Diffusion velocity of

Whether the rate of oxidation of an alloy of copper with a baser metal is less or more than that of copper will depend on the concentration of the alloying element and the relative diffusion velocities of metal atoms or ions in the oxide layers. There is extensive literature on the oxidation behaviour of copper alloys According to Wagner s theory the rate of oxida-... 

Some data for the equilibrium constant XXno and the rate constant k2 for the aniline 7V-nitrosation step (Scheme 3-27) are presented in Table 3-1. For comparison purposes the table also includes data on diazotization with N203. The rate constant k2 for the nitrosation step (Scheme 3-27) with NOC1 and NOBr is close to the limits given by the diffusion velocity of particles in a solvent. As postulated by... 

In these equations x and y denote independent spatial coordinates T, the temperature Tib, the mass fraction of the species p, the pressure u and v the tangential and the transverse components of the velocity, respectively p, the mass density Wk, the molecular weight of the species W, the mean molecular weight of the mixture R, the universal gas constant A, the thermal conductivity of the mixture Cp, the constant pressure heat capacity of the mixture Cp, the constant pressure heat capacity of the species Wk, the molar rate of production of the k species per unit volume hk, the speciflc enthalpy of the species p the viscosity of the mixture and the diffusion velocity of the A species in the y direction. The free stream tangential and transverse velocities at the edge of the boundaiy layer are given by = ax and Vg = —ay, respectively, where a is the strain rate. The strain rate is a measure of the stretch in the flame due to the imposed flow. The form of the chemical production rates and the diffusion velocities can be found in (7-8). 

Such a dependence was interpreted within the scope of the model of chain oxidation with diffusionally controlled chain termination on the surface of solid antioxidant (for example, Mo or MoS2). According to the Smolukhovsky equation, the diffusion velocity of radical R02 at the distance //2 is v = 0.2DkS13, where S is the surface of the solid inhibitor and k is the coefficient of proportionality between the surface and number n of the solid particles (S=k x ). The function F for such diffusionally controlled chain termination is the following ... 

Particles of a size of less than 2 turn are of particular interest in Process Engineering because of their large specific surface and colloidal properties, as discussed in Section 5.2. The diffusive velocities of such particles are significant in comparison with their settling velocities. Provided that the particles scatter light, dynamic light scattering techniques, such as photon correlation spectroscopy (PCS), may be used to provide information about particle diffusion. 

When ultrasound is used as energy carrier, a sound intensity in the range from 5-10 W cm-2 is employed. This energy is sufficient to heat the material up to or even above its melting point. As a result, the diffusion velocity of the free radicals in turn increased. In addition, in the fluid phase of the matrix, sonochemical reactions are possible, based on cavitation. Such cavitation is associated with... 

The mass diffusion velocity of species k relative to the mass average velocity will be denoted V, which is defined by... 

Writing a generalization of Eq. 12.162, the expression for the mass diffusion velocity of species k in terms of the driving force of species k is... 

The different properties of water with different bonds to organic molecules can be demonstrated also with dye diffusion measurements in polyamide fibres148,149. Acid dyes show a remarkable decrease of diffusion velocity in 6-polyamide if the humidity content is reduced. It is necessary to heat polyamide fibres in air contact at 150 °C to get similar diffusion velocities of acid dyes at 60 °C under water saturation. The diffusion coefficient of water itself in 6-polyamide depends strongly on the water content148,149 (Fig. 29). This was determined by a quartz spring balance method. 

Diffusion velocity of species Mass-average velocity of the gas mixture ... 

The equations governing the steady state, quasi-one-dimensional flow of a reacting gas with negligible transport properties can easily be obtained from equations (l-19)-(l-22). When transport by diffusion is negligible 0 and Dtj 0 for ij = 1,..., N the diffusion velocities, of course, vanish [FJ 0 for / = 1,..., N, see equation (1-14)]. If, in addition, transport by heat conduction is negligible (A 0) and = 0, then the heat flux q vanishes [see equation (1-15)]. Finally, in inviscid flow 0 and K 0), equations (1-16)-(1-18) show that all diagonal elements of the pressure tensor reduce to the hydrostatic pressure, pu = pjj — P33 = P-The steady-state forms of equations (1-20), (l-21a), and (1-22) then become... 

Equation (86) may be taken as qualitatively true in flames even though the diffusion velocities of major species differ. For species r, equation (80) is... 

The summation in equation (14) is extended over all N distinct chemical components. Thus v[ is the mass-weighted average velocity of the fluid mixture, and Vf is said to denote the diffusion velocity of species K. Since... 

When there is no concentration gradient (and thus no molecular mass diffusion) in the fluid, the velocity of all species will be equal to the mass-average velocity of the flow. That is, V = V, — Vg. But when there is a concentration gradient, there will also be a simultaneous flow of species in the direction of decreasing concentration at a diffusion velocity of Vm- Then the average velocity of the species A and B can be determined by superimposing the average flow velocity and the diffusion velocity as (Fig. 14 -31)... 

Note that the diffusion velocity of a species is negative when the molecular diffusi i occurs in the negative x-direction (opposite to flow direction). The mass diffusion rates of the. species A and S at a specified location x can he expressed as... 

The velocity of a species at a point is equal to the sum of the bulk flow velocity and the diffusion velocity of that species at that point. 

Graham s law states that the diffusion velocities of two gas molecules are inversely proportional to the square root of ratio of their molecular masses. 

The ratio of the diffusion velocities of two gases is equal to the square root inverse of the ratio of the molecular masses. 

The equations governing the steady-state, quasi-one-dimensional flow of a reacting gas with negligible transport properties can easily be obtained from equations (l-19)-(l-22). When transport by diffusion is negligible (D,j 0 and Dr,i 0 for i,j = 1,..., N), the diffusion velocities, of course, vanish - 0 for j = see equation (1-14)]. If, in addi-... 

The polarity of macromolecules and the solvent determine the effect of organic solvents on polymer materials. Polymers containing polar groups are resistant to non-polar substances but can swell and be dissolved in polar substances. The polymer permolecular structure exerts a considerable effect on its stability under aging as well. Crystalline polymers dissolve slower than non-crystalline ones, which is due to different diffusion velocities of low-molecular-weight components in the crystalline and amorphous polymers. 

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