Microscopic fluid relaxation times

In these hybrid simulations, coupling happened through the boundary condition. In particular, the fluid phase provided the concentration to the KMC method to update the adsorption transition probability, and the KMC model computed spatially averaged adsorption and desorption rates, which were supplied to the boundary condition of the continuum model, as depicted in Fig. 7. The models were solved fully coupled. Note that since surface processes relax much faster than gas-phase ones, the QSS assumption is typically fulfilled for the microscopic processes one could solve for the surface evolution using the KMC method alone, i.e., in an uncoupled manner, for a combination of fluid-phase continuum model parameter values to develop a reduced model (see solution strategies on the left of Fig. 4). Note again that the QSS approach does not hold at very short (induction) times where the microscopic model evolves considerably. 

The separation of time scales in physical phenomena allows us to smooth over the microscopic fluctuations and construct a differentiable representation of the dynamics on large space scales and long time scales. However, such smoothing is not always possible, examples of physical phenomena that resist this approach include turbulent fluid flow [71], the stress relaxation of viscoelastic materials such as plastics and mbber [72,73], and finally phase transitions [74,75],... 

Although it turned out that a number of essential features concerning dynamics of molecular liquids can be well captured by the theory of the previous subsection (see Secs. 3 and 5), an intense investigation through experimental, theoretical, and molecular-dynamics simulation studies for simple liquids has revealed that the microscopic processes underlying various time-dependent phenomena cannot be fully accounted for by a simplified memory-function approach [18, 19, 20]. In particular, the assumption that the decay of memory kernels is ruled by a simple exponential-type relaxation must be significantly revised in view of the results of the kinetic framework developed for dense liquids (see Sec. 5.1.4). This motivated us to further improve the theory for dynamics of polyatomic fluids. 

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