Fluid Mechanics of Ciliary Propulsion

On the role of copepod antennae in the production of hydrodynamic force during hopping

“…Although such low local Reynolds number might still differ from those characterizing cilia motion by orders of magnitude, the value is sufficiently low to place the problem well in the viscosity dominated regime. It is well known that the cilia regularly use wall, orientation and speed effects to produce thrust in the viscosity-dominated flow environment in which they operate (Blake, 2001) and we have now shown that the copepods do benefit from these effects.…”

“…The experimentally observed copepod antennae motion is strikingly similar to ciliary motion (Blake, 2001), including features such as asymmetric strokes, fast beat during power stoke and slower beat in the return stroke, metachronal strokes, etc. The similarity in kinematics suggests similar mechanisms of thrust production, which could at first appear surprising given the large difference in Reynolds numbers between copepod hopping and ciliary propulsion.…”

“…Beyond this point the antenna continues to unfold and swing forward (Fig.4D) until it reaches its fully open, horizontal initial position. The overall motion of the antenna during the return stroke, as emerges from the experimental observations, is reminiscent of the hand movement of a human performing a breaststroke as well as the kinematics of ciliary propulsion (Blake, 2001).…”

“…Consequently, propulsion in a low Re environment is only possible if the animal employs asymmetric strokes to break the symmetry of the Stokes regime and generate net thrust during each swimming cycle. Blake (Blake, 2001) discusses three possible symmetry-breaking effects in the context of ciliary propulsion that can be deployed by an animal to propel itself in a viscosity-dominated environment: (1) the speed effect, which refers to appendage motion with higher velocity during the power stroke than during the return stroke; (2) the orientation effect, which refers to an appendage that changes its orientation during the swimming cycle such that its largest frontal area is oriented perpendicular to the direction of motion during the power stroke (to maximize thrust) and tangential to the direction of motion On the role of copepod antennae in the production of hydrodynamic force during hopping Iman Borazjani 1 , Fotis Sotiropoulos 1, *, Edwin Malkiel 2 and Joseph Katz during the recovery stroke to minimize drag; and (3) the wall effect, which refers to possible symmetry-breaking effects due to the presence of a solid boundary in the vicinity of the animal appendages (Blake, 1974;Winet, 1973). For a copepod, all three effects could potentially become important.…”

Earliest ciliary swimming effects vertical transport of planktonic embryos in turbulence and shear flow

“…If a limited disruption of ciliary coupling (e.g. Brennan, 1975;Blake and Sleigh, 1975) allows swimmers to attain greater speeds in moderate shear, swimming enhancement should be limited to a range of shear determined by the mechanical properties of the cilia, their length and spacing, and the curvature of the ciliated surface. Shear should have significant effects on swimming speed in a range of ciliated and flagellated planktonic organisms if the mechanism of swimming enhancement acts at the level of ciliary or flagellar coordination, or predictably affects the function of individual organelles.…”