Traveling particles

In the previous chapter, we explored the transport of chemicals from one physical compartment to another—but only in their free molecular form. The reality, however, is much messier than that, as solid particles can travel in water and both solid and liquid aerosols can travel in the air. While particles moving in water and those moving in air are governed by different forces, there are also some striking similarities. One is the relationship between particle size and travel distance the smaller the particle, the greater the distance that it is likely to travel. The second deals with colonization, as toxic chemicals can bind to particles, hitching a ride on them as they travel downstream or downwind. 

Alan S. Kolok, Modern Poisons. A Brief Introduction to Contemporary Toxicology, DOI 10.5822/ 978-l-61091-609-7 7, 2016 Alan S. Kolok. 

The largest sediment particles are known as boulders—chwvks of rock that have diameters in excess of 25 centimeters (about 10 inches). Smaller chunks can be differentiated into cobble, mvel, sand, silt, and clay. The very smallest particles are colloids—so small that they remain suspended in the water even when the water is still. Colloids do not behave stricdy as particles (in that they do not settle out from the water), nor do they behave as true water-soluble compounds (in that they can be filtered out of a solution). Colloids fall between the netherworlds of particles and water-soluble compounds. As is true with plasma proteins in the blood, colloids can influence the concentration of chemicals in water by binding with them, removing them from the dissolved phase, and thereby reducing their toxicity. 

The specific surface area of differently sized particles explains a lot about the interaction between chemicals and sediments, but it is not the full story. As the particle size decreases, the space between particles also decreases (consider the size of the space between stacked basketballs and the size of the spaces between stacked marbles). In aquatic systems these spaces are filled with water, which is specifically known zspore water—water in the spaces, or pores, between sediment particles. 

For most people, mud and muck evoke negative images, and for good reason. Bluntly, they stink. Muds and mucks are the site of decomposition (biotransformation on a macromolecular scale), and that decomposition gives off gases and vapors that can smell bad. The bacterial residents within these communities are the bacteria of decomposition and decay, necessary functions performed by the ecosystem, but ones that we would just as soon not think about. 

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The mathematical model called diffusion-limited aggregation (DLA) was introduced by Witten and Sander in 1981 [46]. The model starts with a particle at the origin of a lattice. Another particle is allowed to walk at random (simulating Brownian motion) until it arrives at a site adjacent to the seed particle. At each time step, the traveling particle moves from one site to... 

An illustrative example is provided by investigating the possible momenta for a single particle travelling in the v-direction, p First, one writes the equation that defines the eigenvalue condition... 

The average time between collisions is then v and in this time tlie particle will typically travel a distance X, the mean free path, where... 

An electron or atomic beam of (projectile or test) particles A with density N, of particles per cm travels with speed V and energy E tln-ongh an infinitesimal thickness dv of (target or fielc0 gas particles B at rest with... 

As mentioned previously, a particle such as an ion traveling at high speed causes a number of secondary electrons to be ejected when it strikes a metal surface. This principle is utilized in the electron multiplier (Figure 28.3). 

Since the diffusion coefficient is constant for a given material, Eq. (2.63) shows that the time required for a displacement increases with the square of the distance traveled. This can be understood by thinking that the displacement criterion would be met by finding the diffused particle anywhere on the surface of a sphere of radius x after time t if it started at the origin. The surface area of a sphere is proportional to the square of its radius. 

There is an intimate connection at the molecular level between diffusion and random flight statistics. The diffusing particle, after all, is displaced by random collisions with the surrounding solvent molecules, travels a short distance, experiences another collision which changes its direction, and so on. Such a zigzagged path is called Brownian motion when observed microscopically, describes diffusion when considered in terms of net displacement, and defines a three-dimensional random walk in statistical language. Accordingly, we propose to describe the net displacement of the solute in, say, the x direction as the result of a r -step random walk, in which the number of steps is directly proportional to time ... 

The picture of the electron in an orbit as a standing wave does, however, pose the important question of where the electron, regarded as a particle, is. We shall consider the answer to this for the case of an electron travelling with constant velocity in a direction x. The de Broglie picture of this is of a wave with a specific wavelength travelling in the x direction as in Figure 1.4(a), and it is clear that we cannot specify where the electron is. 

At the other extreme we can consider the electron as a particle which can be observed as a scintillation on a phosphorescent screen. Figure 1.4(b) shows how, if there is a large number of waves of different wavelengths and amplitudes travelling in the x direction, they may reinforce each other at a particular value of x, x say, and cancel each other elsewhere. This superposition at x is called a wave packet and we can say the electron is behaving as if it were a particle at x. ... 

Sedimentation (qv) techniques, whether based on gravitational forces or centrifugation, derive the particle size from the measured travel rates of particles in a Hquid. Before the particle analysis is carried out, the sample is usually dispersed in a medium to break down granules, agglomerates, and aggregates. The dispersion process might involve a simple stirring of the powder into a Hquid, but the use of an ultrasonic dispersion is preferred. 

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