The Effect Of Weak Buoyancy On Dendritic Growth And Stability In Binary Mixtrues

In this paper,we study the mathematical formulation for dendrite growth with weak buoyancy flow(the case of S C= O(1) and G 1) in binary mixtures,by assumeing that the surface tension is zero,the solution of the mathematical formulation,which is a free boundary problem,is asymptotically expanded,the basic solution of dendrite growth is obtained.From this solution,one can conclude that,with weak buoyancy effect,the solution of dendrite growth is no longer an exact similar solution.Accordingly,in the first–order approximation,the shape of the dendrite is no longer a parabolid.The small buoyancy effect introducrs many small non–similar ingredients to the solution,which are represented,in the Laguerre series represen–tation,by the infinitely many components,so it is proper to call our solution a"nearly"Similar solution.