Capillary, viscous, and geometrical effects on the buckling of power-law fluid filaments under compression stresses

Abstract

Thanks to an adaptive variational multi-scale method for multiphase flows with surface tension, we investigate through direct numerical simulations and scaling laws the buckling of filaments of power-law fluids compressed at a constant velocity by two parallel pistons. Under low gravity (the Laplace pressure exceeds the hydrostatic pressure) and inertial conditions (very small Reynolds numbers), two regimes are observed for slender filaments: a first one driven by the capillary force and during which there is no deflection; and a second folding regime that is dominated by the compressive viscous force. The transition between these two scenarios is given by a critical capillary number, which in turn appears as an increasing function of the flow behaviour index. Our main results are summarised in two-dimensional phase diagrams whose axes are a slenderness parameter and the capillary number.