Mean distance: between particles factor

DLVO theory explained major principles of coagulation of hydrosols by electrolytes and brought to common grounds all previous observations (primarily of qualitative nature) that related to individual cases and often seemed to be contradictory. In years that followed further extensions of DLVO theory that took into account the possibility of reversible particle aggregation were developed. At very small distances between particles in addition to the usual long-range interaction, molecular attraction and electrostatic repulsion, one must account for other factors that play role at a direct particle contact. The formation of peculiarly structured hydration layers in the vicinity of solid surface, the appearance of elastic forces that are responsible for the Born repulsion between surface atoms at the point of contact, the repulsion between the adsorbed surfactant molecules in contact zone between two particles, all represent the so-called non-DLVO stability factors . This means that more or less deep primary minimum remains finite. 

Initial particle (when dissolving starts) diameter, ft Mass mean particle diameter, ft Impeller diameter, ft Fanning friction factor, dimensionless Distance between feedpipe end and impeller disk or impeller blade, ft... 

VmaY = the frequency at which the band has a maximum fimax = the intensity of the absorption Ho = the applied magnetic field g = the spectroscopic splitting factor r = the distance between protons P = the angle between a line joining the protons and Hq S2 = the mean-square deviation of the field firom the center of the line Hq Mn = the mass of a neutron particle A = the wave length of a neutron beam V = the partiele velocity A (= X2 - xi) = changing path distance r = is the reflection coefficient T = the transmission coefficient of the beam splitter yl(v) = the fi quency distribution 1(D) and B(n) = orthogonal fimctions F y) = the fi-equency distribution N = number of points in a Fourier Transform 9 = a set of normal coordinates... 

To understand heat conduction, diffusion, viscosity and chemical kinetics the mechanistic view of molecule motion is of fundamental importance. The fundamental quantity is the mean-free path, i. e. the distance of a molecule between two collisions with any other molecule. The number of collisions between a molecule and a wall was shown in Chapter 4.1.1.2 to be z = CNQvdtl6. Similarly, we can calculate the number of collisions between molecules from a geometric view. We denote that all molecules have the mean speed v and their mean relative speed with respect to the colliding molecule is g. When two molecules collide, the distance between their centers is d in the case of identical molecules, d corresponds to the effective diameter of the molecule. Hence, this molecule will collide in the time dt with any molecule centre that lies in a cylinder of a diameter 2d with the area Jid and length gdt (it follows that the volume is Jtd gdt). The area where d is the molecule (particle) diameter is also called collisional cross section a. This is a measure of the area (centered on the centre of the mass of one of the particles) through which the particles cannot pass each other without colliding. Hence, the number of collisions is z = c n gdt. A more correct derivation, taking into account the motion of all other molecules with a Maxwell distribution (see below), leads to the same expression for z but with a factor of V2. We have to consider the relative speed, which is the vector difference between the velocities of two objects A and B (here for A relative to B) ... 

The initial distances to the star are just behind the 2/1 resonance a = (i /(12 = 0.612. When the semi-major axis of mi increases, ai increases and the mean-motion resonance (a = 0.63) between mi and m2 is reached. Capture then can take place. The probability of capture depends on the rate of variation of ai - if the rate is high, the orbit crosses the resonance without capture, one phenomenon very well studied in the case of one massless particle. Other factors influencing the probability of capture are the orbital eccentricities - capture is more probable when orbital eccentricities are small (Dermott et al., 1988 Gomes, 1995). In our calculations, initial eccentricities were lower than 0.001 and the physical parameters were adjusted to have slow resonance approximation. Figure 9 shows the evolution of the semi-major axes. 

One can see that the thickness of the electrical double layer is inversely proportional to the concentration of electrolyte in the system and to the square of the valency of the ions involved. In terms of colloidal stability, this means that the distance of separation between two particles that can be maintained under a given set of circumstances will depend on, among other things, those two factors. And their important effect gives one a handle for manipulating the characteristics and stabihty of many colloidal systems. 

The mean free path of the molecule in the gas phase is another useful parameter. This is the average distance traveled by a molecule before it strikes another molecule. As would be expected, this depends on pressure, temperature, and radii of particles. The collisional cross section a) can be described by a cylinder of radius (r) such that all particles that fall within an area of nr collide with this particle. As both are traveling with respect to each other, a Jl factor is also inserted. In units of centimeter, the average distance traveled between collisions (the mean free path) is ... 

The path taken by an ion from one electrode to the other will not be a straight one, as it has to evade the solid structures by making detours. The ratio of the mean actual path in comparison with the direct distance is called the tortuosity factor T. For plastic bodies consisting essentially of spherical, interconnected particles with voids in between, with a porosity of about 60%, this value is roughly 1.3 for higher porosities it decreases to approach a value of 1.0 at very high porosities. 

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