Characteristic lengths at moving contact lines for a perfectly wetting fluid: the influence of speed on the dynamic contact angle

It is common to relate the dynamic contact angle $\theta_d$ to the relative speed between the substrate and the contact line; theory suggests $\theta_d^3 \propto U$. In fact, available physical models show that the dynamic angle involves speed logarithmically and in a model dependent manner. Experimental data consistent with this interpretation is cited.