Fluids by design using chaotic surface waves to create a metafluid that is Newtonian, thermal, and entirely tunable

Abstract

In conventional fluids, viscosity depends on temperature according to a strict relationship. To change this relationship, one must change the molecular nature of the fluid. Here, we create a metafluid whose properties are derived not from the properties of molecules but rather from chaotic waves excited on the surface of vertically agitated water. By making direct rheological measurements of the flow properties of our metafluid, we show that it has independently tunable viscosity and temperature, a quality that no conventional fluid possesses. We go on to show that the metafluid obeys the Einstein relation, which relates many-body response (viscosity) to single-particle dynamics (diffusion) and is a fundamental result in equilibrium thermal systems. Thus, our metafluid is wholly consistent with equilibrium thermal physics, despite being markedly nonequilibrium. Taken together, our results demonstrate a type of material that retains equilibrium physics while simultaneously allowing for direct programmatic control over material properties.Faraday waves | metafluid | emergent thermodynamics M aterials science seeks not only to understand but also to control the properties of matter. To do so, one must dynamically change the nature of conventional materials at the molecular scale. Recent work circumvents this problem by rejecting the molecule as the fundamental unit and substituting a macroscopic structural element. This approach has successfully created metamaterials with novel optical (1-3), acoustic (4-6), mechanical (7-9), and fluid properties (10, 11) that would otherwise be impossible. However, this approach comes at a cost: by deriving their properties from macroscopic, nonequilibrium, or anisotropic elements, these materials necessarily abandon the physics of thermal systems. In this work, using a combination of active and passive rheology, we show that macroscopic chaotic surface waves on a vertically agitated fluid form a fully thermal metafluid with dynamically tunable material properties. In contrast to a conventional fluid in which viscosity and temperature are inextricably linked, we show that these quantities are independently tunable in our system. We further demonstrate that by satisfying the barest criteria of isotropy and steady-state chaos [as required by kinetic theory (12, 13)], we have created a system that obeys the Einstein relation (14). Thus, despite being macroscopic and nonequilibrium, the system is well described by equilibrium thermal physics.The "molecules" of our metafluid are chaotic Faraday waves (15, 16), generated in a water-filled aluminum dish that is vertically oscillated with rms amplitude A s and at frequency f s (Fig. 1 A and C; see Materials and Methods for technical details). The waves uniformly cover the surface of the water and experience significant pinning only at the boundary, far from where our measurements are conducted. The chaos and wave density is holistically steady state, although the existence of a particular wave is transient. Thus, "collisions" in our syste...

Tunable diffusion in wave-driven two-dimensional turbulence

“…It confirms the existence of a relation analogous to the Stokes-Einstein relation for low values of C corresponding to large floating objects. Similar relations have recently been studied in the Faraday wave system (Welch, Liebman-Pelaez & Corwin 2016). It would be interesting to see how they can be connected to other properties of the liquid-gas interface perturbed by waves (Domino et al 2016).…”

“…These two distinct behaviours are directly reflected by how the diffusion coefficient depends on both the object size and the flow kinetic energy. This finding opens ways of engineering a non-equilibrium liquid interface with tunable diffusion coefficient (Welch et al 2016;Francois et al 2017). In the case of a liquid surface perturbed by Faraday waves, our results offer methods to externally tune the diffusion coefficient of a floating object by changing the amplitude or the frequency of the vertical oscillation.…”

Wave-based liquid-interface metamaterials

“…Beyond these analogies, the scope of the recently introduced concept of a wave-driven metafluid 15 can be broadened to that of a wave-based liquid-interface metamaterial. As we show, by dynamically shaping a fluid interface using rotating waves, one can produce an effective 2D material endowed with prescribed transport properties.…”

“…This motion represents a macroscopic Brownian walk, where the diffusion of particles at the surface can be modified by changing the wave height and the wave length 14 . It has been shown that the properties of this interface are consistent with diffusion at thermal equilibrium, and as such, it can be viewed as a tunable thermal metafluid 15 .…”

Rectification of chaotic fluid motion in two-dimensional turbulence

“…The diffusion coefficient of the disk floater is 10 times lower than that measured using fluid tracers. It has been recently demonstrated that for large circular objects (size much greater than λ) drifting in the Faraday waves there exists a relation between the wave-driven diffusion and the drag coefficient [25], analogous to the fluctuation-dissipation theorem used in equilibrium statistical mechanics. However, there is ample evidence that wave-driven flows show many properties of twodimensional turbulence, a strongly out-of-equilibrium state [14][15][16].…”