Rotationally-axisymmetric Motion of a Binary Mixture with a Flat Free Boundary at Small Marangoni Numbers
Rotationally-axisymmetric motion of a binary mixture with a ﬂat free boundary at small Marangoni numbers is investigated. The problem is reduced to the inverse linear initial-boundary value problem for parabolic equations. Using Laplace transformation properties the exact analytical solution is obtained. It is shown that a stationary solution is the limiting one with the growth of time if there isa certain relationshipbetween the temperature of the solidwall and the external temperature of the gas. If there is no connection, the convergence to the stationary solution is broken. Some examples of numerical reconstructionofthetemperature, concentrationandvelocityﬁeldsaregiven,which conﬁrm the theoretical conclusions.