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

Spreading of an axisymmetrical drop on a dry plane horizontal wall under the action of gravity and surface tension (or capillarity) is studied in the inertialess approximation for arbitrary Bond numbers. It is shown that the initial stage of spreading is completely dominated by gravity, and rolling motion sets in at the contact line (CL). When the rate of the CL motion reduces to the order of the characteristic wetting velocity expected from the Hoffman's well-known law, wetting effects begin to play an important role. However, the apparent contact angle at this stage is still affected by the bulk flow and only at its end approaches 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, owing the fact that the bulk flow effects driven by gravity are stronger, the higher the Bond number. Accordingly the apparent contact angle increases with the Bond number, which is in qualitative agreement with experimental observations. Comparison with known analytical solutions is presented.