Boundary conditions theoretic-numerical approach

Diffusion is intricately linked with all aspects of the radical-pair mechanism. The CIDNP kinetics for the reaction of a sensitizer with a large spherical molecule that has only a small reactive spot on its surface were studied theoretically. This situation is t)qjical for protein CIDNP, where only three amino acids are readily polarizable, and where such a polarizable amino acid must be exposed to the bulk solution to be able to react with a photoexcited dye. Goez and Heun carried out Monte Carlo simulations of diffusion for radical ion pairs both in homogeneous phase and in micelles. The advantage of this approach compared to numerical solutions of the diffusion equation is that it can easily accommodate arbitrary boundary conditions, such as non-spherical symmetry, as opposed to the commonly used "model of the microreactor" ° where a diffusive excursion starts at the micelle centre and one radical is kept fixed there. 

The hydrodynamics of the experimental system can be described theoretically. Such approach is very important for correct interpretation of the experimental results, and for their extrapolation for the conditions not attainable in the existing experimental system. With the mathematical model the parametric study of the system is also possible, what can reveal the most important factors responsible for the occurrence of the specific transport phenomena. The model was presented in details elsewhere [2]. It was based on the equations of the momentum and mass transfer in the simplified two-dimensional geometry of the air-water-surfactant system. Those basic equations were supplemented with the equation of state for the phopsholipid monolayer. The resultant set of equations with the appropriate initial and boundary conditions was solved numerically and led to temporal profiles of the surface density of the surfactant, T [mol m ], surface tension, a [N m ], and velocity of the interface. Vs [m s ]. The surface tension variation and velocity field obtained from the computations can be compared with the results of experiments conducted with the LFB. 

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