Non-monotonic die swell of liquid foams

Liquid jets extruded through narrow orifices can expand significantly upon exiting, a phenomenon known as die swell. While extensively studied for polymers, die swell in other complex fluids remains poorly understood. We present an experimental investigation of die swell in foams extruded from a capillary tube at the outlet of a syringe (whipped cream and shaving foam). The experiments show a very large die swell that is, in addition, non-monotonic: contrary to what happens for polymers, with increasing flow rate, the die swell of the foam first decreases, passes through a minimum and then increases again. We show that these two regimes can be explained by a balance of capillary and viscous forces at low pressure and the compressibility of the foam at high pressure, respectively. These results will facilitate the prediction of extruded filaments' diameter in the additive manufacturing of aerated liquids, with applications in food, medicine, or construction. We show that die swell scales as 1/Ca at low capillary numbers and as D/D₀ ∼ (1+ΔP/P₀)^1/3 at high pressures. Die swell ratios reach ∼2 for small capillaries (D₀ < 1 mm) at low pressures, decrease to ∼1 at intermediate pressures (0.15–0.2 bar), then increase again at higher pressures .