Upstream wall vortices in viscoelastic flow past a cylinder

• Published in: Soft matter 2022-07, Vol.18 (26), p.4868-488
• Main Authors: Hopkins, Cameron C, Haward, Simon J, Shen, Amy Q
• Format: Article
• Language: English
• Subjects: Aspect ratio; Average flow; Cylinders; Flow stability; Flow velocity; Fluid flow; Instability; Micelles; Microfluidics; Relaxation time; Shear thinning (liquids); Symmetry; Time dependence; Upstream; Viscoelasticity; Vortices
• ISSN: 1744-683X; 1744-6848
• DOI: 10.1039/d2sm00418f

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 B R = 2 R / W = 0.5 and aspect ratio α = H / W 5, where R 100 μm is the cylinder radius, W is the channel width, and H is the channel height. The instability manifests upstream of the cylinder and changes form with increasing Weissenberg number over the range 0.5 Wi = Uλ / R 900, where U is the average flow velocity and λ 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. We report a new elastic instability in the flow of a viscoelastic shear-thinning fluid past a microcylinder that blocks 50% of the channel width. The instability causes wall-attached, and cylinder-attached vortices to form upstream of the cylinder.