Self-similar solution of the one-dimensional problem of thermocapillary motion of an emulsion

It is proved that the problem of one-dimensional motion of an emulsion under the action of thermocapillary forces has a self-similar solution in a semi-infinite interval. The behavior of the solution is illustrated by numerical examples for aluminum-lead emulsions, in which the carrier phase is lead or aluminum. The solution is compared with the solution of the self-similar problem linearized in the low impurity concentration.