Average particle mass

On the other hand, mass-transfer inside tbe viscous polymer particles will occur by molecular diffusion. According to an analytical solution Co the diffusion equation inside tbe particles, average mass-transfer coefficient between time 0 is given as follows (Newman, 1931) ... 

True Density or Specific Gravity. The average mass per unit volume of the individual particles is called the tme density or specific gravity. This property is most important when volume or mass of the filled composition is a key performance variable. The tme density of fillers composed of relatively large, nonporous, spherical particles is usually determined by a simple Hquid displacement method. Finely divided, porous, or irregular fillers should be measured using a gas pycnometer to assure that all pores, cracks, and crevices are penetrated. 

The diametei of average mass and surface area are quantities that involve the size raised to a power, sometimes referred to as the moment, which is descriptive of the fact that the surface area is proportional to the square of the diameter, and the mass or volume of a particle is proportional to the cube of its diameter. These averages represent means as calculated from the different powers of the diameter and mathematically converted back to units of diameter by taking the root of the moment. It is not unusual for a polydispersed particle population to exhibit a diameter of average mass as being one or two orders of magnitude larger than the arithmetic mean of the diameters. In any size distribution, the relation ia equation 4 always holds. 

The smallest unit having the chemical properties of the element are the atoms. All atoms are made up from a number of elementary particles known as the protons, neutrons, and electrons. The protons and neutrons make up an atomic nucleus at the center of the atom, while the electrons, distributed in electron shells, surround the atomic nucleus. The atoms of each element are identical to each other but differ from those of other elements in atomic number (the number of protons in the atomic nucleus) and atomic weight (their weighted average mass) as listed in the table below. 

Sieve No. Mesh Size (mm) Average Particle Size Mass (kg) Mass Fraction Cumulative Mass Fraction Oversize Cumulative Mass Fraction Undersize... 

Turk et al. (1989) measured particle concentrations in 38 buildings that had both smoking and nonsmoking areas. The average mass concentration of respirable particles in smoking areas was 70 /xg m-3 compared to 19 /xg m-3 in nonsmoking areas, whereas the outdoor concentrations were essentially the same, 19 /xg m-3. 

Chemical techniques of analysis deal with a very large number of atoms and yield averages over the sample. Once the concept of isotopes was accepted, a search for different isotopes of every element was pursued. The key to the success of this search was the development of a precision instrument that sampled the atoms one at a time. It had been known since the development of the cathode ray tube that positive ions were also produced, and early experiments with these particles revealed singly and doubly charged species of the atoms and molectrles that were contained in the tube. Sir J.J. Thomson observed in 1912 that when neon was the background gas, particles of mass ntrmber 20 and 22 were observed. Attempts to obtain pure samples of the two different atoms by fractionation techniques were unsuccessful, but in retrospect this was because they were both neon isotopes. 

Let us consider A molecules (or n moles, with N = nNA, NA = Avogadro s number), each a point particle of mass m and average velocity,... 

The porous volumes measured by N2 adsorption are listed in Table 3. After the boronation, the total porous volumes (Vt) of the samples increase, corresponding to the increase of benzene adsorption capacity mentioned above. This should be resulted from the following aspects (1) The average mass of zeolite crystallite decrease and the number of crystal particles in unit weight of sample increases after the boronation owing to a limited introduction of trivalent atoms and Na+cations as counterions, as well as a severe dissolution of silicon. Thus, the total porous volume (mL/g) and the adsorption capacity increase. (2) The transformation of pore size occurs during the boronation. As shown in Table 3, the mesoporous volumes increase and the microporous volumes decrease after the boronation, meaning that some micropores are developed into mesopores due to the removal of silicon from the framework. This is also one of the important reasons why the total porous volumes as well as the adsorption capacities increase after the boronation. 

The C stars are another case their average mass loss is slightly more than 10 times the value for solar-type stars with the same atmospheric parameters. This must indicate that C-star mass loss is dust-driven, for the driving efficiency of Carbon dust particles is about ten times the value for silicates (sedlmayr, private comm. 1987). 

For a single particle with mass m and (average) velocity v, the kinetic energy is given by ... 

We start to follow the relative motion between two particles of mass mp separated by a specified initial distance. This initial distance is chosen to be large compared to the correlation length Xr (the average distance over which the relative velocity of the particle pair is correlated). Therefore, the initial relative motion of the particle pair, which is considered as the initial condition in the calculations, is uncorrelated and its initial relative velocity distribution is Maxwellian. The correlation length Xr is given by (1)... 

Single Sphere Model II (Equations 4, 5, 8, 9 and 10 in reference 6) In this model allowance is made for the resistance to mass transfer offered by the surface film surrounding the herb particles. The mass transfer coefficient kf was obtained from correlations proposed by Catchpole et al (8, 9) for mass transfer and diffusion into near-critical fluids. An average of the binary diffusivities of the major essential oil components present was used in calculating kf (these diffusivities were all rather similar because of their similar structures). 

There are a number of different mean or median values which can be defined for a particle size distribution. These means or medians are useful depending on where the data came from or how the data are to be used. For example, the diameter of average mass (volume) can be defined as representing the diameter of a particle whose mass (volume) times the number of particles gives the total mass (volume) of all the particles. Similarly, the diameter of average surface represents the diameter of a particle whose surface times the number of particles gives the total surface. 

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