Particle mass constant

The origin of the isotope effect is the dependence of coq and co on the reacting particle mass. Classically, this dependence comes about only via the prefactor coq [see (2.14)], and the ratio of the rate constants of transfer of isotopes with masses mj and m2 m2 > mj) is temperature-independent and equal to... 

Exponent given by equations Mass of particle, lb mass Constant given in table Reynolds number, dimensionless (use consistent units)... 

Zone I combustion proceeds at an overall rate equal to the product of the intrinsic burning rate, evaluated at the ambient oxygen concentration, and the total internal surface area. The char diameter necessarily stays constant and the particle density continually decreases as particle mass is evenly removed throughout the particle on the pore surfaces (constant-diameter combustion). 

In Zone III combustion, the burning rate is determined by the diffusive flux of oxygen through the particle boundary layer. The particle density remains constant throughout burnout and the particle size continually decreases as mass is removed solely from the particle surface (constant-density combustion). 

If the material being sampled consists of discrete particles such that an average particle mass can be calculated, then still another method is useful. In this procedure the constants and B of Equation 5 are obtained from the intraclass correlation coefficient between pairs of small, single-increment samples of equal mass, the increments of each pair being collected near each other and the pairs distributed over the population under study. The value of r can be estimated from the relation ... 

X = himv, where h is Planck s constant, m the particle mass and v the particle speed. As the speed is proportional to the square root of the temperature mv 12 = kT),vit see that the quantum effect is much more pronounced at high densities and low temperatures, and when the particle in question is very light. The pressure then becomes independent of the temperature. Conversely, for a given density, the quantum effects disappear above a certain critical temperature and the stellar material reassumes its initial flexibility. 

The definition of the surface-volume mean diamefer given by equation 1.11 must be modified for use wifh dafa from a sieve analysis. By assuming that the shape and density of fhe particles are constant for all size fractions, a number distribution can be transformed fo a mass distribution (Smith, 2003) and therefore the surface-volume diameter becomes... 

We consider either isothermal mass transfer (Gq == 0) or uniform composition heat transfer (Gr = 0) from a particle with constant surface composition or temperature. The Rayleigh number Ra is used for both GqPr and Gr Sc. 

K Langmuir constant (m moL ) k reaction rate constant (m moL s ) k overall adsorption rate parameter (s ) k intra-particle mass transfer coefficient (s )... 

Measurements of extinction by small particles are easier to interpret and to compare with theory if the particles are segregated somehow into a population with sufficiently small sizes. The reason for this will become clear, we hope, from inspection of Fig. 12.12, where normalized cross sections using Mie theory and bulk optical constants of MgO, Si02, and SiC are shown as functions of radius the normahzation factor is the cross section in the Rayleigh limit. It is the maximum infrared cross section, the position of which can shift appreciably with radius, that is shown. The most important conclusion to be drawn from these curves is that the mass attenuation coefficient (cross section per unit particle mass) is independent of size below a radius that depends on the material (between about 0.5 and 1.0 fim for the materials considered here). This provides a strong incentive for deahng only with small particles provided that the total particle mass is accurately measured, comparison between theory and experiment can be made without worrying about size distributions or arbitrary normalization. 

Since the liquid is saturated with hydrogen, only the liquid-to-particle mass transfer coefficient and the intrinsic rate constant will be significant. In the case that the reaction is fast, the reaction rate will depend only on the liquid-sold mass transfer resistance. Since the particle are very small (10 micrometers), and the loading is moderate (0.8% mass), the Sherwood number will be that of lonely spheres, so Sh = 2. For this case we can take Sh = =4 [50], rather safely. 

The lowest energy solution of the Schrodinger equation for a particle (mass m) moving in a constant potential energy (V), and in a onedimensional box of length L, takes the form ... 

For the Rosin-Rammler distribution, the distribution constants (a and f ) are obtained from the particle mass distribution data. To obtain the mass density distribution, the data on... 

Modification of silica gel with volatile or gaseous compounds is performed in the vapour phase. Industrial-scale reactors and laboratory scale gas adsorption apparatus have been used. In the industrial field, fluidized bed and fluid mill reactors are of main importance. In fluidized bed reactors,82 the particles undergo constant agitation due to a turbulent gas stream. Therefore, temperatures are uniform and easy to control. Reagents are introduced in the system as gases. Mass transport in the gas phase is much faster than in solution. Furthermore, gaseous phase separations require fewer procedural steps than solution phase procedures, and may also be more cost-effective, due to independence from the use and disposal of non-aqueous solvents. All these advantages make the fluidized bed reactors preferential for controlled-process industrial modifications. 

Here, k is Boltzmann s constant and mp particle mass. In analogy to a simple kinetic theory of gases, the definition of a mean free path for particles is Ap = vpsi l. The average thermal speed of particle is... 

VLDL containing apoB-100, apoE, and apoC is secreted by the liver into the space of Disse. Metabolism of this triglyceride-rich particle by lipoprotein lipase leads to shrinkage of the core triglyceride component. As Eisen-berg and others have shown experimentally (E4), other VLDL components must be removed before the mature LDL particle is formed. These changes include removal of about 75% of the phospholipid, 85% of the unesterified cholesterol, and most of the apoC and apoE from the VLDL surface (E3). The mass of apoB per particle stays constant during metabolism of VLDL to LDL, but all other surface and core materials are diminished. 

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