Computational study of fluid flow in tapered orifices for needle-free injectors

Transdermal drug delivery using spring-powered jet injection has been studied for several decades and continues to be highly sought after due to the advent of targeted needle-free techniques, especially for viscous and complex fluids. As such, this paper reports results from numerical simulations to study the role of fluid rheology and cartridge geometry on characteristics such as jet exit velocity, total pressure drop and boundary layer thickness, since these all factor in to jet stability and collimation. The numerical approach involves incompressible steady flow with turbulence modelling based on the system Reynolds number at the orifice (Re = ρd_ov_j/μ). The results are experimentally validated for a given geometry over a wide range of Reynolds numbers (10¹ < Re < 10⁴), and our results indicate a sharp decrease in dimensionless pressure drop (Eu = 2∆P/ρv_j²) for Re < 10²⁾ and gradually approaching the inviscid limit at Re ≥ 10⁴. By extending the study to non-Newtonian fluids, whose rheological profile is approximated by the Carreau model, we also elucidated the effect of different rheological parameters. Lastly by studying a range of nozzle geometries such as conical, sigmoid taper and multi-tier tapers, we observe that fluid acceleration suppresses the boundary layer growth, which indicates there may be optimal geometries for creating jets to target specific tissue depths.