Analytical Solutions and Computer Simulations of the Evolution of Flat Temperature Profiles in Spherical FRRPP Systems

Abstract

The free-radical retrograde-precipitation (FRRPP) process was recently brought into the quantitative areas of work, based on the discovery of possibility of flat temperature profiles in spherical reactive domain systems. With an approximate decoupling analysis of the energy equation from the component-balance equations, these flat temperature profiles were found to be either stable or unstable. Moreover, resulting evolution of the flat profiles has been found to be expressed analytically through the so-called exponential Integral function, which has been shown to be quantitatively inaccurate during the early times of the process. This work tries to resolve this inaccuracy problem, by comparing the exponential integral results with polynomial approximation and numerical results. The result is that for the stable sys-tem, the linearized treatment of the evolution of flat temperature profiles is valid at the early 30% - 40% in the tem-perature axis, while the remainder of the evolution curve is well-represented by the application of the exponential integral function. For the unstable system, the only thing that can be generalized is that both linear and cubic polynomial approximations are reasonably accurate at very small times and temperatures close to initial values.