On simple scaling laws for pumping fluids with electrically-charged particles

As 3D printing has matured, the use of more complex materials has increased. In particular, particle-functionalized inks are now relatively wide-spread. Because of the desire to have faster throughput for industrial-scale printing, electrically-driven flow of such materials is being pursued. In many cases, such fluids consist of an electrically-neutral base solvent with embedded charged particles. As one increases the volume fraction of particles, two effects effects arise: (1) an increase in effective overall viscosity fluid and (2) an increase in the induced electrical force that can be applied. In the present analysis, the governing equations for the required pressure gradient in a pipe to move the fluid with a constant flow rate are derived. A key nondimensional scaling ratio governing the relative contribution of electrical and viscous fluid forces to the system behavior is also identified. Numerical examples are provided to illustrate the results.