Spreading of a viscous drop due to gravity and capillarity on a horizontal or an inclined dry wall

Spreading of a drop on a plane dry wall (horizontal or inclined) due to gravity and capillarity is studied in the inertialess approximation for arbitrary Bond numbers. In the case of a horizontal wall it is shown that the initial stage of spreading is fully dominated by gravity, and rolling motion sets in at the contact line (CL). When the rate of the CL motion reaches the order of the characteristic wetting velocity, wetting effects are accounted for. The apparent contact angle at this stage is affected by the bulk flow and only at the end approaches the well-known Hoffman's law. Deviations from the latter are shown to be important in the region of contact angles close to ∏ and to increase with the Bond number. This follows from the fact that the bulk flow effects driven by gravity are stronger as the Bond number is higher. They affect the apparent contact angle. The latter increases as the Bond number increases which agrees qualitatively with experimental observations. A comparison with the known analytical solutions is proceeded. In the case of an inclined surface it is shown that rolling motion near the leading contact line sets in only when the slope angle exceeds a certain threshold value. On inclined surfaces drops develop bump near the leading contact line, as well as a long tail emerges.