Gas dynamic virtual nozzle induced flow of viscoelastic fluids

Abstract

We fabricated a gas dynamic virtual nozzle using a three-dimensional (3D) printer to produce a jet of viscoelastic fluid. Aqueous alginate with concentrations of 0.5%, 1%, and 1.5% served as the dispersed phase, air as the continuous phase, and a high-speed camera for flow visualization. Viscosity and relaxation time measurements indicated that the zero shear rate viscosities of aqueous alginates were 0.055, 0.2, and 1.2 Pas, with relaxation times of 0.15, 0.79, and 2.3  ms for concentrations of 0.5%, 1%, and 1.5%, respectively. The emphasis was on understanding the effects of shear-thinning, alginate concentrations, and elasticity on regimes, jet size, and intact jet length. Analytical solutions and scaling laws were derived and compared with experimental data and literature. For Newtonian and laminar flow, we demonstrated the linear dependency of jet diameter on the Reynolds number through the derived scaling law. The measured jet diameter for non-Newtonian fluids significantly deviates from water due to their viscoelastic nature. At 0.5 psi, the dimensionless diameter differences were nearly 42% and 37% for flow rates of 5 and 15 μl/s, respectively. The peak intact jet length, observed at 0.5 psi, was nearly 60% higher for 0.5% aqueous alginate than for water. Using the Buckingham π theorem, we identified nondimensional groups and developed correlations to predict jet diameter across a wide range of viscosities, relaxation times, and operating conditions.