Diffusive random motion

In the second type of transport process, a chemical moves from one location in the air or water where its concentration is relatively high to another location where its concentration is lower, due to random motion of the chemical molecules (molecular diffusion), random motion of the air or water that carries the chemical (turbulent diffusion), or a combination of the two. Transport by such random motions, also called diffusive transport, is often... 

Ordinary diffusion involves molecular mixing caused by the random motion of molecules. It is much more pronounced in gases and Hquids than in soHds. The effects of diffusion in fluids are also greatly affected by convection or turbulence. These phenomena are involved in mass-transfer processes, and therefore in separation processes (see Mass transfer Separation systems synthesis). In chemical engineering, the term diffusional unit operations normally refers to the separation processes in which mass is transferred from one phase to another, often across a fluid interface, and in which diffusion is considered to be the rate-controlling mechanism. Thus, the standard unit operations such as distillation (qv), drying (qv), and the sorption processes, as well as the less conventional separation processes, are usually classified under this heading (see Absorption Adsorption Adsorption, gas separation Adsorption, liquid separation). 

Static temperature is the temperature of the flowing fluid. Like static pressure, it arises because of the random motion of the fluid molecules. Static temperature is in most practical instaUations impossible to measure since it can be measured only by a thermometer or thermocouple at rest relative to the flowing fluid that is moving with the fluid. Static temperature will increase in a diffuser and decrease in a nozzle. 

Mixing Mechanisms There are several basic mechanisms by which solid particles are mixed. These include small-scale random motion (diffusion), large-scale random motion (convec tion), and shear. 

Wind speed has velocity components in all directions so that there are vertical motions as well as horizontal ones. These random motions of widely different scales and periods are essentially responsible for the movement and diffusion of pollutants about the mean downwind path. These motions can be considered atmospheric turbulence. If the scale of a turbulent motion (i.e., the size of an eddy) is larger than the size of the pollutant plume in its vicinity, the eddy will move that portion of the plume. If an eddy is smaller than the plume, its effect will be to difhise or spread out the plume. This diffusion caused by eddy motion is widely variable in the atmosphere, blit even when the effect of this diffusion is least, it is in the vicinity of three orders of magnitude greater than diffusion by molecular action alone. 

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. 

It has already been mentioned that in an aqueous solution of KC1 at a concentration of 3.20 X 10-6 mole per liter, the equivalent conductivity was found to have a value, 149.37, that differed appreciably from the value obtained by the extrapolation of a series of measurements to infinite dilution. We may say that, even in this very dilute solution, each ion, in the absence of an electric field, does not execute a random motion that is independent of the presence of other ions the random motion of any ion is somewhat influenced by the forces of attraction and repulsion of other ions that happen to be in its vicinity. At the same time, this distortion of the random motion affects not only the electrical conductivity but also the rate of diffusion of the solute, if this were measured in a solution of this concentration. 

Ionic transport in solid electrolytes and electrodes may also be treated by the statistical process of successive jumps between the various accessible sites of the lattice. For random motion in a three-dimensional isotropic crystal, the diffusivity is related to the jump distance r and the jump frequency v by [3] ... 

When ionic conductivity is by way of interstitials, both conductivity and diffusion can occur by random motion, so that the correlation factor and HR are both equal to 1. In general, the correlation factor for a diffusion mechanism will differ from 1, and in such a case D can be described by the following relationship ... 

Photon correlation spectroscopy (PCS) has been used extensively for the sizing of submicrometer particles and is now the accepted technique in most sizing determinations. PCS is based on the Brownian motion that colloidal particles undergo, where they are in constant, random motion due to the bombardment of solvent (or gas) molecules surrounding them. The time dependence of the fluctuations in intensity of scattered light from particles undergoing Brownian motion is a function of the size of the particles. Smaller particles move more rapidly than larger ones and the amount of movement is defined by the diffusion coefficient or translational diffusion coefficient, which can be related to size by the Stokes-Einstein equation, as described by... 

When the regular motion is simply uniform rotation of the absorption and emission dipoles with angular velocity to around the helix axis, one has p(t) - p(0) = cot. For the corresponding random motion, one might have m)2> = 2Dt, where D is the effective diffusion coefficient for Brownian rotation of the transition dipole around the helix axis. When these expressions are incorporated in Eqs. (4.31) and (4.24), the latter becomes a generalization of a relation recently derived using a more cumbersome approach/104-1... 

Molecular diffusion The random motion of solutes in a soluhon. In the absence of external forces, solutes spontaneously undergo net diffusion from regions of higher concentrahon to lower concentration. This conhnues until a homogeneous distribution of the solute is achieved. 

If the Einstein equation for diffusion (H9) is used (which again assumes random motion), the dispersion coefficient may be approximated,... 

The static pressure in a flnid has the same vmue in all directions and can be considered as a scalar point function. It is the pressure of a flowing fluid. It is normal to the surface on which it acts and at any given point has the same magnitude irrespective of the orientation of the surface. The static pressure arises because of the random motion in the fluid of the molecules that make up the fluid. In a diffuser or nozzle, there is an increase or decrease in the static pressure due to the change in velocity of the moving fluid. 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

Diffusion is due to random particle motion in a phase. The random motion leads to a net mass flux when the concentration of a component is not uniform (more strictly speaking, when the chemical potential is not uniform). Hence, a zoned crystal can be homogenized through diffusion. Some examples of diffusion are shown in Figure 1-6. 

Another m3dh is that there is a driving force for diffusion. The truth is that diffusion is due to the random motion of atoms. There is no driving force to move atoms along a direction, but random motion is able to produce a directional change of concentrations if there is an initial concentration gradient. 

Diffusion is due to the random motion of particles (atoms, ions, molecules). The random motion is excited by thermal energy. In the case of pure diffusion, there is no bulk flow, only the redistribution of the components. Nonetheless, exchange of components may result in a shift of the mass center if a heavier particle such as Fe exchanges with a lighter particle such as it may result in a... 

Now, consider particle motion in a phase (solid, liquid, gas). If the phase is initially inhomogeneous, random motion of atoms tends to homogenize the phase. If several phases are present and there are exchanges between the phases, the interphase reaction or exchange tends to make the chemical potential of all exchangeable components the same in all phases and diffusion again works to homogenize each phase. Hence, at equilibrium, the chemical potential of a component is constant. 

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