# Viscous Thread Falling on a Spinning Surface

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

## 3. Experimental Results

## 4. Comparison with FMSM

## 5. Concluding Remarks

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FMSM | Fluid-mechanical sewing machine |

## References and Note

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**Figure 1.**Photograph of the experimental system. The rotating table is connected to a motor by a yellow rubber band. Constant flux of silicon oil was maintained by the syringe pump on the left. The metal rail over the table allowed the nozzle to be moved radially.

**Figure 2.**Comparison of patterns obtained at different radial distances (

**a**,

**c**) and thus different velocities $\widehat{V}=\widehat{\omega}\phantom{\rule{0.166667em}{0ex}}\widehat{R}$ (

**b**,

**d**) for a selection of angular speeds $\widehat{\omega}$ for two similar heights of $\widehat{H}=0.9$ (

**a**,

**b**) and $\widehat{H}=1.1$ (

**c**,

**d**) for a constant flow rate $\widehat{Q}=0.40$. Shaded areas show the standard deviation of the measured angular velocity.

**Figure 3.**Phase diagram of patterns obtained at different radial distances (

**a**) and different velocities (

**b**) for a selection of angular speeds $\widehat{\omega}$ for the height $\widehat{H}=1.4$ at the higher flow rate $\widehat{Q}=0.60$. Shaded areas show the standard deviation of the measured angular velocity.

**Figure 4.**Some examples of stitch patterns of the spinning FMSM observed in a single experimental run with $\widehat{H}=1.7$, $\widehat{\omega}=2.20\pm 0.05$, and $\widehat{Q}=0.40$. Radial spokes are drawn every 10${}^{\circ}$, while concentric circles are drawn at a radial distance of 0.5 cm from each other. See Figure 5 for details of radii $\widehat{R}$ and velocities $\widehat{V}$ at which these patterns were obtained.

**Figure 5.**Comparison of patterns obtained at different radial distances (

**a**) or velocities $\widehat{V}$ (

**b**) for a nozzle positioned at $\widehat{H}=1.7$ at a fixed angular velocity $\widehat{\omega}=2.2$ and two different flow rates.

**Figure 6.**Geometric details of alternating loops patterns within a single experiment with $\widehat{H}=1.1$, $\widehat{\omega}=1.33\pm 0.08$, and $\widehat{Q}=0.40$. (

**a**,

**b**) At closer distances from the axis, “outward looping” coils are seen, which means that the angular velocity of the coiling stream (indicated by blue arrows) is of the same sign as the angular velocity of the spinning table (black arrow). (

**c**) Further away from the center, the direction of local rotation of the coiling stream reverses.

**Figure 7.**Novel FMSM stitch patterns observed in spinning table experiments. We call the pattern (

**a**) two-by-one, since each two inward loops are succeeded by an outward loop. It was observed for $\widehat{H}=0.89$, $\widehat{\omega}=1.42\pm 0.03$, and $\widehat{Q}=0.40$. The pattern (

**b**), seen here for $\widehat{H}=1.1$, $\widehat{\omega}=1.92\pm 0.10$, and $\widehat{Q}=0.40$, is the analogue of alternating loops in the linear case but its details are affected by centrifugal effects.

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**MDPI and ACS Style**

Lisicki, M.; Adamowicz, Ł.; Herczyński, A.; Moffatt, H.K.
Viscous Thread Falling on a Spinning Surface. *Symmetry* **2022**, *14*, 1550.
https://doi.org/10.3390/sym14081550

**AMA Style**

Lisicki M, Adamowicz Ł, Herczyński A, Moffatt HK.
Viscous Thread Falling on a Spinning Surface. *Symmetry*. 2022; 14(8):1550.
https://doi.org/10.3390/sym14081550

**Chicago/Turabian Style**

Lisicki, Maciej, Łukasz Adamowicz, Andrzej Herczyński, and Henry Keith Moffatt.
2022. "Viscous Thread Falling on a Spinning Surface" *Symmetry* 14, no. 8: 1550.
https://doi.org/10.3390/sym14081550