average concentration inside particle and the particle surface concentration is ... 

The definitions of the adsorber and particle transfer functions can be applied to various kinetic mechanisms and different types of adsorbers. They are valid for the general nonlinear. 

Thus as (y) will always be greater than unity, the resistance to mass transfer term in the mobile phase will be, at a minimum, about forty times greater than that in the stationary phase. Consequently, the contribution from the resistance to mass transfer in the stationary phase to the overall variance per unit length of the column, relative to that in the mobile phase, can be ignored. It is now possible to obtain a new expression for the optimum particle diameter (dp(opt)) by eliminating the resistance to mass transfer function for the liquid phase from equation (14). 

This is our principal result for the rate of desorption from an adsorbate that remains in quasi-equihbrium throughout desorption. Noteworthy is the clear separation into a dynamic factor, the sticking coefficient S 6, T), and a thermodynamic factor involving single-particle partition functions and the chemical potential of the adsorbate. The sticking coefficient is a measure of the efficiency of energy transfer in adsorption. Since energy supply from the... 

The acceptance criteria for the Gibbs ensemble were originally derived from fluctuation theory [17]. An approximation was implicitly made in the derivation that resulted in a difference in the acceptance criterion for particle transfers proportional to 1/N relative to the exact expressions given subsequently [18]. A full development of the statistical mechanics of the ensemble was given by Smit et al. [19] and Smit and Frenkel [20], which we follow here. A one-component system at constant temperature T, total volume V, and total number of particles N is divided into two regions, with volumes Vj and Vu = V - V, and number of particles Aq and Nu = N - N. The partition function, Q NVt is... 

Linear energy transfer (LET) A function of the capacity of the radiation to produce ionization. LET is the rate at which charged particles transfer their energies to the atoms in a medium and a function of the energy and velocity of the charged particle. See Radiation dose. 

Polymerizable surfactants capable of working as transfer agents include thiosulfonates, thioalkoxylates and methyl methacrylate dimer/trimer surfactants. Thioalkoxylates with 17-90 ethylene oxide units were produced from ethoxylated 11 bromo-undecanol by replacing the bromine with a thiol group via the thiazonium salt route [8]. In the presence of water-soluble azo initiator the thio ended Transurfs (used at a concentration above the CMC) gave monodispersed latex particles in emulsion polymerization of styrene. However, the incorporation of the Transurf remained low, irrespective of the process used for the polymerization (batch, semibatch, seeded). The stability of the lattices when the surfactant and the transfer function were incorporated in the same molecule was better than when they were decoupled. 

The measured heat transfer coefficients are often represented as a function of solids concentration, as shown in the experimental data of Fig. 2 for a wide range of operating conditions, bed temperatures and solids sizes. It has been found that there exists the relation h oc (1 - e)n, in which the values of exponent n generally ranges from 0.5 to 1.0. The strong dependence of heat transfer coefficient on solids concentration implies that heat transfer between suspension and surfaces is dominated by a convective particle transfer process. 

In some situations where one or more of the latex properties are measured either directly or indirectly through their correlation with surrogate variables and where extreme nonlinearities such as the periodic generation of polymer particles does not occur, one can use much simpler modehng and control techniques. Linear transfer function-type models can he identified directly from the plant reactor data. Conventional control devices such as PID controllers or PID controllers with dead-time compensation can then be designed. If process data is also used to identify... 

The performance of the FBI is a function of a variety of experimental parameters, related to solvent nebulization, desolvation, particle-transfer through the momentum separator and the transfer tube, the evaporative collisions in the ion source, and the ionization process. The various parameters are highly interrelated. Systematic optimization of the various FBI parameters for (pharmaceutical) applications was reported by Voyksner et al. [90] and Tiller [91]. 

The statistical description of multiphase flow is developed based on the Boltzmann theory of gases [37, 121, 93, 11, 94, 58, 61]. The fundamental variable is the particle distribution function with an appropriate choice of internal coordinates relevant for the particular problem in question. Most of the multiphase flow modeling work performed so far has focused on isothermal, non-reactive mono-disperse mixtures. However, in chemical reactor engineering the industrial interest lies in multiphase systems that include multiple particle t3q)es and reactive flow mixtures, with their associated effects of mixing, segregation and heat transfer. 

The particle transfer coefficient k has dimensions of velocity and is often called the deposition velocity. At a given location on the collector surface the dimensionless group kL/D, known as the Sherwood number, is a function of the Reynolds. Peclet, and interception numbers. Rates of particle deposition measured in one fluid over a range of values of Pe, Re, and R can be u.sed to predict deposition rate.s from another fluid at the same values of the dimensionless groups. In some cases, it is convenient to work with the Schmidt number Sc = u/D = Pe/Re in place of Pe as one of the three groups, because Sc depends only on the nature of the fluid and the suspended particles. 

Models are constructed which suggest that these optical measurements can be used to determine the effective particle size distribution parameters, mean diameter and sigma. Assumptions include multilayer particle deposit, the lognormal distribution of the diameters of the spherical, opaque particles, and no sorting of size classes during particle deposition. The optical measurement include edge trace analysis to derive the contrast transfer function, and density fluctuation measurements to derive the Wiener spectrum. Algorithms to perform these derivations are outlined. 

The corresponding functions which do contain information over a range of dimensions are the contrast transfer function, CTF, and the Wiener spectrum, or noise content of the deposit as a function of spatial frequency (8). These functions also have been found to contain information which correlates to the particle size distribution, as will now be discussed. 

The correlation analyses of toner particle size and size distribution parameters and image quality characteristics of toner deposits as measured by the spectral dependence of contrast transfer function and noise show high coefficients of correlation Specifically the Wiener spectrum data appear to yield the weight geometric mean and standard deviation of the toner population in this study. Therefore the Wiener spectrum may be another analytical tool in characterizing particle populations. It must be pointed out that the analysis reported here is mainly empirical. Further work is needed to refine the models and to examine the limits of applicability of these tests. Factors such as particle clumping, non-uniform depositions and optical limitations are specific areas for examination. 

In 1923, Broensted was the first to develop an acid-base concept that was no longer related to substances, but rather to the function of particles. Acids are proton donors and are capable, with suitable reaction partners, to donate protons to base particles or proton acceptors, i.e. protolysis or proton transfer reaction. For example, HC1 molecules, as acid particles, transfer protons when colliding with H20 molecules (see Fig. 7.3). In this sense, the proton donors of pure sulfuric acid are H2S04 molecules, the acid particles of the sulfuric acid solution are the hydronium ions (or also the hydrogen sulfate ions in concentrated solutions). In weak acids, the protolysis equilibrium is to be considered, equilibria and their constants are well defined. 

Percent Error in the Calculated Transfer Rate when Particle B Functions as the Acceptor... 

As can be seen from eqn (14.8), the calculation of the tensor reduces to the calculation of two-particle correlation functions. The lack of sufficiently detailed data on the exciton band structure and the exciton-phonon coupling constants considerably complicates the accurate calculation of the two-particle correlation functions and the exciton diffusion coefficients. However, the temperature dependence of this coefficient differs significantly for coherent and incoherent excitons (see below). Therefore, studying the temperature dependence of diffusion has always been an important tool to analyze the character of the energy transfer in molecular crystals. In the remainder of this chapter, we will focus on the main characteristics of the diffusion constant and its temperature dependence... 

If, however, the alumina particles are represented by the pseudohomoge-neous model, assuming slab geometry, neglecting the axial dispersion and the film mass transfer resistance (it has been demonstrated (ref. 2) that the effects of these two variables are negligible in comparison with the effect of the internal diffusion resistance), the theoretical transfer function for the study zone is given by ... 

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