50 Years of Image Analysis

Cilia are hair-like organelles, present in arrays that collectively beat to generate flow. Given their small size and consequent low Reynolds numbers, asymmetric motions are necessary to create a net flow. Here, we developed an array of six soft robotic cilia, which are individually addressable, to both mimic nature's symmetry-breaking mechanisms and control asymmetries to study their influence on fluid propulsion. Our experimental tests are corroborated with fluid dynamics simulations, where we find a good agreement between both and show how the kymographs of the flow are related to the phase shift of the metachronal waves. Compared to synchronous beating, we report a 50% increase of net flow speed when cilia move in an antiplectic wave with phase shift of -π/3 and a decrease for symplectic waves. Furthermore, we observe the formation of traveling vortices in the direction of the wave when metachrony is applied.

https://advances.sciencemag.org/content/advances/6/49/eabd2508.full.pdf

Metachronal patterns in artificial cilia for low Reynolds number fluid propulsion

Flight speed is positively correlated with body size in animals1. However, miniature featherwing beetles can fly at speeds and accelerations of insects three times their size2. Here we show that this performance results from a reduced wing mass and a previously unknown type of wing-motion cycle. Our experiment combines three-dimensional reconstructions of morphology and kinematics in one of the smallest insects, the beetle Paratuposa placentis (body length 395 μm). The flapping bristled wings follow a pronounced figure-of-eight loop that consists of subperpendicular up and down strokes followed by claps at stroke reversals above and below the body. The elytra act as inertial brakes that prevent excessive body oscillation. Computational analyses suggest functional decomposition of the wingbeat cycle into two power half strokes, which produce a large upward force, and two down-dragging recovery half strokes. In contrast to heavier membranous wings, the motion of bristled wings of the same size requires little inertial power. Muscle mechanical power requirements thus remain positive throughout the wingbeat cycle, making elastic energy storage obsolete. These adaptations help to explain how extremely small insects have preserved good aerial performance during miniaturization, one of the factors of their evolutionary success. 

/pdf/novel-flight-style-and-light-wings-boost-flight-performance-2b84xa00.pdf

Novel flight style and light wings boost flight performance of tiny beetles

Negatively buoyant freely swimming crustaceans such as krill must generate downward momentum in order to maintain their position in the water column. These animals use a drag-based propulsion strategy, where pairs of closely spaced swimming limbs are oscillated rhythmically from the tail to head. Each pair is oscillated with a phase delay relative to the neighbouring pair, resulting in a metachronal wave travelling in the direction of animal motion. It remains unclear how oscillations of limbs in the horizontal plane can generate vertical momentum. Using particle image velocimetry measurements on a robotic model, we observed that metachronal paddling with non-zero phase lag created geometries of adjacent paddles that promote the formation of counter-rotating vortices. The interaction of these vortices resulted in generating large-scale angled downward jets. Increasing phase lag resulted in more vertical orientation of the jet, and phase lags in the range used by Antarctic krill produced the most total momentum. Synchronous paddling produced lower total momentum when compared with metachronal paddling. Lowering Reynolds number by an order of magnitude below the range of adult krill (250-1000) showed diminished downward propagation of the jet and lower vertical momentum. Our findings show that metachronal paddling is capable of producing flows that can generate both lift (vertical) and thrust (horizontal) forces needed for fast forward swimming and hovering.

/pdf/hydrodynamics-of-metachronal-paddling-effects-of-varying-4klbpeullp.pdf

Hydrodynamics of metachronal paddling: effects of varying Reynolds number and phase lag.

Aerodynamic force generation capacity of the wing of a miniature beetle Paratuposa placentis is evaluated using a combined experimental and numerical approach. The wing has a peculiar shape reminiscent of a bird feather, often found in the smallest insects. Aerodynamic force coefficients are determined from a dynamically scaled force measurement experiment with rotating bristled and membrane wing models in a glycerin tank. Subsequently, they are used as numerical validation data for computational fluid dynamics simulations using an adaptive Navier–Stokes solver. The latter provides access to important flow properties such as leakiness and permeability. It is found that, in the considered biologically relevant regimes, the bristled wing functions as a less than 
$$50\%$$

 leaky paddle, and it produces between 66 and 
$$96\%$$

 of the aerodynamic drag force of an equivalent membrane wing. The discrepancy increases with increasing Reynolds number. It is shown that about half of the aerodynamic normal force exerted on a bristled wing is due to viscous shear stress. The paddling effectiveness factor is proposed as a measure of aerodynamic efficiency.

/pdf/aerodynamic-performance-of-a-bristled-wing-of-a-very-small-23tr0iswna.pdf

Aerodynamic performance of a bristled wing of a very small insect

In contrast to larger flight-capable insects such as hawk moths and fruit flies, miniature flying insects such as thrips show the obligatory use of wing–wing interaction via “clap and fling” during the end of upstroke and start of downstroke. Although fling can augment lift generated during flapping flight at chord-based Reynolds number (Re) of 10 or lower, large drag forces are necessary to clap and fling the wings. In this context, bristles observed in the wings of most tiny insects have been shown to lower drag force generated in clap and fling. However, the fluid dynamic mechanism underlying drag reduction by bristled wings and the impact of bristles on lift generated via clap and fling remain unclear. We used a dynamically scaled robotic model to examine the forces and flow structures generated during clap and fling of: three bristled wing pairs with varying inter-bristle spacing, and a geometrically equivalent solid wing pair. In contrast to the solid wing pair, reverse flow through the gaps between the bristles was observed throughout clap and fling, resulting in: (a) drag reduction; and (b) weaker and diffuse leading edge vortices that lowered lift. Shear layers were formed around the bristles when interacting bristled wing pairs underwent clap and fling motion. These shear layers lowered leakiness of flow through the bristles and minimized loss of lift in bristled wings. Compared to the solid wing, peak drag coefficients were reduced by 50–90% in bristled wings. In contrast, peak lift coefficients of bristled wings were only reduced by 35–60% from those of the solid wing. Our results suggest that the bristled wings can provide unique aerodynamic benefits via increasing lift to drag ratio during clap and fling for Re between 5 and 15.

Leaky Flow through Simplified Physical Models of Bristled Wings of Tiny Insects during Clap and Fling

The smallest flying insects with body lengths under 2 mm show a marked preference for wings consisting of a thin membrane with long bristles, and the use of clap and fling kinematics to augment lift at Reynolds numbers (Re) of approximately 10. Bristled wings have been shown to reduce drag forces in clap and fling, but the aerodynamic roles of several bristled wing geometric variables remain unclear. This study examines the effects of varying the ratio of membrane area (A M) to total wing area (A T) on aerodynamic forces and flow structures generated during clap and fling at Re on the order of 10. We also examine the aerodynamic consequences of scaling bristled wings to Re  =  120, relevant to flight of fruit flies. We analyzed published forewing images of 25 species of thrips (Thysanoptera) and found that A M/A T ranged from 14% to 27%, as compared to 11% to 88% previously reported for smaller-sized fairyflies (Hymenoptera). These data were used to develop physical bristled wing models with A M/A T ranging from 15% to 100%, which were tested in a dynamically scaled robotic clap and fling model. At all Re, bristled wings produced slightly lower lift coefficients (C L) when compared to solid wings, but provided significant drag reduction. At Re  =  10, largest values of peak lift over peak drag ratios were generated by wing models with A M/A T similar to thrips forewings (15% to 30%). Circulation of the leading edge vortex and trailing edge vortex decreased with decreasing A M/A T during clap and fling at Re  =  10. Decreased chordwise circulation near the wing tip, vortex shedding, and interaction between flow structures from clap with those from fling resulted in lowering C L generated via clap and fling at Re  =  120 as compared to Re  =  10. Clap and fling becomes less beneficial at Re  =  120, regardless of the drag reduction provided by bristled wings.

Aerodynamic effects of varying solid surface area of bristled wings performing clap and fling.

Metachronal paddling is a common method of drag-based aquatic propulsion, in which a series of swimming appendages are oscillated, with the motion of each appendage phase-shifted relative to the neighboring appendages. Ecologically and economically important Euphausiid species such as Antarctic krill (E. superba) swim constantly in the pelagic zone by stroking their paddling appendages (pleopods), with locomotion accounting for the bulk of their metabolic expenditure. They tailor their metachronal swimming gaits for behavioral and energetic needs by changing pleopod kinematics. The functional importance of inter-pleopod phase lag (ϕ) to metachronal swimming performance and wake structure is unknown. To examine this relation, we developed a geometrically and dynamically scaled robot ('krillbot') capable of self-propulsion. Krillbot pleopods were prescribed to mimic published kinematics of fast-forward swimming (FFW) and hovering (HOV) gaits of E. superba, and the Reynolds number and Strouhal number of the krillbot matched well with those calculated for freely-swimming E. superba. In addition to examining published kinematics with uneven ϕ between pleopod pairs, we modified E. superba kinematics to uniformly vary ϕ from 0% to 50% of the cycle. Swimming speed and thrust were largest for FFW with ϕ between 15%-25%, coincident with ϕ range observed in FFW gait of E. superba. In contrast to synchronous rowing (ϕ=0%) where distances between hinged joints of adjacent pleopods were nearly constant throughout the cycle, metachronal rowing (ϕ>0%) brought adjacent pleopods closer together and moved them farther apart. This factor minimized body position fluctuation and augmented metachronal swimming speed. Though swimming speed was lowest for HOV, a ventrally angled downward jet was generated that can assist with weight support during feeding. In summary, our findings show that inter-appendage phase lag can drastically alter both metachronal swimming speed and the large-scale wake structure.

/pdf/on-the-role-of-phase-lag-in-multi-appendage-metachronal-1uh7j4cgkt.pdf

On the role of phase lag in multi-appendage metachronal swimming of euphausiids.

Numerous species of aquatic invertebrates, including crustaceans, swim by oscillating multiple closely spaced appendages. The coordinated, out-of-phase motion of these appendages, known as "metachronal paddling", has been well-established to improve swimming performance relative to synchronous paddling. Invertebrates employing this propulsion strategy cover a wide range of body sizes and shapes, but the ratio of appendage spacing (G) to the appendage length (L) has been reported to lie in a comparatively narrow range of 0.2 < G/L ≤ 0.65. The functional role of G/L on metachronal swimming performance is unknown. We hypothesized that for a given Reynolds number and stroke amplitude, hydrodynamic interactions promoted by metachronal stroke kinematics with small G/L can increase forward swimming speed. We used a dynamically scaled self-propelling robot to comparatively examine swimming performance and wake development of metachronal and synchronous paddling under varying G/L, phase lag, and stroke amplitude. G/L was varied from 0.4 to 1.5, with the expectation that when G/L is large, there should be no performance difference between metachronal and synchronous paddling due to a lack of interaction between vortices that form on the appendages. Metachronal stroking at non-zero phase lag with G/L in the biological range produced faster swimming speeds than synchronous stroking. As G/L increased and as stroke amplitude decreased, the influence of phase lag on the swimming speed of the robot was reduced. For smaller G/L, vortex interactions between adjacent appendages generated a horizontally-oriented wake and increased momentum fluxes relative to larger G/L, which contributed to increasing swimming speed. We find that while metachronal motion augments swimming performance for closely spaced appendages (G/L < 1), moderately spaced appendages (1.0 ≤ G/L ≤ 1.5) can benefit from metachronal motion only when the stroke amplitude is large.

Mitchell Ford

Papers

Leaky Flow through Simplified Physical Models of Bristled Wings of Tiny Insects during Clap and Fling

Hydrodynamics of metachronal paddling: effects of varying Reynolds number and phase lag.

Aerodynamic effects of varying solid surface area of bristled wings performing clap and fling.

On the role of phase lag in multi-appendage metachronal swimming of euphausiids.

Closer appendage spacing augments metachronal swimming speed by promoting tip vortex interactions.