Equilibrium-chemistry limit chemical time scales

Recall that the Jacobian of S will generate Ny chemical time scales. In the equilibrium-chemistry limit, all Ny chemical times are assumed to be much smaller than the flow time scales. 

For elementary chemical reactions, it is sometimes possible to assume that all chemical species reach their chemical-equilibrium values much faster than the characteristic time scales of the flow. Thus, in this section, we discuss how the description of a turbulent reacting flow can be greatly simplified in the equilibrium-chemistry limit by reformulating the problem in terms of the mixture-fraction vector. 

The Nr eigenvalues of the Jacobian of S,p will be equal to the Nr non-zero eigenvalues of the Jacobian of Sc. Thus, in the equilibrium-chemistry limit, the chemical time scales will obey... 

In the last years the theoretical organic chemistry has been increasingly extended beyond the gas phase realm of quantum mechanics to the study of the course of chemical reactions in solution. The success of these methods will indicate the begin of a new period for modeling chemistry in solution. Here, we mainly restrict our attention to a static solvent treatment. The discussion of the limitation of this approach was recently continued.Such studies assume the solvation to be in equilibrium with the chemical system at each point along a HP. This basic hypothesis may first be questioned from possibly different time scales of solvent relaxation and the chemical process and, secondly, from the motion of a (limited number) of solvent molecules which may form an important part of the motion of the whole system along the HP. But apart from dynamical nonequilibrium solvation effects and other limitations in the application of TST to reaction in solvents (see Chap. 1.4), static approaches will give much information on the intermolecular interactions and may represent a suitable ansatz for the estimation and interpretation of solvent effects in many cases. 

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