Abstract
Abstract
A nonlinear one-degree-of-freedom model is formulated for the effective radial deformation of
water droplets impacting smooth and nanowall-textured hydrophobic silicon surfaces. The model
is a lumped radial surrogate, not a resolved volume-of-fluid, phase-field, or other multiphase
simulation. Capillary stiffness is fixed by an inertial–capillary timescale, a cubic stiffness
is calibrated to one graphically extracted smooth-surface spread factor, and the nanowall
contribution is represented by regularized kinetic resistance together with an explicit moving-to-
stuck event. For a 20 µL droplet released from 20 mm, the linear unpinned oscillator gives a
maximum spread factor of 3.955, the calibrated nonlinear unpinned oscillator gives 2.253, and
the nonlinear textured-surface model gives 1.810. With the parameters fixed, the predicted
maximum spread increases with reconstructed Weber number and remains lower for the textured
surface over the investigated volume and release-height conditions, consistent with the qualitative
trends reported by Yilbas et al. Pointwise experimental errors are not claimed because numerical
response data were not available. Local deterministic sensitivity identifies nonlinear stiffness and
pinning magnitude as the principal controls on maximum spread; solver refinement, event-root
tolerance, and the kinetic-force smoothing speed have negligible effects at the reported precision.
The model does not predict physical lift-off, vertical rebound, wetting-state transitions, or the
experimental normal restitution coefficient.