Modeling of lubricant performance in Kurt Orbahn tests for viscosity modifiers based on star polymers

The kinetics of stress-induced degradation of a star polymer additive dissolved in a mineral oil lubricant is modeled. The polymer degradation is modeled on the basis of a new system of kinetic integro-differential equations for the distribution densities of star polymer molecules with different numbers of arms and arm chain lengths. Some properties of the solution are established. Among these properties are the existence and uniqueness of the solution of the initial-value problem for the above mentioned system of integro-differential kinetic equations for star polymer degradation. A number of numerical solutions of the problem are obtained and analyzed. Some of the numerically simulated molecular weight distributions are compared with the independently obtained experimental ones. The lubricant viscosity losses due to polymer degradation are determined and compared with the experimentally measured ones. The theoretical and experimental data are in very good agreement.