Residual heel volume during the pressure-driven discharge of complex fluids from consumer dispensing bottles

The discharge of complex fluids from consumer bottles containing liquid soaps, creams, lotions, and others, typically results in heel formation, i.e., the ultimate residual amount of fluid left the container. Here, we investigated the fluid rheology effect on heel formation in a commercial hand pump bottle containing different complex fluids and including humectants, polymer solutions, and pastes. Computational Fluid Dynamics (CFD) was used to simulate the flow of fluids whose rheology was based on the Carreau equation, resulting in the prediction of the heel volume. These results were validated using weight measurements to quantify the volume of fluid left in the container and, separately, with an imaging method based on the use of Particle Image Velocimetry (PIV). All these results were in good agreement. The effective yield stress σ₀ at a predefined level was found to be the critical parameter to predict the heel volume.