The M Number: A Novel Parameter to Evaluate the Performance of Static Mixers

Publication Date


Document Type





Static mixers (SM) have become standard equipment in the process industries. They are widely used in applications that involve chemical reactions, heat transfer, blending of fluids, or a combination of these. Compared to mechanically agitated vessels, SMs consume less energy, require less maintenance, and can provide mixing with shorter residence time. Assessment of the performance of SM provides a means to categorize and rank the available devices and new designs, which in turn facilitates selection for specific applications. Applying the second law efficiency (SLE) principle, we derived and proposed a novel mixing parameter, the M number, which is a dimensionless ratio of mixing level to energy loss. The parameter is compared to an industry-standard method of mixing evaluation that relies on the coefficient of variation (CoV) change across the mixer. Both CoV and the M number are used to evaluate mixing performance from computational fluid dynamics (CFD) results for a static mixer for various inlet conditions. Unlike the CoV-based parameters considered, the M number offers the advantages of accounting for energy loss and the natural mixing effects of the system. In addition, an empirical relationship is obtained that relates the M number to the Reynolds number (Re). Potential applications for the M number are discussed and its limitations are noted. Work in progress includes investigation with other SM.