Fig. 3: Wilhelmy plate tensiometry and capillary rise method for contact angle evaluation.

a Schematic illustration of the experimental setup. b Typical procedure to determine θ_adv and θ_rec from advancing and receding force curves F_adv and F_rec during immersion and emersion, respectively. c Uncertainties in θ estimates calculated with standard error propagation (Equation (3)) for two different wetted perimeters p = 2 mm and p = 5 cm (left and right y-axes, respectively). Here, we assume δF = 1μN, and the relative uncertainties for the wetted perimeter Δ_p = δp/p = 0.01 and surface tension Δ_γ = δγ/γ = 0.01⁷⁵. d Using the capillary rise at a vertical plate, θ can be deduced from the meniscus height z observed optically (See Equation (4)). No force measurement is required. e Contact angle measurements as a function of immersion (advancing) and emersion (receding) speed U. The liquid used is decane which wets the silicon surface grafted with silicone polymer brushes. Adapted from ref. ⁷⁸. f Error in contact angle obtained using the capillary rise method for δz = 5 μm and 30 nm (left and right y-axis, respectively) and assuming that L_c = 2 mm (true for most liquids), as predicted by Equation (5).