Diffusion velocities

The method of solution is now straightforward, in principle. Equations (4.16) provide n-1 independent relations between the diffusion velocities, and another relation follows directly from their definition, namely ... 

Equations (4.16) and (4.17) can therefore be solved for the diffusion velocities and, since each of Che variables x, and p depends only... 

A final interpretation of the regrouped expression given in item (2) is that 2D equals the diffusion velocity for a particle undergoing unit displacement, X = 1 m in the SI system. 

Aside from the side chains, the movement of the backbone along the main reptation tube is still given by Eq. (2.67). With the side chains taken into account, the diffusion velocity must be decreased by multiplying by the probability of the side-chain relocation. Since the diffusion velocity is inversely proportional to r, Eq. (2.67) must be divided by Eq. (2.69) to give the relaxation time for a chain of degree of polymerization n carrying side chains of degree of polymerization n ... 

The reduced velocity compares the mobile phase velocity with the velocity of the solute diffusion through the pores of the particle. In fact, the mobile phase velocity is measured in units of the intraparticle diffusion velocity. As the reduced velocity is a ratio of velocities then, like the reduced plate height, it also is dimensionless. Employing the reduced parameters, the equation of Knox takes the following form... 

For the mass balance of component A, diffusion velocity and the corresponding diffusion factor are defined with regard to the mean molar velocity V, defined by the equation... 

In a boundary layer equation the mass center is considered with the help of the velocity (u, Uy, u ) and therefore a distribution of the velocity of the mass center is desirable. The diffusion velocity and diffusion factor are determined with regard to velocity v, giving a formula for Vax /x, but not for /ax - x useful approach is offered by Eq. (4.268c), using the artificial multiplication factor (v - ax /... 

Chemicals have to pass through either the skin or mucous membranes lining the respiratory airways and gastrointestinal tract to enter the circulation and reach their site of action. This process is called absorption. Different mechanisms of entry into the body also greatly affect the absorption of a compound. Passive diffusion is the most important transfer mechanism. According to Pick s law, diffusion velocity v depends on the diffusion constant (D), the surface area of the membrane (A), concentration difference across the membrane (Ac), and thickness of the membrane (L)... 

The conditions for model experiments can be explained in the following way. The governing equations are made nondimensional in the full scale and in the reduced scale used in the model experiments. For example, the velocity in the room is divided by the diffuser velocity in the room, and the velocity in the model is divided by the supply velocity in the model in order to normalize all velocities. The two sets of equations are identical and they describe the same solution provided that requirements f, 2, and 3 mentioned at the beginning of this section have been met. 

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... 

The concept of a stationary component may be envisaged by considering the effect of moving the box, discussed in Section 10.1, in the opposite direction to that in which B is diffusing, at a velocity equal to its diffusion velocity, so that to the external observer B appears to be stationary. The total velocity at which A is transferred will then be increased to its diffusion velocity plus the velocity of the box. 

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). 

The q(T) can be independently measured by a viscometer and the value of y is determined by the PCS measurement at a certain temperature (typically 21 22 °C). Under the condition that the hydrodynamic diameter of the probe molecule is constant in the temperature range examined, we can obtain the temperature of the confocal area. It is worth noting that the present method estimates average temperature inside the confocal volume of the microscopic system because ECS provides the average value of the translational diffusion velocity over multiple fluorescent molecules passing through the sampling area. 

In reality, the slip velocity may not be neglected (except perhaps in a microgravity environment). A drift flux model has therefore been introduced (Zuber and Findlay, 1965) which is an improvement of the homogeneous model. In the drift flux model for one-dimensional two-phase flow, equations of continuity, momentum, and energy are written for the mixture (in three equations). In addition, another continuity equation for one phase is also written, usually for the gas phase. To allow a slip velocity to take place between the two phases, a drift velocity, uGJ, or a diffusion velocity, uGM (gas velocity relative to the velocity of center of mass), is defined as... 

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 ... 

To consider the control volume form of the conservation of mass for a species in a reacting mixture volume, we apply Equation (2.14) for the system and make the conversion from Equation (3.12). Here we select/ = pt, the species density. In applying Equation (3.13), v must be the velocity of the species. However, in a mixture, species can move by the process of diffusion even though the bulk of the mixture might be at rest. This requires a more careful distinction between the velocity of the bulk mixture and its individual components. Indeed, the velocity v given in Equation (3.13) is for the bulk mixture. Diffusion velocities, Vi, are defined as relative to this bulk mixture velocity v. Then, the absolute velocity of species i is given as... 

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. 

Fatty acids are clearly larger in size and show markedly slower diffusion velocity than the small water (or creatine) molecules which have been examined so far by diffusion weighted NMR spectroscopy. However, assessment of diffusion properties of lipids could be a key step for further experimental studies of skeletal muscle lipid metabolism. Diffusion properties of FFA and triglycerides are likely different due to differences in molecular weight. In addition, effects of temperature, chemical surroundings, and the mobility of small lipid droplets in the cytosol may also lead to measurable differences in the diffusion characteristics. 

Lipophilic compounds diffuse easily through capillary walls. Their diffusion velocity is related to their Upid-water partition coefficient (Goldstein et al., 1974). 

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