Optimal Loading For Injection

The injection of fluids loaded with a precise number of particles, polymers, and other solutes is common in many areas of chemical engineering. By definition, injection of these fluids is meant to occur over the shortest possible duration. This raises the question that is answered in this note: At what concentration should a fluid be loaded in order to inject that fluid fastest? A similar question has been addressed for flows of Newtonian fluids in biophysical and physiological studies. We generalize that analysis. We show for Newtonian fluids containing a single suspended component that the optimal loading is determined from a common tangent construction for the viscosity as a function of concentration. We extend this formulation to describe optimal injection of a multicomponent Newtonian fluid. Additionally, we study the injection problem for a simple, model non-Newtonian fluid carrying a single suspended component. Finally, we discuss applications for optimally loaded injections.