SOME NON-NEWTONIAN EFFECTS IN HELE-SHAW DISPLACEMENTS

We consider a non-Newtonian fluid displaced by air in a Hele-Shaw cell and study the modal linear stability. The particular flow geometry a very thin Hele-Shaw cell allows us to use some simplified flow equations. The novelty of the paper is an approximate formula for the growth constant (of perturbations), which can grow unbounded when the corresponding Weissenberg number is located in a certain range. We get a strong destabilization effect, compared with the Newtonian case studied by Saffman and Taylor (1958). This phenomenon was observed in experiments, during the flow of some complex fluids in thin HeleShaw cells. While we used the linear stability method, the (possible) very large values of the growth constant should be studied in the frame of the nonlinear stability.