Turbulent reacting flows with moderate or high Reynolds (Re), Schmidt (Sc) and Damkoehler (Da) numbers can be calculated only approximately. Lagrangian probability density function (PDF) methods are especially attractive for computing such flows, because approximations are restricted to the simulation of mixing processes. For the calculation of these processes, a new Lagrangian multi-scale scalar mixing model is presented here. In contrast to previously applied methods, this model describes for high-Sc flows mixing also at the Kolmogorov- and Batchelor-scales. This is relevant, because the characteristic scalar mixing time may be much larger than for flows without extended Kolmogorov- and Batchelor-scale. The significant effect of this delay of the onset of chemical reactions is illustrated by means of the simulation of mixing and parallel chemical reactions of species in a turbulent pipe flow. It is shown, that the neglect of such effects by conventional techniques results in errors of about 50% for the case considered. This application reveals the remarkable effects of Re and Da, which are closely related to each other.