Spreading of drops on solid surfaces in a quasi-static regime

The problem of interaction of a drop with a solid boundary is formulated in the framework of a recently developed theory of the three-phase contact line motion and analyzed in the case of finite Bond and small capillary and Weber numbers. Evolution of the free-surface shape in a quasi-static regime of the drop spreading under gravity on a horizontal plane and on the surface of a rotating disk is investigated. In the considered regime, the free-surface shape deformation in time is independent of the initial conditions of the drop deposition onto the solid surface, while the three-phase contact-line motion is described by the same equations as in a general case. This feature makes the quasi-static regime informative and desirable from the point of view of investigation of the wetting phenomenon. Accuracy of the so-called “spherical cap approximation’’ often used in experimental studies of wetting is discussed. The theory describes both the “spontaneous” and “forced” regimes of the drop spreading and the transition between them. The results are compared with experimental data.