Diffusivity directionally-dependent

The value of the coefficient of turbulent diffusion, D, depends upon the air change rate in the ventilated space and the method of air supply. Studies by Posokhin show that approximate D values for locations outside supply air jets is equal to 0.025 m-/s. Air disturbance caused by operator or robot movement results in an increase in the D value of at least two times. Studies by Zhivov et al. showed that the D value is affected by the velocity and direction of cross-drafts against the hood face, and the presence of an operator e.g., for a cross-draft directed along the hood face with velocity u = 0.5 m/s with D = 0.15 m-/s (with the presence of an operator), an increase to = 1.0 m/s results in D = 0.3 m-/s. 

In the present chapter we shall be concerned with quantitative treatment of the swelling action of the solvent on the polymer molecule in infinitely dilute solution, and in particular with the factor a by which the linear dimensions of the molecule are altered as a consequence thereof. The frictional characteristics of polymer molecules in dilute solution, as manifested in solution viscosities, sedimentation velocities, and diffusion rates, depend directly on the size of the molecular domain. Hence these properties are intimately related to the molecular configuration, including the factor a. It is for this reason that treatment of intramolecular thermodynamic interaction has been reserved for the present chapter, where it may be presented in conjunction with the discussion of intrinsic viscosity and related subjects. 

Desorption of an analyte from the SPME fibre depends on the boiling point of the analyte, the thickness of the coating on the fibre, and the temperature of the injection port. The fibre can immediately be used for a successive analysis. Some modifications of the GC injector or addition of a desorption module are required. It is possible to automate SPME for routine analysis of many compounds by either GC-MS or HPLC. A significant advantage of SPME over LLE is the absence of the solvent peak in SPME chromatograms. SPME eliminates the separate concentration step from the SPE and LLE methods because the analytes diffuse directly into the coating of the SPME device and are concentrated there. 

The diffusion of larger organic vapor molecules is related to absorption. The rate of diffusion is dependent on the size and shape of the diffusate molecules, their interaction with the polymer molecules, and the size, shape, and stiffness of the polymer chains. The rate of diffusion is directly related to the polymer chain flexibility and inversely related to the size of the diffusate molecules. 

Diffusion through Cases A principal mechanism for this steady-state release is direct diffusion of the explosive molecules through the munition case. Clearly, the rate of this diffusion is dependent on the case material, through a property called the diffusivity. Metal cases offer essentially zero diffusion, but cases made of some polymers or natural rubber have high enough diffusivities to enable substantial diffusion rates. 

In the presence of EOF, the observed velocity is due to the contribution of electrophoretic and electroosmotic migration, which can be represented by vectors directed either in the same or in opposite direction, depending on the sign of the charge of the analytes and on the direction of EOF, which depends on the sign of the zeta potential at the plane of share between the immobilized and the diffuse region of the electric double layer at the interface between the capillary wall and the electrolyte solution. Consequently, is expressed as... 

The reaction rate constant and the diffusivity may depend weakly on pressure (see previous section). Because the temperature dependence is much more pronounced and temperature and pressure often co-vary, the temperature effect usually overwhelms the pressure effect. Therefore, there are various cooling rate indicators, but few direct decompression rate indicators have been developed based on geochemical kinetics. Rutherford and Hill (1993) developed a method to estimate the decompression (ascent) rate based on the width of the break-dovm rim of amphibole phenocryst due to dehydration. Indirectly, decompres-... 

In an isotropic medium, D is a scalar, which may be constant or dependent on time, space coordinates, and/or concentration. In anisotropic media (such as crystals other than cubic symmetry, i.e., most minerals), however, diffusivity also depends on the diffusion direction. The diffusivity in an anisotropic medium is a second-rank symmetric tensor D that can be represented by a 3 x 3 matrix (Equation 3-25a). The tensor is called the diffusivity tensor. Diffusivity along any given direction can be calculated from the diffusivity tensor (Equation 3-25b). Each element in the tensor may be constant, or dependent on time, space coordinates and/or concentration. 

Let us conclude this section with a few general remarks. If we assume phase boundary rate control, the rate of advance is co-determined by the interface mobility, which in turn is related to the mobilities of the atoms in the interface. We note that 1) the directional dependence of mobilities or diffusivities in the interface may be quite pronounced (depending on 5) and 2) the mobilities or diffusivities depend on the component chemical potentials, which change over time at the interface until diffusion control eventually becomes rate determining. 

Considering the track structures as spherical or cylindrical formations and using the methods of diffusion kinetics, it proved to be possible to explain many experimental facts concerning the radiolysis of water solutions, in particular, the dependence of yields on LET.361 It is owing to this that the LET was considered to be a universal qualitative characteristic of radiation, and the concentration of active particles was considered to be in direct dependence on the LET with no regard for the type of charged particle. 

This expresses the rate of change of concentration with time at given coordinates (t, x, y, z) in terms of second space derivatives and three different diffusion coefficients. It is theoretically possible for D to be direction-dependent (in anisotropic media) but for a solute in solution, it is equal in all directions and usually the same everywhere, so (2.3) simplifies to... 

A comparison of Equations (3) and (4) shows that, in both equations, the amounts of released drug are directly dependent on the area of the device, the square root of the time t, the drug-loading concentration C0, the respective saturated drug concentrations, and the drug diffusion coefficients. In addition, the release rate (the time derivate of the amount of released material) depends on the square root of time and can be stated as... 

Because of volume changes due to the reaction, pressure gradients may occur inside the catalyst pellet. This can give rise to two effects. First, it influences the effective diffusion coefficients, since the gas-phase diffusion coefficients depend on pressure. Second, the pressure gradients affect the concentrations (or more accurately, chemical activities), which determine the reaction rate. Hence pressure gradients must directly influence the effectiveness factor. 

Experimentally, the most convenient way to achieve such movement is to fix the source on a constant-acceleration oscillator allowing imposition of velocities in positive and negative direction depending on whether the source moves toward or away from the absorber E — Eq (1 p/c) (Fig. 1). For convenience, Mossbauer spectrum is taken to correspond to the plot of the intensity of the transmitted or diffused X-rays as a function of the Doppler velocity v instead of the corresponding energy. 

A good agreement is generally obtained between the models based on transport equations and the SDE for mass and heat molecular transport. However, as explained above, the SDE can only be applied when convective flow does not take place. This restrictive condition limits the application of SDE to the transport in a porous solid medium where there is no convective flow by a concentration gradient. The starting point for the transformation of a molecular transport equation into a SDE system is Eq. (4.108). Indeed, we can consider the absence of convective flow in a non-steady state one-directional transport, together with a diffusion coefficient depending on the concentration of the transported property... 

The consideration of wavelength and direction dependence of properties makes radiation calculalions very complicated. Therefore, the gray and diffuse approximations are commonly utilized in radiation calculalions. A surface is said to be diffiise if its properties are independent of direction and gray if its properties are independent of wavelength. 

Figure 50.9. Example of a non-spherical cell with directional dependence of diffusion. Primary laboratory frame of reference is given by X, y and z axes, while the primary axes of diffusion are given as Xjj (major), (intermediate) and (minor). Determination of the values of elements of the diffusion tensor allows determination of the magnitude and direction of the primary axes of diffusion (eigenvalues)...

For film diffusion, but not particle diffusion, the rate of exchange is directly dependent upon the total external concentration. Consider a very small degree of exchange such that F( ) 1 in which case the Maclaurin series expansion gives log (1 — F) = — F, and the boundary conditions more nearly approach those for trace exchange (infinite volume). In such a case, equation 6.19 may be written ... 

The change of the selectivity term in the resolution is directly expressible by im. Interestingly, the effect of the EOF on the dispersion effects, expressed by the plate height H, also depends directly on im. For longitudinal diffusion. Joule self-heating, and concentration overload, the variation of the plate height in the presence of the EOF is directly dependent upon this reduced mobility according to... 

In the following sections we will look at the radiation properties of real bodies, which, with respect to the directional dependence and the spectral distribution of the radiated energy, are vastly different from the properties of the black body. In order to record these deviations the emissivity of a real radiator is defined. Kirch-hoff s law links the emissivity with the absorptivity and suggests the introduction of a semi-ideal radiator, the diffuse radiating grey body, that is frequently used as an approximation in radiative transfer calculations. In the treatment of the emissivities of real radiators we will use the results from the classical electromagnetic theory of radiation. In the last section the properties of transparent bodies, (e.g. glass) will be dealt with. 

Growth of the hydrogen bubbles due to gas diffusion directed inside the bubble from the solution and depending on dimensions of the initial nucleus, the initial content of hydrogen in the melt, the amplitude of sound pressure, and duration of cavitation action. 

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