Mathematical Models for Mixing Time of Some Additive Free Calcium Soap Lubricating Greases

Abstract

Mixing is among the most common processes in chemical, biochemical, pharmaceutical, polymer, mineral, food, and wastewater treatment industries [1]. Several examples of greases mixing processes can be found in the literature [2]-[5]. Four greases were prepared with different concentration of calcium soap: 5%, 10%, 15% and 20% in paraffin oil. The preparation formulas for these four greases and manufacture method were presented in a recent work [6]. The aim of this study was to find a mathematical model for the mixing time of some additive-free lubricating greases. The mathematical modeling consisted on finding an accurate equation linking the mixing time (tm) and the Reynolds number (Re) at different soap concentrations and temperatures. The mixing experiments were carried out in a laboratory autoclave equipped with an anchor impeller, without baffles, at 8 speed ratio, from 100 to 800 rpm. The models resulted from the tm variation versus Re are power function type tm = a x Reb, where the coefficients a and b are functions of soap concentration in base oil and the processing temperature