# Upstream Wall Vortices - Soft Matter

The movies below accompany the Supplementary Information section of our paper entitled "Upstream Wall Vortices in Viscoelastic Flow Past a Cylinder", Soft Matter, 2022 — Currently under revisions. Link when available.

The movies illustrate the time-dependent velocity fields for the flow of the wormlike micellar solution past the microcylinder at the Weissernberg numbers Wi = Uλ/R, where U is the average flow speed, λ is the terminal relaxation time of the fluid, and R = 102 μm is the radius of the cylinder. For reference, Wi_{c1} is the critical Wi for the onset of the upstream bending streamline instability, Wi_{c2} is the critical Wi for the formation of upstream wall-attached vortices, Wi_{c2} is the critical Wi for the onset of time dependence, and Wi_{c4} is the critical Wi for the significant growth of the upstream cylinder vortex.

**Movie S1** — Particle images and calculated velocity field at Wi_{c1} < Wi = 38 < Wi_{c2}, at the z = 0 plane, the same case as shown in Fig. 3 (b) in the main text. This is a time-steady flow within the regime where there are bending streamlines upstream of the cylinder but no wall vortices.

Movies S2-S5 are at the same Wi as shown in Fig. 7 in the main text. These videos show the time-dependent velocity fields along with the time series of the probe velocity \(|v_{p}/U|\), the middle position of the wall vortices χ, their widths \(\mathcal{W}\), and the length of the cylinder vortex \(\mathcal{L}\) (if present).

** Movie S2 **— Wi_{c2} < Wi = 90 < Wi_{c3} at the z = 0 plane. Time-steady with small wall vortices.

**Movie S3 **— Wi_{c3} < Wi = 148 < Wi_{c4} at the z = 0 plane. Time-dependent with small wall vortices at a Wi near the initial transition to time dependence.

**Movie S4 **— Wi_{c3} < Wi = 190 < Wi_{c4 }at the z = 0 plane. Time-dependent with asymmetric wall vortices at a higher Wi than in Movie S3.

**Movie S5 **— Wi = 507 > Wi_{c4} at the z = 0 plane. Time-dependent at a Wi within the cylinder vortex regime.

Movies S6-S8 show the time-dependent velocity fields recorded in the \(x-z\) plane at the positions \(y \approx \pm 1.8R\) to illustrate how the wall vortices are shaped and behave in the \(z\) direction. The movies correspond to the time-averaged velocity fields shown in Fig. S1 in the Supplementary Information. Note that the videos were not recorded coincidentally at a given Wi, so it is not possible to directly compare the shape of the vortices and time-dependent behaviour between the two planes in each video.

**Movie S6 **— Wi_{c2} < Wi = 97 < Wi_{c3} at the \(y \approx \pm 1.8R\) planes. Approximately time-steady small wall vortices.

**Movie S7 **— Wi_{c3} < Wi = 145 < Wi_{c4} at the \(y \approx \pm1.8R\) planes. Time-dependent asymmetric wall vortices.

**Movie S8 **— Wi_{c3} < Wi = 175 < Wi_{c4} at the \(y \approx \pm 1.8R\) planes. Time-dependent asymmetric wall vortices at slightly higher Wi than in Movie S7.