Velocity of retrograde cathode spot motion and thermocapillary convection during local heating of a liquid surface

A thermocapillary vortex cell of well-determined diameter is shown to form when an unconfined liquid surface is locally heated by a moving source. The heating leaves the state of the liquid essentially unchanged except inside the cell, and the circulation of liquid along the meridian transports heat out of the cell. The shape of the meniscus and the nature of the convection away from the source are independent of how the liquid is heated. An approximate expression is derived for the velocity of retrograde motion of a cathode spot on a homogeneous molten cathode.