Modeling of kinetics of strain induced degradation of polymer additives in lubricants
Mathematical Models and Methods in Applied Sciences
A kinetics problem for a degrading polymer additive dissolved in a fluid lubricant is studied. The polymer degradation may be caused by the combination of such lubricant flow parameters as pressure, strain rate, and temperature as well as lubricant viscosity and the polymer characteristics (dissociation energy, bead radius, bond length, etc.). A fundamental approach to the problem of modeling stress-induced polymer degradation is proposed. The polymer degradation is modeled on the basis of a kinetic equation for the density of the statistical distribution of polymer molecules as a function of their molecular weight. The existence and uniqueness of the solution to the initial-value problem for the kinetic equation is proven. Moreover, some properties of the solution are established. The integrodifferential kinetic equation for polymer degradation is solved numerically for a number of different input data. The effects of pressure, strain rate, temperature, and lubricant viscosity on the process of lubricant degradation are considered. The increase of pressure promotes fast degradation while the increase of temperature delays degradation. In some cases, the density of the molecular weight distribution function maintained in time its initial single-modal shape and in other cases it changed with time from a single-modal shape to a bi-modal shape. A comparison of numerically calculated molecular weight distributions with experimental ones obtained in bench tests showed that they are in excellent agreement with each other.
Kudish, Ilya I.; Hayrapetyan, Ruben; and Covitch, Michael J., "Modeling of kinetics of strain induced degradation of polymer additives in lubricants" (2011). Mathematics Publications. 77.