Particle number solid phase

In a number of these processes, a liquid heat- and mass-transfer medium is in direct contact with the catalyst and the reaction mixture. The main function of the liquid is to act as a heat sink and as a medium for convective heat transfer. However, since the liquid may be assumed to cover the solid particles and in this way act as a barrier between the gaseous and the solid phases, it must therefore also function as a mass-transfer medium. 

The heat transfer path through the solid phase offers considerable thermal resistance for many porous materials, particularly if the pellet is formed by tableting of microporous particles. Such pellets may be regarded as an assembly of particles that contact one another at only a relatively small number of points that act as regions of high thermal resistance. 

In this section, we will only discuss the basic principles of kinetic theory, where for detailed derivations we refer to the classic textbook by Chapman and Cowling (1970), and a more recent book by Liboff (1998). Of central importance in the kinetic theory is the single particle distribution function /s(r, v), which can be defined as the number density of the solid particles in the 6D coordinate and velocity space. That is, /s(r, v, t) dv dr is the average number of particles to be found in a 6D volume dv dr around r, v. This means that the local density and velocity of the solid phase in the continuous description are given by... 

The terms Jga and Jsa are the diffusive fluxes of species a in the gas and solid phases, respectively. Note that in addition to molecular-scale diffusion, these terms include dispersion due to particle-scale turbulence. The latter is usually modeled by introducing a gradient-diffusion model with an effective diffusivity along the lines of Eqs. (149) and (151). Thus, for large particle Reynolds numbers the molecular-scale contribution will be negligible. The term Ma is the... 

The specific surface area. 1 of a porous solid that is formed of the monodisperse particles (solid phase) of volume I, and surface area. , is equal to the multiplication of the surface area of one particle by the number of particles Am in unit of mass. Using Equation 9.50,... 

Fig. 7.1 gives a size spectrum of water-borne particles. Particles with diameters less than 10 pm have been called colloids. In soils, the clay-sized and fine silt-sized particles are classified as colloids. Colloids do not dissolve, but instead remain as a solid phase in suspension. Colloids usually remain suspended because their gravitational settling is less than 10 2 cm s 1. Under simplifying conditions (spherical particles, low Reynolds numbers), Stokes law gives for the settling velocity, vs... 

It is reasonable to assume that clay colloids exhibit a similar surface chemistry as clay which is sorbed, bonded, or precipitated in the stationary solid phase. Mineral colloids may be formed when precipitation or dissolution generate particles which are resistant to settling. These particles maybe formed by any number of conditions whereby the solubility of a particular solute is exceeded or a stable solid is disrupted mechanically [21,24]. 

An important consideration of reactions in which a new solid phase appears is the number, source and location of nucleation sites and the form of the new phase. A needle-like new phase can result in a marked apparent expansion of the material leading to particle disintegration in packed beds. 

The concept of reducing the number of reaction vessels and exponentially increasing the number of synthesized compounds was brought to a next level of simplicity by the split-and-pool method of Furka et al.5 The split-and-pool method was independently applied by Lam et al.6 in a one-bead-one-compound concept for the combinatorial synthesis of large compound arrays (libraries) and by Houghten et al.7 for the iterative libraries. Now several millions peptides could be synthesized in a few days. In Furka s method the resin beads receiving the same amino acid were contained in one reaction vessel—identical to Frank s method—however, the beads were pooled and then split randomly before each combinatorial step. Thus the method is referred to as the random split-and-pool method to differentiate it from Frank s method in which each solid-phase particle was directed into a particular reaction vessel (the directed split-and-pool method). 

The current version of the Encore synthesizer has been designed for the synthesis of up to 960 compounds using an algorithm to handle 10,8, and 12 building blocks in the first, second, and third combinatorial steps, respectively (Fig. 2). The total number of combinatorial compounds produced this way is n = 10 x 8 x 12 = 960. For the first combinatorial step, 10 reaction vessels are charged with 96 (8 x 12) solid-phase supports and the first set of building blocks is chemically attached to solid-phase supports. After this step, all 96 particles per reaction vessel are identical and particles from different reaction vessels differ only by the kind of first building block attached to solid-phase particles. 

Inputting solid particles at fixed positions, of different sizes simulates a solid phase in the fluid lattice (Fig. 4). The number of fluid particles per node and their interaction law (collisions) affect the physical properties of real fluid such as viscosity. Particle movements are divided into the so called propagation step (spatial shift) and collisions. Not all particles take part in the collisions. It strongly depends on their current positions on the lattice in a certain LGA time step. In order to avoid an additional spurious conservation law [13], a minimum of two- and three-body collisions (FHP1 rule) is necessary to conserve mass and momentum along each lattice line. Collision rules FHP2 (22 collisions) and FHP5 (12 collisions) have been used for most of the previous analyses [1],[2],[14], since the reproduction of moisture flow in capillaries, in comparison to the results from NMR tests [3], is then the most realistic. 

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