Propulsion generated by diffusion-driven flow

Abstract

Buoyancy-driven flow, which is flow driven by spatial variations in fluid density 1 , lies at the heart of a variety of physical processes, including mineral transport in rocks 2 , the melting of icebergs 3 and the migration of tectonic plates 4 . Here we show that buoyancy-driven flows can also generate propulsion. Specifically, we find that when a neutrally buoyant wedgeshaped object floats in a density-stratified fluid, the diffusiondriven flow at its sloping boundaries generated by molecular diffusion produces a macroscopic sideways thrust. Computer simulations reveal that thrust results from diffusion-driven flow creating a region of low pressure at the front, relative to the rear of an object. This discovery has implications for transport processes in regions of varying fluid density, such as marine snow aggregation at ocean pycnoclines 5 , and wherever there is a temperature difference between immersed objects and the surrounding fluid, such as particles in volcanic clouds 6 .A fluid system with spatially varying density, resulting from temperature and/or salinity variations, for example, is stably-stratified when increasing density is parallel to the direction of gravity. When an object is released in a quiescent, stably-stratified fluid, it is expected to settle or rise to the neutral buoyancy level at which the density of the object matches that of the surrounding fluid, and remain stationary thereafter. We carried out a control experiment in which a 19.05-mm-diameter sphere of density ρ = 1,115 kg m −3 was released in a tank of height H = 0.40 m, width W = 0.20 m and length L = 0.40 m, filled with salt-stratified water with density gradient dρ/dz = −511 ± 3 kg m −4 . As expected, the sphere settled to its neutral buoyancy height, where it remained stationary for 24 hours. A similar experiment was then carried out using a triangular wedge ( Fig. 1) of length l = 99.9 ± 0.1 mm, base h = 17.6 ± 0.10 mm (corresponding to slope angle α = 5.0 ± 0.1 • ) and width w = 25.1 ± 0.10 mm. In striking contrast to the stationary sphere, the wedge moved at a constant speed u = 10.2 ± 0.1 × 10 −3 m h −1 (2.83 ± 0.03 × 10 −6 m s −1 ) in the direction of its tip, without any obvious cause ( Fig. 1 and its top inset; also see Supplementary Movie S1).To investigate the cause of this spontaneous propulsion, we visualized the velocity fields in the horizontal and vertical midplanes of the moving wedge using particle image velocimetry (PIV; Fig. 2). Here, z is the vertical coordinate antiparallel to gravity and x and y are the coordinates in the horizontal plane, parallel and perpendicular to the long axis of the wedge, respectively. These experiments reveal that fluid is drawn in towards the wedge tip in the horizontal plane to supply up-slope flow in a thin boundary layer above the sloping surface. Furthermore, fluid immediately behind the wedge moves with the same speed as the wedge; this phenomenon, known as blocking, occurs for obstacles in stratified flow when buoyancy forces dominate inertia and viscous forces 1 . As ...

Diffusion-Induced Effects in a Stratified Fluid Around a Motionless Wedge

“…3, a). The principal mechanism of the phenomena lies in the pressure deficiency which is sufficient for description of the observed displacement of a body under conditions of laboratory experiment [10]. The minimum pressure values are fixed on the impermeable wall of the wedge (Fig.…”

“…The integral force action of convergent flows, absent in the symmetric obstacles (sphere, cylinder or horizontal plate), assumes a finite value on the inclined plate and other bodies, non-symmetrical with respect to the line of gravity. The resulting pressure gradients are large enough and capable of inducing self-motion of the neutral buoyancy free bodies («diffusion fish» in parlance of article [10,11]), which plays an important role in the dynamics of the hydrosphere. Calculation of steady flows on the flat fixed wedge is carried out in [12].…”

Self-Propulsion of Immersed Objects via Natural Convection

“…Despite almost a century of research [6], although there have been a few studies of the motion of objects floating on the surface of [7], or immersed within [8], flows driven by natural convection, studies of boundary-induced natural convection have been restricted to systems with fixed boundaries [9]. Recently it has been demonstrated that a related class of boundary-layer flow, driven by molecular diffusion, can propel objects immersed in a fluid [10], albeit very slowly. Boundary-layer flows generated via natural convection are typically orders of magnitude stronger than their diffusive counterpart, and therefore have the potential to generate substantially faster propulsion speeds.…”

Boundary layer dynamics and deep ocean mixing in Mid-Atlantic Ridge canyons

“…This gives a full boundary thickness δπ = 16 mm. This should be resolvable with careful use of PIV, as it is about 50% the thickness of the well-resolved velocity field in Allshouse et al [2010].…”