Open chemical systems

Many times in geochemical modeling we want to understand not only what reactions proceed in an open chemical system, but where they take place (e.g., Steefel et al., 2005). In a problem of groundwater contamination, for example, we may wish to know not only the extent to which a contaminant might sorb, precipitate, or degrade, but how far it will migrate before doing so. 

A much larger variety of phenomena can be described as stationary states of open chemical systems, i.e., systems in which molecules can be injected and from which molecules can be extracted. The simplest possibility for injection of molecules X is at a constant rate b. Extraction of X can only be done as long as there are some X present the rate of extraction must therefore vanish when n = 0 the simplest possible choice for it is an. Then the macroscopic equation for the number n of molecules X has the form... 

Finally, it appears that the kinetic models of complex reactions contain two types of components independent of and dependent on the complex mechanism structure [4—7]. Hence the thermodynamic correctness of these models is ensured. The analysis of simple classes indicates that an unusual analog arises for the equation of state relating the observed characteristics of the open chemical system, i.e. a kinetic polynomial [7]. This polynomial distinctly shows how a complex kinetic relationship is assembled from simple reaction equations. 

The existence of two stable steady states for the same values of the externally controlled constraints is known as bistability . A mechanical analogy to such a situation is the double well potential shown in Fig. 2. (No potential function is known to exist for open chemical systems that would play the role of the gravitational potential energy in... 

H. Qian. Phosphorylation energy hypothesis open chemical systems and their biological functions. Annu. Rev. Phys. Chem., 58 113-142, 2007. 

Feinberg, M., and Horn, F., Dynamics of open chemical systems and the algebraic structure of the underlying reaction network. Chem. Eng. Sci. 29,775 (1974). 

III B) 1980 Boissonade, J., De Kepper, P. Transitions from Bistability to Limit Cycle Oscillations. Theoretical Analysis and Experimental Evidence in an Open Chemical System. J. Phys. Chem. vol. 84, 501-506... 

Qian H. 2007. Phosphorylation energy hypothesis Open chemical systems and then biological functions. Annual Review of Physical Chemistry 58 113. 

Many physical and chemical processes occurring in chemical reactors determine the temporal evolution of the reaction mixture. In an open chemical system, the steady state is a state in which the composition and other characteristics (temperature, pressure, volume, etc.) are considered to be constant in time. In contrast, in a nonsteady-state regime, the system... 

Besides these two regimes, another regime, with a temporally periodic change of the chemical composition (chemical oscillation or self-oscillation), may also be observed. A famous example of this phenomenon is the Belousov-Zhabotinsky reaction. Another example of complex kinetic behavior in open chemical systems is the occurrence of multiple steady states due to the fact that for some components of the reaction mixture the rate of consumption and rate of production can be balanced at more than one point. This type of behavior has become the subject of detailed theoretical and computational analyses (Marin and Yablonsky, 2011 Yablonskii et al., 1991). Bespite the fact that there are many experimental data concerning such complex behavior, the steady-state regime with characteristics that are constant in time still is the most observed phenomenon. 

For a closed chemical system, that is, a system without exchange of matter with the environment, the rest point is termed the equilibrium point, the equilibrium state, or just equilibrium, with concentration vector Ceq. For an open chemical system, in which there is exchange of matter, the rest point is termed the steady state, with corresponding concentration vector Css- Since a closed system is a particular case of an open system, equilibrium is a particular case of steady state. 

A special mathematical problem is that of determining the number of rest points. Rest points can be classified as internal with all variables nonzero or as boundary with at least one variable equal to zero. In a closed chemical system, the internal rest point is unique. Zel dovich (1938) provided the first version of the proof of this uniqueness. Gorban (1980) analyzed the boundary equilibrium points in a closed chemical system. For an open chemical system, isothermal or nonisothermal, multiple internal steady states may exist. 

Feinberg, M. Horn, F. J. M. 1974. Dynamics of Open Chemical Systems and the Algebraic Structure of the Underlying Reaction Network, Chem. Eng. Sci. 29, 775-787. 

In an open chemical system that exchanges matter and energy with the exterior, we can identify the energy and entropy flows associated with the exchange of matter and energy. Using the kinetic equations, we can obtain the stationary state. As an example, let us consider a chemical system undergoing a mono-molecular reaction such as isomerization ... 

Figure 17.2 An open chemical system in which the chemical potentials Pb are maintained at a...

Consider the open chemical system shown above with the following chemical reactions. 

Now consider an one-variable open chemical system, either linear... 

The next concept which proves useful in developing new chemical oscillators is that of bistability along with the related notion of hysteresis. An open chemical system, such as a reaction in a CSTR, may have two (or more) different stable steady states under the same external constraints, i.e., values of the input flow rate, reservoir concentrations, temperature and pressure. In such a situation, transitions from one state to another show hysteresis, occurring at different points depending upon the direction in which the constraints are changed. An example of this behavior is shown in Figure 2. As the iodide... 

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