Diffusion defined

To determine the number of stages, using the impeller and diffuser defined as the stage, assume 10,000 ft-lb/lb of head per stage. This value can be used if the molecular weight is in the range of 28 to 30. For other... 

Diffusion activation energy for diffusion defined by equation 12.3.84... 

The turbulent diffusivity defined by (4.74) is proportional to the turbulent viscosity defined by (4.46). Turbulent-diffusivity-based models for the scalar flux extend this idea to arbitrary mean scalar gradients. The standard gradient-diffusion model has the form... 

Here, D< )s is the fractional diffusivity defined as (4-2d,) (2d,-4) )(3-dP) j js a constant related to the fractal dimension and R0 is the side length of a square electrode), and dv dtv means the Riemann-Liouville mathematical operator of fractional derivative ... 

Chapter 16 - It is shown, that there is principal difference between the description of generally reagents diffusion and the diffusion defining chemical reaction course. The last process is described within the framework of strange (anomalous) diffusion concept and is controled by active (fractal) reaction duration. The exponent a, defining the value of active duration in comparison with real time, is dependent on reagents structure. 

To measure how much the reaction rate is lowered because of the resistance to pore diffusion, define the quantity ( called the effectiveness factor as follows ... 

Another experimental method to investigate diffusion is the so-called half-space method, in which the sample (e.g., rhyolitic glass with normal oxygen isotopes) is initially uniform with concentration C, but one surface (or all surfaces, as explained below) is brought into contact with a large reservoir (e.g., water vapor in which oxygen is all 0). The surface concentration of the sample is fixed to be constant, referred to as Cq. The duration is short so that some distance away from the surface, the concentration is unaffected by diffusion. Define the surface to be X = 0 and the sample to be at x > 0. This diffusion problem is the so-called halfspace or semi-infinite diffusion problem. 

The diffusion couple discussed above consists of two halves of the same phase. If the two halves are two minerals, such as Mn-Mg exchange between spinel and garnet (Figure 3-5), there would be both partitioning and diffusion. Define the diffusivity in one half (x < 0) to be D, and in the other half (x > 0) to be D. Both and are constant. Let w be the concentration (mass fraction) of a minor element (such as Mn). The initial condition is... 

Diffusion processes occur in all systems where concentration differences exist. Diffusion is the main mechanism which aids Ln the elimination of concentration gradients. Fick s first law of diffusion defines this phenomenon by correlating mass flow and concentration gradient. This law may be shown as... 

Thermal diffusivity, defined in eqn. (2.3), is the material property that governs the process of thermal diffusion over time. The thermal diffusivity in amorphous thermoplastics decreases with temperature. A small jump is observed around the glass transition temperature due to the decrease in heat capacity at Tg. Figure 2.17 [24] presents the thermal diffusivity for selected amorphous thermoplastics. 

It is convenient to correlate transport data in terms of a diffusivity defined according to Fick s first equation,... 

Depending on the conditions of the diffusion experiment, the diffusivities defined by eq 1 are given particular names. For one-component diffusion under the influence of a concentration gradient, eq 1 reduces to... 

Let us reiterate that diffusion defined by (102) can be derived using the Brownian motion approach and a continuity equation. Moreover, one can imply... 

Off-diagonal entries of B arise from the fact that the coordinate system in which Equations (8.1) and (8.2) are expressed does not necessarily coincide with the principle directions of anisotropic diffusion defined by B. The principle diffusion directions correspond to the eigenvectors of B, with the highest rate of diffusion occurring in the direction associated with the largest eigenvalue of B. To see this we introduce the coordinate transformation = Rx (or = RijXj). Application... 

For binary and multicomponent mixtures, the thermal conductivity depends on the concentrations as well as on temperature, and the formulas of the accurate kinetic theory are quite complicated [5]. Empirical expressions for X are therefore more useful for both binary [9] and ternary [6], [26] mixtures, although few data exist for ternary mixtures. Tabulations of available experimental and theoretical results for thermal conductivities may be found in [5], [6], [13], and [18]-[21], for example. The thermal diffusivity, defined as 2p/Cp, often arises in combustion problems its pressure and temperature dependences in gases are XjpCp T7p ( < a < 2), and its typical values in combustion lie between 10 cm /s and 1 cm s at atmospheric pressure. 

Molecular transport and tracer diffusion in porous solids are conveniently correlated in terms of diffusivities defined in accordance with Pick s first equation ... 

C Surface concentration of growing hydrocarbon chain D Effective diffusivity of n-olefins and n-praffins Do Reference diffusivity defined by Eq. (26)... 

The Maxwell-Stefan diffusivities defined in Eqs. (20) and (21) for one- and two-component systems should be identical if they are independent of occupancy. Diffusivities... 

In this equation, Dj y is the Maxwell-Stefan surface diffusivity defined as... 

It should be noted that the diffusivity D in Eq. (35) is the molecular diffusivity in the case of mass transfer, which is typically of the order of lO m /sec or thermal diffusivity defined as... 

Using the Maxwell-Stefan equations for nonideal fluids, Eqs. 2.2.1, as a basis, develop a general expression for an effective diffusivity defined in terms of the generalized driving force as... 

Combining equations 17 and 18 yields, for the Fickian diffusivity (defined by J... 

The units of thermal conductivity are defined from Fourier s law and are shown for some of the common systems of units in Table 2.3.1. The thermal diffusivity defined by... 

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