Modified diffusivity

Polarization curves showing the effect of modified diffusion layers (air/Hj, 2/1.5 stoichiometry, 3.1/3.1 bara, 100/100% relative humidity, 80°C). (Reprinted from D. P. Wilkinson and ]. St-Pierre. ]oumal of Power Sources 113 (2003) 101-108. With permission from Elsevier.)... 

We need develop the unsupported finite case no further. Apart from the modified diffusion coefficient, the results developed in Sect. 4.6 apply to concentration profiles in the two-ion case. 

Assuming that the constant diffusion coefficients are equal to Z)avg, and the concentration dependent parameters fi are as above, modified diffusion coefficients were calculated from ... 

Figure 1.14. L-t plot results using the modified diffusion equation [Eq. (1.5)] for several values of x.

This structure is generated via the modified diffusion-limited aggregation (DLA) algorithm of [205] using the law p = a (m/N). Here, N = 2, 000 (the number of particles of the DLA clusters), a = 10 and ft = 0.5 are constants that determine the shape of the cluster, p is the radius of the circle in which the cluster is embedded, pc = 0.1 is the lower limit of p (always pc < p), and to is the number of particles sticking to the downstream portion of the cluster. This example corresponds to a radial Hele-Shaw cell where water has been injected radially from the central hole. Due to heterogeneity a sample cannot be used to calculate the dissolved amount at any time, i.e., an average value for the percent dissolved amount at any time does not exist. This property is characteristic of fractal objects and processes. 

Helfand (25,26,27,28,29) has formulated a statistical thermodynamic model of the microphases similar to that of Meier. This treatment, however, requires no adjustable parameters. Using the so-called mean-field-theory approach, the necessary statistics of the molecules are embodied in the solutions of modified diffusion equations. The constraint at the boundary was achieved by a narrow interface approximation which is accomplished mathematically by applying reflection boundary conditions. 

Modified diffusion model that assumes that the solutes react reversibly with the internal reagents and the effective diffiisivity of the solutes in the emulsion globules is dependent upon the local solute concentration in the membrane phase. 

Lin CC and Long RL. Phenol removal by emulsion liquid membrane A modified diffusion model. Chem Eng Comm 1996 156 45-58. 

Fig. 5 (A) Travel length (L) as a function of time (i) obtained from Fig. 3B for monodisperse Zdol T = 26°C, under dry nitrogen and (B) L-t plot results using the modified diffusion equation (Eq. 7) for several values of t. (View this art in color at WWW. dekker. com.)...

By combining Eqs. (3) and (6), and assuming xd/dt to be small, we obtained the following modified diffusion equation ... 

This transformation can be done using the method suggested by Curtiss and Bird [18] [19] which is in accordance with the work of Merk [71]. To shorten the notation they temporary define a modified diffusion velocity, by ... 

The modified diffusion velocity (2.290) can be related to the standard diffusion velocity (1.28), and expressed by ... 

Serious efforts have been made to explain the atypical lithium transport behavior using modified diffusion control models. In these models the boundary conditions -that is, "real potentiostatic constraint at the electrode/electrolyte interface and impermeable constraint at the back of the electrode - remain valid, while lithium transport is strongly influenced by, for example (i) the geometry of the electrode surface [53-55] (ii) growth of a new phase in the electrode [56-63] and (iii) the electric field through the electrode [48, 56]. 

TABLE 12.2.1 Modified Diffusion Equations and Boundary Conditions for... 

A systematic deviation from this modified diffusion equation was observed with coarse particles. This led to a positive concentration gradient near the bottom of the pipe in some circumstances (4-6). This deviation was attributed to the effect of the dispersive stress discovered by Bagnold (99). 

Equation (17.60) neglects noncontinuum effects that may influence very small cloud droplets. These effects can be included in this equation by introducing a modified diffusivity D v, where (Fukuta and Walter 1970)... 

Normal procedures for estimation of the effectiveness factor, rj, in reaction with single-phase flow were discussed in Chapter 7, and if the pores in the catalyst particles are completely filled with liquid, then similar methods can be used with appropriately modified diffusivities for trickle-bed reactors. Since diffusion coefficients in the liquid phase are considerably smaller than those in the gas phase, catalyst effectiveness can be low for trickle-bed reactors, even for relatively small particle sizes. Following the development in Chapter 7 we can still say that. 

This Chapter discusses lithium transport through transition metal oxides and carbonaceous material (graphite) during CT experiments. The structure of this review is as follows in Section II, the conventional and modified diffusion control models for explaining the CTs are briefly summarized. Typical experimental CTs from transition metal oxides and carbonaceous material (graphite) are presented and then several anomalous behaviors in these curves are pointed out in Section... 

The role of phase transformation of lithium-poor phase to lithium-rich phase in lithium transport during the CT experiments has been discussed independently by Pyun et and Funabiki et under the assumption that phase boundary movement is controlled by the lithium diffusion in each phase. The former authors have focused on the shape of the CTs and the onset/end of the phase boundary movement by solving numerically the modified diffusion equation, while the latter authors have determined the rate of the phase boundary movement by... 

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