Upstream wall vortices in viscoelastic flow past a cylinder.

Abstract

We report a novel inertia-less, elastic flow instability for a viscoelastic, shear-thinning wormlike micellar solution flowing past a microcylinder in a channel with blockage ratio <i>B</i>_R = 2<i>R</i>/<i>W</i> = 0.5 and aspect ratio <i>α</i> = <i>H</i>/<i>W</i> ≈ 5, where <i>R</i> ≈ 100 μm is the cylinder radius, <i>W</i> is the channel width, and <i>H</i> is the channel height. The instability manifests upstream of the cylinder and changes form with increasing Weissenberg number over the range 0.5 ≲ Wi = <i>Uλ</i>/<i>R</i> ≲ 900, where <i>U</i> is the average flow velocity and <i>λ</i> is the terminal relaxation time of the fluid. Beyond a first critical Wi, the instability begins as a bending of the streamlines near the upstream pole of the cylinder that breaks the symmetry of the flow. Beyond a second critical Wi, small, time-steady, and approximately symmetric wall-attached vortices form upstream of the cylinder. Beyond a third critical Wi, the flow becomes time dependent and pulses with a characteristic frequency commensurate with the breakage timescale of the wormlike micelles. This is accompanied by a breaking of the symmetry of the wall-attached vortices, where one vortex becomes considerably larger than the other. Finally, beyond a fourth critical Wi, a vortex forms attached to the upstream pole of the cylinder whose length fluctuates in time. The flow is highly time dependent, and the cylinder-attached vortex and wall-attached vortices compete dynamically for space and time in the channel. Our results add to the rapidly growing understanding of viscoelastic flow instabilities in microfluidic geometries.