Solution (source code)

= Solution

The intended chemically matched surface approximation is $\gamma_{SL}\simeq0$. It gives $S\simeq23-21.3=1.7\,\mathrm{mN\,m^{-1}}>0$, so increasing the wetted area lowers <free energy>. The initially steep drop spreads and flattens toward <complete wetting>:
$$
\boxed{\theta_{\rm eq}=0\quad\text{in the negligible-}\gamma_{SL}\text{ approximation}.}
$$
The initial $90^\circ$ angle describes a nonequilibrium shape and must not be inserted into equilibrium <Young's equation> to fix $\gamma_{SL}$. More precisely, complete wetting requires $\gamma_{SL}\leq1.7\,\mathrm{mN\,m^{-1}}$ in this surface-energy model; chemical similarity alone is not a measurement of that interfacial energy.

Water on such a low-energy, oil-like surface is expected to bead into a comparatively rounded, high-angle drop because the substrate does not compensate its cohesive interactions. Its numerical <contact angle> needs the water-solid interfacial energy, which is not supplied.