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Non-local transport

Let us discuss briefly the solution to the stress induced transport problem for short times after loading one side of the specimen at = 0 with species i (q( = 0)). Under the given initial and boundary conditions, the non-local transport term in... [Pg.340]

Kushner J, Blankschtein D, Langer RS. Evaluation of hydrophilic permeant transport parameters in the localized and non-localized transport regions of skin treated simultaneously with low-frequency ultrasound and sodium lauryl sulfate. Journal of Pharmaceutical Sciences 2008, 97, 894—906. [Pg.214]

The effective diffusivity depends on the statistical distribution of the pore transport coefficients W j. The derivation shows that the semi-empirical volume-averaging method can only be regarded as an approximation to a more complex dynamic behavior which depends non-locally on the history of the system. Under certain circumstances the long-time (t —> oo) diffusivity will not depend on t (for further details, see [191]). In such a case, the usual Pick diffusion scenario applies. The derivation presented above can, with minor revisions, be applied to the problem of flow in porous media. When considering the heat conduction problem, however, some new aspects have to be taken into accoimt, as heat is transported not only inside the pore space, but also inside the solid phase. [Pg.245]

On the submicron scale, the current distribution is determined by the diffusive transport of metal ion and additives under the influence of local conditions at the interface. Transport of additives in solution may be non-locally controlled if they are consumed at a mass-transfer limited rate at the deposit surface. The diffusion of additives in solution must then be solved simultaneously with the flux of reactive ion. Diffusive transport of inhibitors forms the basis for leveling [144-147] where a diffusion-limited inhibitor reduces the current density on protrusions. West has treated the theory of filling based on leveling alone [148], In his model, the controlling dimensionless groups are equivalent to and D divided by the trench aspect ratio. They determine the ranges of concentration within which filling can be achieved. [Pg.185]

For comparison, we present in Fig. 5.3.2 some numerical results for the following non-locally-electro-neutral generalization of the classical Teorell-Meyer-Sievers (TMS) model of membrane transport (see [11], [12] and 3.4 of this text). [Pg.180]

The aim of this chapter is to clarify the conditions for which chemical kinetics can be correctly applied to the description of solid state processes. Kinetics describes the evolution in time of a non-equilibrium many-particle system towards equilibrium (or steady state) in terms of macroscopic parameters. Dynamics, on the other hand, describes the local motion of the individual particles of this ensemble. This motion can be uncorrelated (single particle vibration, jump) or it can be correlated (e.g., through non-localized phonons). Local motions, as described by dynamics, are necessary prerequisites for the thermally activated jumps responsible for the movements over macroscopic distances which we ultimately categorize as transport and solid state reaction.. [Pg.95]

As an illustration, consider the isothermal, isobaric diffusional mixing of two elemental crystals, A and B, by a vacancy mechanism. Initially, A and B possess different vacancy concentrations Cy(A) and Cy(B). During interdiffusion, these concentrations have to change locally towards the new equilibrium values Cy(A,B), which depend on the local (A, B) composition. Vacancy relaxation will be slow if the external surfaces of the crystal, which act as the only sinks and sources, are far away. This is true for large samples. Although linear transport theory may apply for all structure elements, the (local) vacancy equilibrium is not fully established during the interdiffusion process. Consequently, the (local) transport coefficients (DA,DB), which are proportional to the vacancy concentration, are no longer functions of state (Le., dependent on composition only) but explicitly dependent on the diffusion time and the space coordinate. Non-linear transport equations are the result. [Pg.95]

There is a local (Fickian transport) and a non-local (stress induced) term in this flux equation. In the local term, the stress acts in the same way as an activity coefficient does. It always increases local diffusion since V] is positive and independent of the sign of the partial molar volume of /. [Pg.340]

In this equation g(t) represents the retarded effect of the frictional force, and /(f) is an external force including the random force from the solvent molecules. We see, in contrast to the simple Langevin equation with a constant friction coefficient, that the friction force at a given time t depends on all previous velocities along the trajectory. The friction force is no longer local in time and does not depend on the current velocity alone. The time-dependent friction coefficient is therefore also referred to as a memory kernel . A short-time expansion of the velocity correlation function based on the GLE gives (fcfiT/M)( 1 — (g/M)t2/(2r) + ), where r is the decay time of g(t), and it therefore does not have a discontinuous first derivative at t = 0. The discussion of the properties of the GLE is most easily accomplished by using so-called linear response theory, which forms the theoretical basis for the equation and is a powerful method that allows us to determine non-equilibrium transport coefficients from equilibrium properties of the systems. A discussion of this is, however, beyond the scope of this book. [Pg.276]

On a phenomenological level the in-plane anisotropy of Hc2 cannot be explained within the (local) GL theory. In principle, non-local extension introduced by Hohenberg and Werthamer (1967) might be helpful to overcome this difficulty. In this approach, which is valid for weak anisotropies, in addition to the second rank mass tensor, a fourth rank tensor is introduced. The non-local effects were predicted to be observable in sufficiently clean materials where the transport... [Pg.232]

Typical options for turbulent transport in the boundary layer include a level 2.5 Mellor-Yamada closure parametrization (Mellor and Yamada 1982), or a non-local approach implemented by scientists from the Yong-Sei University (YSU scheme, Hong and Pan, 1996). Transport in non-resolved convection is handled by an ensemble scheme developed by Grell and Devenyi (2002). This scheme takes time-averaged rainfall rates from any of the convective parametrizations from the meteorological model to derive the convective fluxes of tracers. This scheme also parameterizes the wet deposition of the chemical constituents. [Pg.43]

The conventional macroscopic Fourier conduction model violates this non-local feature of microscale heat transfer, and alternative approaches are necessary for analysis. The most suitable model to date is the concept of phonon. The thermal energy in a uniform solid material can be jntetpreied as the vibrations of a regular lattice of closely bound atoms inside. These atoms exhibit collective modes of sound waves (phonons) wliich transports energy at tlie speed of sound in a material. Following quantum mechanical principles, phonons exhibit paiticle-like properties of bosons with zero spin (wave-particle duality). Phonons play an important role in many of the physical properties of solids, such as the thermal and the electrical conductivities. In insulating solids, phonons are also (he primary mechanism by which heal conduction takes place. [Pg.405]

The formalism of the transformed Eulerian mean circulation shows that meridional transport in the middle atmosphere is generated primarily by non-local momentum forcing associated with wave dissipation. This forcing, represented by the Eliassen-Palm flux divergence in equation (3.67), acts as an extratropical pump producing strong upward air motions in the tropics and downward return ... [Pg.104]

It has been recognized for a long time that the problem of upscaling is non-local and thus depends on the specific local conditions of the flow and transport problems under study. Yet, some qualitative conclusions can be drawn from this study. [Pg.248]

To calculate cavitation in a macroscopic specimen, one must determine the concentration and crystallization history of each volume element in the sample during the sorptloii process and apply Equation 6 to each from the time saturation occurs. This has been done for films by solving a non-Ficklan transport equation, an equation for local crystallization and Equation 6 simultaneously. The transport and crystallization equations (without their initial and boundary conditions) are... [Pg.320]


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See also in sourсe #XX -- [ Pg.386 , Pg.387 ]




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