Fig. 3: Friction force on superhydrophobic etched silicon substrates—experiment vs. theory.

a–e Scanning electron microscopy images taken at a \(45^\circ\) angle of the A (spikes), B, C, D, and E (grass) samples, respectively. Scale bars 1 μm. f Measured kinetic friction force as a function of contact region diameter. The solid lines are linear fits (through origin) to the data with the slopes \(F_{\upmu}/D = (2.7 \pm 0.4),\,(1.6 \pm 0.3),\,(0.6 \pm 0.2),\,(0.11 \pm 0.04),\,(0.03 \pm 0.02)\) nN μm⁻¹ for the E (grass), D, C, B, and A (spikes) samples, respectively. g Measured friction force as a function of the theoretically calculated lateral adhesion force (\(F_{{\mathrm{LA}}}\), Eq. (1)). The solid line (going though origin) has a slope of unity. h The ratio between the relative errors (\(\delta F = {\mathrm{{\Delta}}}F/F\), where \({\mathrm{{\Delta}}}F\) is the absolute error) of the theoretical (CAG) and experimental (MFS) force estimates as a function of \(F_{\upmu}/D\). Measuring the friction force with MFS renders from 10 (min) to 1000 (max) times more precise results as the surface becomes more slippery. As the lower limit of the micropipette technique is approached for small droplets on the most slippery spikes (A) surface (red crosses), the relative error still remains more than 10 times lower when using MFS instead of Eq. (1). The legend in g also applies to the markers in f and h. The error bars in all graphs are standard deviations or error propagations including these (see Supplementary Note 2).