Instabilities in multi-hole converging flow of viscoelastic fluids

Studies of the onset of instabilities were conducted on single hole and multi-hole contractions using laser speckle visualization. A well characterized elastic fluid was used with constant viscosity of 13.1 Pa · s and elasticity characterized by a longest relaxation time constant of 2.233 s. The onset of instabilities was characterized in terms of the Deborah number and the contraction ratio. Three types of instabilities were observed: pulsing vortices, azimuthally rotating vortices, and swirling vortices. For the single hole contractions the critical Deborah number for instability increased from 4.4 to 5.07 to 5.25 as the contraction ratio increased from 4: 1 to 8: 1 to 12: 1. The magnitude of the instabilities was much greater for the 4: 1 contraction than for the other two contraction ratios. For the multi-hole contraction a square array of nine holes was used and the ratio of the hole diameter to hole spacing was varied. The height of the vortices is very similar for the single hole and multi-hole contractions at low Deborah numbers. At high Deborah numbers the effect of adjacent holes is to reduce the height of the vortices by a factor of three. For the 4: 1 spacing no secondary vortex was observed below a Deborah number of De = 3.7. Secondary vortices occurred for the 8:1 and 10:1 spacing at all Deborah numbers. Unstable pulsing vortices appeared for all spacings at a critical Deborah number around 5.5. Adjacent holes decreased the strength of the unsteady vortex motions. The centerline velocities were measured for the multi-hole contraction at shear rates of 5, 30, and 300 s^-1. The elongational strain rates are similar at a low shear rate of 5 s^-1. As shear rate is increased the onset of stretching occurs closer to the plane of the contraction for the smaller contraction ratios.