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In 1805, Young was the first who introduced an expression for contact anglein static, but today, the motion of the contact-line formed at the intersectionof two immiscible fluids and a solid is still subject to dispute. By means ofthe new physical concept of line viscosity, the equations of motions andboundary conditions for fluids in contact on a solid surface together withinterface and contact-line are revisited. A new Young-Dupr\'e equation for thedynamic contact angle is deduced. The interfacial energies between fluids andsolid take into account the chemical heterogeneities and the solid surfaceroughness. A scaling analysis of the microscopic law associated with theYoung-Dupr\'e dynamic equation allows us to obtain a new macroscopic equationfor the motion of the contact-line. Here we show that our theoreticalpredictions fit perfectly together with the contact angle hysteresis phenomenonand the experimentally well-known results expressing the dependence of thedynamic contact angle on the celerity of the contact-line. We additively get aquantitative explanation for the maximum speed of wetting (and dewetting).

The wetting problem of fluids on solid surfaces: Dynamics of lines and contact angle hysteresis