Random movement

Brownian movement The rapid and random movement of particles of a colloidal sol, observed brightly lit against a dark ground. First observed with a pollen suspension. The Brownian movement is due to the impact on the dispersed particles of the molecules of the dispersion medium. As the particles increase in size, the probability of unequal bombardment from different sides decreases, and eventually collisions from all sides cancel out and the Brownian movement becomes imperceptible at a particle size of about 3-4/z. From the characteristics of the movement, Perrin calculated Avogadro s number L. 

Monte Carlo a simulation technique that incorporates a random movement of atoms or molecules... 

Photon Correlation Spectroscopy. Photon correlation spectroscopy (pcs), also commonly referred to as quasi-elastic light scattering (qels) or dynamic light scattering (dls), is a technique in which the size of submicrometer particles dispersed in a Hquid medium is deduced from the random movement caused by Brownian diffusion motion. This technique has been used for a wide variety of materials (60—62). 

Consider a local concentration of solute migrating down a column. During this migration, adsorption and desorption steps will continuously and frequently occur. In addition, each occurrence will be a random event. Now a desorption step will be a random movement forward as it releases a molecule into the mobile phase, where it can move forward. Conversely, an adsorption step is a step backward, as it results in a period of immobility for the molecule while the rest of the zone moves forward. The total number of random steps taken as the solute mean position moves a distance (l) along the column is the number of forward steps plus the number of backward... 

Brownian diffusion (Brownian motion) The diffusion of particles due to the erratic random movement of microscopic particles in a disperse phase, such as smoke particles in air. 

These models are designed to reproduce the random movement of flexible polymer chains in a solvent or melt in a more or less realistic way. Simulational results which reproduce in simple cases the so-called Rouse [49] or Zimm [50] dynamics, depending on whether hydrodynamic interactions in the system are neglected or not, appear appropriate for studying diffusion, relaxation, and transport properties in general. In all dynamic models the monomers perform small displacements per unit time while the connectivity of the chains is preserved during the simulation. 

Having this view of the make-up of the heat content of a substance, we can now visualize the effects brought on by warming the substance. If the temperature is low at first, the substance will be a solid. Warming the solid increases the kinetic energy of the back-and-forth motions of the molecules about their regular crystal positions. As the temperature rises, these motions disturb the regularity of the crystal more and more. Too much of this random movement destroys the lattice completely. At the temperature... 

Equation 10.4, which describes the mass transfer rate arising solely from the random movement of molecules, is applicable to a stationary medium or a fluid in streamline flow. If circulating currents or eddies are present, then the molecular mechanism will be reinforced and the total mass transfer rate may be written as ... 

In this approach, it is assumed that turbulence dies out at the interface and that a laminar layer exists in each of the two fluids. Outside the laminar layer, turbulent eddies supplement the action caused by the random movement of the molecules, and the resistance to transfer becomes progressively smaller. For equimolecular counterdiffusion the concentration gradient is therefore linear close to the interface, and gradually becomes less at greater distances as shown in Figure 10.5 by the full lines ABC and DEF. The basis of the theory is the assumption that the zones in which the resistance to transfer lies can be replaced by two hypothetical layers, one on each side of the interface, in which the transfer is entirely by molecular diffusion. The concentration gradient is therefore linear in each of these layers and zero outside. The broken lines AGC and DHF indicate the hypothetical concentration distributions, and the thicknesses of the two films arc L and L2. Equilibrium is assumed to exist at the interface and therefore the relative positions of the points C and D are determined by the equilibrium relation between the phases. In Figure 10.5, the scales are not necessarily the same on the two sides of the interface. 

This separation is an impressive example of an entropically driven distribution system where the normally random movements of the solute molecules are restricted to different extents depending on the spatial orientation of the substituent groups. For further information the reader is directed to an excellent review of chiral separations by LC (Taylor and Maher (12)) and a monograph on CYCLOBOND materials from ASTEC Inc. (13). 

This response time should be compared to the turbulent eddy lifetime to estimate whether the drops will follow the turbulent flow. The timescale for the large turbulent eddies can be estimated from the turbulent kinetic energy k and the rate of dissipation e, Xc = 30-50 ms, for most chemical reactors. The Stokes number is an estimation of the effect of external flow on the particle movement, St = r /tc. If the Stokes number is above 1, the particles will have some random movement that increases the probability for coalescence. If St 1, the drops move with the turbulent eddies, and the rates of collisions and coalescence are very small. Coalescence will mainly be seen in shear layers at a high volume fraction of the dispersed phase. 

Consider a monatomic gas such as heiium or argon. Recaii from Chapter 5 that the atoms of this gas move continuousiy with a distribution of kinetic energies. The totai energy of these random movements is caiied thermai... 

All the transport properties derive from the thermal agitation of species at the atomic scale. In this respect, the simplest phenomenon is the diffusion process. In fact, as a consequence of thermal kinetic energy, all particles are subjected to a perfectly random movement, the velocity vector having exactly the same probability as orientation in any direction of the space. In these conditions, the net flux of matter in the direction of the concentration gradient is due only to the gradient of the population density. 

The surprising result is that net atom displacement will occur due to random movement alone. It is possible to use Eq. (5.5) to define a diffusion coefficient. To agree with Fick s first law, the relationship chosen is... 

One of the simplest models for diffusion is that of the random movement of atoms. The model is generally called a random (or drunkard s) walk.4 A random walk produces a path that is governed completely by random jumps (Fig. S5.3). That is, each individual jump is unrelated to the step before and is governed solely by the probabilities of taking the alternative steps. The application of random walks to diffusion was first made by... 

For convenience, only one-dimensional random movement will be considered. In this case, an atom is constrained to jump from one stable site to the next in the x direction, the choice of +x or -x being selected in a random way.6 For example, imagine a diffusion experiment starting with a thin layer of N atoms on the surface of a crystal. 

Stupor, eyes open, random movements, resting nystagmus, hyperreflexia, hypertension onset 30-60 min, duration 8-24 hr... 

Brownian motion is the random movement of small, solid particles sitting on the surface of water. They are held in position by the surface tension y of the meniscus. When looking at the dust under a microscope, the dust particles appear to dance and move randomly. But when the water is warmed, the particles, be they chalk or house dust, move faster than on cold water. 

These are the weakest of all intermolecular bonds. They result from the random movement of electrons within an atom or molecule. This movement can result in a separation of charge across the atom or molecule (an instantaneous dipole Fig. 11.7). This small separation of charge (indicated by <5+ and 8 ) will then influence neighboring atoms or molecules, and cause an induced dipole. These van der Waals bonds (sometimes known as London forces) occur between nonpolar molecules or atoms such as I2, 02, H2, N2, Xe, Ne, and between the aliphatic chains of lipids (see below). 

Protrusion may be due to growth of new actin filaments, which requires net polymerisation of new filaments, and also by the organisation of actin-binding proteins into higher-order structures. Random movements of flexible membranes away from the filaments may result in gross distortion of actin polymerisation at the barbed ends. Thus, once a critical size is reached, ion pumping (i.e. of Ca2+) may occur at the tip of a pseudopod, which further aids directional changes in the network. 

Handley fluidised soda glass particles using methyl benzoate, and obtained data on the flow pattern of the solids and the distribution of vertical velocity components of the particles. It was found that a bulk circulation of solids was superimposed on their random movement. Particles normally tended to move upwards in the centre of the bed and downwards at the walls, following a circulation pattern which was less marked in regions remote from the distributor. 

Most researchers attribute slow kinetics to some sort of diffusion limitation (e.g., diffusion is random movement under the influence of a concentration gradient [193]), because sorbing molecules are subject to diffusive constraints throughout almost the entire sorption/desorption time course due to the porous nature of particles. Particles are porous by virtue of their aggregated nature and because the lattice of individual grains in the aggregate may be fractured. 

Passive Diffusion Diffusion is the random movement of molecules in fluid. If a fluid is separated by a semipermeable membrane, more dissolved molecules will diffuse across the membrane from the higher concentration side to the lower concentration side than in the reverse direction. This process will continue until equihbrium is achieved, whereby both sides have the same concentration. When equilibrium is reached, there are equal numbers of molecules crossing the membrane in both directions. 

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