Unknown pressure distribution in the onion mesophyll stress zone during blade indentation and rupture

Determine the spatial pressure distribution within the stressed mesophyll region of the first onion layer during blade indentation and fracture, and characterize how this distribution differs from the epidermal critical fracture stress σ_{c,skin} at the blade tip. Quantify this distribution to enable predictive relations between blade tip width r_b and the initial ejected droplet velocity V_d,0.

Background

To relate blade sharpness to the speed of ejected droplets, the paper examines pressurization beneath the blade tip in the onion’s composite first layer (a tough epidermis over a softer mesophyll). At rupture, the mesophyll is highly pressurized, yet the precise spatial distribution of this pressure is required to predict initial droplet velocities and fracture forces.

The authors explicitly note that the full pressure distribution within the stress zone is not known a priori, motivating their use of an approximate strain-based scaling. Establishing this distribution would resolve a key uncertainty in connecting blade geometry (r_b) to droplet ejection dynamics and improve mechanistic modeling beyond the simplified average-strain and membrane-on-spring approximations.