Dimensional analysis and scaling in mechanical mixing for fabrication of metal matrix nanocomposites

For a successful enhancement of mechanical properties of metal matrix nanocomposites, a homogeneous nanoparticle dispersion and distribution in the solidified metal is required. Mechanical mixing can be used for initial break-up of agglomerates, and its study can be simplified with dimensional analysis. Using this technique, mixing time and vortex height were assessed while varying fluid properties, impeller angle, and angular speed. Three relevant dimensionless numbers were recognized: the Reynolds (Re), Froude and Galilei (Ga) numbers. Based on blade and impeller shaft angles, a modified Froude number (Fr*) was defined. These parameters were calculated experimentally, varying angular speed from 200 to 1000 rpm for three different impeller angles: 0°, 15° and 30°. This procedure was performed with three fluids: water, and two aqueous glycerin solutions (25% and 50% by volume). Digital images were taken and processed to measure vortex height. Mixing time was measured for water at 0° impeller angle, angular speed ranging from 200 to 1200 rpm. Results showed an optimal dimensionless mixing time with respect to Re. A linear relationship was found between dimensionless vortex height and Fr*. The first had a second order polynomial relationship with the product ReFr*, regardless of impeller angle. This relationship, together with the Ga, specific for each fluid, allows scaling the results to other fluids such as molten pure aluminum. This study allows experimenting in simpler systems that involve transparent fluids, room temperature and low cost, to then elaborate a prediction of vortex height in fluids where measurements are difficult and costly, such as molten metals.