Numerical simulation of the drop spreading on a horizontal plane

A shallow water model of film flow is used to describe the process of a drop spreading on a horizontal plane, taking into account the liquid viscosity, heat-mass transfer and surface tension forces. To simulate this flow numerically in polar coordinates an unconditionally stable implicit difference scheme has been developed, which (in the case of evaporation) can calculate the drop spreading over a dry surface without special allocation of the drop boundary. A region of dimensionless parameters is singled out under which the evaporating droplet, as a result of surface tension forces, transforms into a circular ring before complete evaporation.