Moving medium, diffusion

Transient Mass Diffusion 796 14-8 Diffusion in a Moving Medium... 

To this point we have limited onr consideration to mass diffitsion in a station aiy medium, and thus the only ntotion involved was the creeping motion of molecules in the direction of decreasing concentration, and there was no motion of the mixture as a whole. Many practical problems, such as the evaporation of water from a lake under the iiifliience of the wind or the mixing of two fluids as they flow in a pipe, involve diffusion in a moving medium where the hoik motion i.s caused by an external force. Mass diffusion in such c.nses is complicated by the fact that chemical species are transported both by diffusion and by the bulk motion of the medium (i.e., convection). The velocities and mass flow rates of species in a moving medium consist of two components one due to molecular diffusion and one due to convection (Fig. 14-29). 

FIGURE 14-29 In a moving medium, mass transfer is due to both diffusion and convection. 

During mass transfer in a moving medium, chemical species are transported both by molecular diffusion and by the bulk fluid motion, and the velocities of lire species are expressed as... 

The special case K = 0 corresponds to a stationary medium. Using Pick s law of diffusion, the total mass fluxes J = m/A in a moving medium are expressed as... 

SC Define the following tei/ns mass-average velocity, diffusion velocity, stationary medium, and moving medium. 14-76C What is diffusion velocity How does it affect the mass-average velocity Can the velocity of a species in a moving medium relative to a fuxed reference point be zero in a moving medium Explain. 

The renormalized diffusivity D1 accounts for the process of diffusion from cell to cell as a result of the nontrivial interaction of advection and molecular diffusion [6], The renormalized reaction time xeff is the time it takes for a single cell to be filled by inert material, and it depends on the interaction of advection and production. F indicates the functional form of the renormalized chemistry. Therefore, the limiting speed of the front in the moving medium is given by veff JDE /Teff [13,14]. The problem is now reduced to derive the expressions for the renormalized parameters by means of physical considerations. 

Equation (3.1.1) reflects the fact that the transfer of a substance in a moving medium is due to two distinct physical mechanisms. First, there is molecular diffusion due to concentration difference in a liquid or gas, which tends to equalize the concentrations. Second, the solute is carried along by the moving medium. The combination of these two processes is usually called convective diffusion [133, 270],... 

The equation of heat transfer in a moving medium is similar to Eq. (3.1.1) of convective diffusion and has the form... 

Let us now study the inner mass transfer problems involving a volume chemical reaction. We assume that the diffusion process is quasi-stationary and takes place inside a solid spherical inclusion or a drop of radius a filled with a stagnant or moving medium. 

Liquid Diffusion Molecules move fast (v = hi ) Distance between collisons is short (A = small) Diffusion is medium (D ft) viiqAii, = mod) Vliq.BMS )... 

This model is developed in the works of Frank-KamenetzJd [21], Levich [22], Sherwood [23], Ruckenstein [24] and others and is based on the simultaneous consideration of the equations of hydrodynamics and convective diffusion in moving medium. Because of veiy si l thickness of the diffusion film, it is enou to take into account only the diffusion in direction to the interface. Thus, the equation of the convective diffusion of the liquid phase can be written as follows. 

The friction coefficient determines the strength of the viscous drag felt by atoms as they move through the medium its magnitude is related to the diffusion coefficient, D, through the relation Y= kgT/mD. Because the value of y is related to the rate of decay of velocity correlations in the medium, its numerical value determines the relative importance of the systematic dynamic and stochastic elements of the Langevin equation. At low values of the friction coefficient, the dynamical aspects dominate and Newtonian mechanics is recovered as y —> 0. At high values of y, the random collisions dominate and the motion is diffusion-like. 

At medium and high temperatures copper ultimately follows the parabolic law " . It has been shown " using radioactive tracers that the diffusion of copper ions in cuprous oxide is the rate-determining step at 8(X)-1 000°C, and there is considerable evidence in favour of the view that metal moves outwards through the film by means of vacant sites in the oxide lattice . 

The estimation of the diffusional flux to a clean surface of a single spherical bubble moving with a constant velocity relative to a liquid medium requires the solution of the equation for convective diffusion for the component that dissolves in the continuous phase. For steady-state incompressible axisym-metric flow, the equation for convective diffusion in spherical coordinates is approximated by... 

If the electric field E is applied to a system of colloidal particles in a closed cuvette where no streaming of the liquid can occur, the particles will move with velocity v. This phenomenon is termed electrophoresis. The force acting on a spherical colloidal particle with radius r in the electric field E is 4jrerE02 (for simplicity, the potential in the diffuse electric layer is identified with the electrokinetic potential). The resistance of the medium is given by the Stokes equation (2.6.2) and equals 6jtr]r. At a steady state of motion these two forces are equal and, to a first approximation, the electrophoretic mobility v/E is... 

Second, hydration of drug molecules may affect their hydrodynamic radii. The diffusion coefficient D is related to the frictional resistance,/, that the diffusing particle experiences in moving through a medium by the equation [51]... 

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