On the stability of steady surface-tension driven flows

In this paper, we study the stability of similarity solutions for the probl em f''' + Q(Aff" - (f')(2)) = beta, with Q > 0, A greater than or equal to 1 and beta is an element of R. The given problem was derived from the symme tric reduction of similarity transformations from the Navier-Stokes equatio n for the planar flows. By imposing additional eigenvalue problems, our num erical studies show that the resultant steady flows are unstable as Q becom es large for various A < 2. Furthermore, our analytical result gives that t he steady flows are stable for small Q, when 1 <less than or equal to> A < 2, or for any Q > 0 when A greater than or equal to 2. Moreover, the existe nce of asymmetric flows for various A < 2 is also found numerically.