Momentum conservation macroscale

When (7.10)-(7.12) are combined with the expressions for mass and momentum conservation, we are then able to compare assumptions regarding and v with macroscale observations such as wave profiles, for example. The conservation laws are (in Lagrangian form Pq dX = p dx )... 

Local thermodynamic equilibrium in space and time is inherently assumed in the kinetic theory formulation. The length scale that is characteristic of this volume is i whereas the timescale is xr. When either L i, ir or t x, xr or both, the kinetic theory breaks down because local thermodynamic equilibrium cannot be defined within the system. A more fundamental theory is required. The Boltzmann transport equation is a result of such a theory. Its generality is impressive since macroscopic transport behavior such as the Fourier law, Ohm s law, Fick s law, and the hyperbolic heat equation can be derived from this in the macroscale limit. In addition, transport equations such as equation of radiative transfer as well as the set of conservation equations of mass, momentum, and energy can all be derived from the Boltzmann transport equation (BTE). Some of the derivations are shown here. 

Mesoscale modeling of SOFCs focuses on modeling the transport and reactions of gas species in the porous microstructures of the electrodes [3, 34, 56-59]. In these models, the porous microstructure is explicitly resolved, which negates the need for the effective parameters of macroscale models. The transport and reactions of species in mesoscale models are described by the species [Eq. (26.1)], momentum [Eq. (26.5)], and energy [Eq. (26.7)] conservation equations, which are solved at the pore scale. At the pore scale, the conservation equations are solved in two separate domains the solid domain of the tri-layer and the gas domain of the pore space within the tri-layer. Mesoscale models aim to understand the effects of microstructure and local conditions near the electrode-electrolyte interface on the SOEC physics and performance. These models have been used to investigate a number of design and degradation issues in the electrodes such as the effects of microstructure on the transport of species in the anode [19, 56] and the reactions of chromium contaminants in the cathode [34]. 

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