Diffusion coefficient units

This is known as Fick s second law of diffusion or more commonly as the diffusion equation. In these equations, J is called the flux of the diffusing species, with units of [amount of substance (atoms or equivalent units) m2 s-1], c is the concentration of the diffusing species, with units of [amount of substance (atoms or equivalent units) m-3] at position x (m) after time t (s) D is the diffusion coefficient, units (m2 s 1). 

The flux of particles is in the opposite sense to the direction of the concentration gradient increase. Equation (6) is Fick s first law, which has been experimentally confirmed by many workers. D is the mutual diffusion coefficient (units of m2 s 1), equal to the sum of diffusion coefficients for both reactants, and for mobile solvents D 10 9 m2 s D = DA + jDb. The diffusion coefficient is approximately inversely dependent upon viscosity and is discussed in Sect. 6.9. As spherical symmetry is appropriate for the diffusion of B towards a spherically symmetric A reactant, the flux of B crossing a spherical surface of radius r is given by eqn. (6) where r is the radial coordinate. The total number of reactant B molecules crossing this surface, of area 4jrr2, per second is the particle current I... 

We can now define the electron-hopping diffusion coefficient (units cm s ) as follows... 

Reference 115 gives the diffusion coefficient of DTAB (dodecyltrimethylammo-nium bromide) as 1.07 x 10" cm /sec. Estimate the micelle radius (use the Einstein equation relating diffusion coefficient and friction factor and the Stokes equation for the friction factor of a sphere) and compare with the value given in the reference. Estimate also the number of monomer units in the micelle. Assume 25°C. 

In this expression, called Pick s first law, the proportionality constant D is the diffusion coefficient of the solute. Since J = (l/A)(dQ/dt) and c = Q/V, where Q signifies the quantity of solute in unspecified units, it follows that D has the units length time", or m sec in the SI system. The minus sign in Eq. (9.69)... 

The diffusion coefficient has been commonly reported ia cm /s ia many apphcations. Hereafter, irP/s will be used since it uses the basic SI units. 

Because of the close similarity in shape of the profiles shown in Fig. 16-27 (as well as likely variations in parameters e.g., concentration-dependent surface diffusion coefficient), a contrdling mechanism cannot be rehably determined from transition shape. If rehable correlations are not available and rate parameters cannot be measured in independent experiments, then particle diameters, velocities, and other factors should be varied ana the obsei ved impacl considered in relation to the definitions of the numbers of transfer units. 

Diffusivity and tortuosity affect resistance to diffusion caused by collision with other molecules (bulk diffusion) or by collision with the walls of the pore (Knudsen diffusion). Actual diffusivity in common porous catalysts is intermediate between the two types. Measurements and correlations of diffusivities of both types are Known. Diffusion is expressed per unit cross section and unit thickness of the pellet. Diffusion rate through the pellet then depends on the porosity d and a tortuosity faclor 1 that accounts for increased resistance of crooked and varied-diameter pores. Effective diffusion coefficient is D ff = Empirical porosities range from 0.3 to 0.7, tortuosities from 2 to 7. In the absence of other information, Satterfield Heterogeneous Catalysis in Practice, McGraw-HiU, 1991) recommends taking d = 0.5 and T = 4. In this area, clearly, precision is not a feature. 

Here / is the number of ink molecules diffusing down the concentration gradient per second per unit area it is called the flux of molecules (Fig. 18.3). The quantity c is the concentration of ink molecules in the water, defined as the number of ink molecules per unit volume of the ink-water solution and D is the diffusion coefficient for ink in water - it has units of m s . ... 

We denote by x the distance from the metal surface, and by n x) and rip x) the concentrations of cation vancancies and positive holes in the oxide. Let and Vp be their mobilities, and and Dp their diffusion coefficients. Let F x) be the electrostatic field in the oxide. J, the flux of cation vacancies (number crossing unit area per second), will be expressed by... 

Here Ceq is the ethylene concentration equilibrium to the concentration in a gaseous phase, Kp the propagation rate constant, N the concentration of the propagation centers on the catalyst surface, Dpe the diffusion coefficient of ethylene through the polymer film, G the yield of polymer weight unit per unit of the catalyst and y0at, ype are the specific gravity of the catalyst and polyethylene. 

In addition, it was concluded that the liquid-phase diffusion coefficient is the major factor influencing the value of the mass-transfer coefficient per unit area. Inasmuch as agitators operate poorly in gas-liquid dispersions, it is impractical to induce turbulence by mechanical means that exceeds gravitational forces. They conclude, therefore, that heat- and mass-transfer coefficients per unit area in gas dispersions are almost completely unaffected by the mechanical power dissipated in the system. Consequently, the total mass-transfer rate in agitated gas-liquid contacting is changed almost entirely in accordance with the interfacial area—a function of the power input. 

The kinetics of transport depends on the nature and concentration of the penetrant and on whether the plastic is in the glassy or rubbery state. The simplest situation is found when the penetrant is a gas and the polymer is above its glass transition. Under these conditions Fick s law, with a concentration independent diffusion coefficient, D, and Henry s law are obeyed. Differences in concentration, C, are related to the flux of matter passing through the unit area in unit time, Jx, and to the concentration gradient by,... 

Since the units of D/2 are the same as velocity we can think of this ratio as the velocity of two imaginary pistons one moving up through the water pushing ahead of it a column of gas with the concentration of the gas in surface water (Ci) and one moving down into the sea carrying a column of gas with the concentration of the gas in the upper few molecular layers (Cg). Por a hypothetical example with a film thickness of 17/im and a diffusion coefficient of 1 x 10 cm /s the piston velocity is 5m/day. Thus in each day a column of seawater 5 m thick will exchange its gas with the atmosphere. 

---