Viscous deluge

Leonardo da Vinci often comes up in conversations about interdisciplinarity, particularly between art and science. The surviving works of this quintessential “Renaissance Man” serve to remind us how these fields were not always treated as separate, if not opposing, entities. In this spirit, da Vinci became the focus of an open call for the APS 2024 Traveling Gallery of Fluid Motion, hosted at The Leonardo, a science museum in Salt Lake City, UT.

Da Vinci’s studies of fluids typically focused on watery, high-Reynolds-number flows, which are typically fast-moving and prone to turbulence. His observations describe a world strongly divided by the dynamic surface of water: above, solid, knowable, and shapable; below, fluid, elusive, and challenging to predict [1, 2]. Da Vinci appears to have seen the world in terms of contrast and delineation, a sensibility aligned with Renaissance aesthetics.

My lab colleagues and I wondered how we might contribute to the call. Our research group’s work, by contrast, explores fluids at the opposite limit: slow, viscous fluids that rarely become turbulent. We tend to study the blurry regions between liquid and solid, where certain fluidic behaviors, such as the shape of an interface or mechanism for pattern formation, can be described by the same physics that governs soft or slender elastic solids.

When illustrating fluid flows, da Vinci often drew analogies between fluidic lines and hair. He drew turbulent flows as braids and curly tendrils, or vice versa, noting the resemblance in his notebooks. Late in life, he returned obsessively to these dynamics in a series of "deluge" drawings that depict roiling visions of water and wind consuming human-altered landscapes [3]. Among a lifetime of fragments and unfinished ideas, these stand out for their completeness. For someone with so many beginnings, the Deluges appear to offer an ending where fluidity and chaos play the final hand over form.

We began our work by reexamining his hair-water analogy and how, in physical terms, he may have gotten it wrong. While da Vinci was observing turbulent flows, a closer physical resemblance between fluids and hair appears in the opposite regime. When hair-like, viscous threads are extruded onto a moving surface, they can form regular meanders, loops, and coils [4]. Here, viscosity plays a role akin to elasticity in hair [4]. So the analogy holds, but only under the conditions da Vinci and many of his peers largely ignored.

In Renaissance thought, the viscous was associated with the monstrous, the impure, and the undifferentiated [5]. It had the dual capacity to flow and also resist flowing. It was material with its own ideas, so to speak. Through disegno, Renaissance aesthetics privileged contrast, clarity, and ideal form: an intellectual ordering of the world through line, ideas, and spirit that presided over matter and bodies. The viscous didn’t fit in this construction. Neither alive nor truly inert, it melted, oozed, morphed, and protested control, blurring distinctions rather than reifying them.

Binarized structures that separate idea from thing can be traced from antiquity to the present. Here, we tried to invoke the viscous to complicate and perhaps repair them. Our approach was by convolution: mixing, blurring, and inverting values so that boundaries between liquid and solid, order and chaos, matter and mimesis might be destabilized. What was small and controlled in da Vinci’s hand becomes large and materially determined in ours: a kind of collaboration between the physics at play and our intentions, also at play.

References

1. Institute for Advanced Study Leonardo’s Watery Chaos
2. Geddes, L. A. (2020). Watermarks: Leonardo Da Vinci and the Mastery of Nature. United Kingdom: Princeton University Press.
3. Didi-Huberman, Georges. “The order of material: Plasticities, malaises, survivals” (1999) in Materiality (2015). United Kingdom: Whitechapel Gallery.
4. Brun, P. T., Audoly, B., Ribe, N. M., Eaves, T. S., & Lister, J. R. (2015). Liquid ropes: a geometrical model for thin viscous jet instabilities. Physical review letters, 114(17), 174501.
5. Jawed, M. K., Da, F., Joo, J., Grinspun, E., & Reis, P. M. (2014). Coiling of elastic rods on rigid substrates. Proceedings of the National Academy of Sciences, 111(41), 14663-14668.

A large work: Rope piece (deluge)

An interesting (and sometimes futile) challenge when working with coiling, and soft materials more generally, is length scale. With coiling, the largest coiling radius we can easily produce from a ~1mm nozzle is on the same order of magnitude, i.e. a few millimeters.

Driving up the coiling radius requires a more and more viscous fluid, to the point where the fluid is essentially a solid. Drawing on the physical similarities in viscous threads and elastic rods [5], we decided to work with elastic rods rather than fluids in the large piece.

The project then primarily became an engineering feat, where we tested various approaches to creating large-scale coils. One such idea was to build a coaxial extruder that deposited a solid rope coated with a layer of silicone gel. It worked in principle, but to achieve the scale we needed within the allotted time, we ultimately decided to place silicone rods on the fabric by hand, which were later secured by a layer of poured liquid silicone. Some of the rods (white with a foam core) we purchased were pre-made for use as sealing gaskets. Others we made ourselves in the lab (glow-in-the-dark).

The design was inspired by da Vinci’s deluge drawings, where we traced paths over his linework and then generated coiling patterns to follow those paths using the three coupled ODEs from Brun, et al [4]. Varying velocity parameters allow us to select different modes, which transition from straight lines to dense coils.

The piece is named after one of sculptor Eva Hesse's final works.

Smaller works

We also worked at the desktop scale, making coils by extruding yield-stress silicone onto fabric. We control the nozzle path, while the coils, meanders, and loop patterns emerge naturally from the mismatch between extrusion and travel speeds. Many thanks to the Davidson Research Group for allowing us to use their Aerotech gantry system for numerical control of the extruder path.

Deluge 2

Silicone, pigment, organza. 22” x 19.5”

Deluge 3

Silicone, pigment, organza, acrylic, birch plywood. 22” x 19.5”.

Here we used a combination of machine-controlled and hand-controlled paths. The thick, glowing coils were made on the Aerotech system. The thin, lace-like white loops were made with a pressure-controlled syringe and traced by hand.

Development

For more images from our development phases, including our adventures with coiling wax and coaxial-extruded ropes, see the page below: