Surface Tension Transport of Prey by Feeding Shorebirds: The Capillary Ratchet

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Original entry: Tony Orth, APPHY 226, Spring 2009

By M. Prakash, D. Quere, J.W.M. Bush, Science (2008) vol.320 p.931

Abstract from paper

"The variability of bird beak morphology reflects diverse foraging strategies. One such feeding mechanism in shorebirds involves surface tension–induced transport of prey in millimetric droplets: By repeatedly opening and closing its beak in a tweezering motion, the bird moves the drop from the tip of its beak to its mouth in a stepwise ratcheting fashion. We have analyzed the subtle physical mechanism responsible for drop transport and demonstrated experimentally that the beak geometry and the dynamics of tweezering may be tuned to optimize transport efficiency. We also highlight the critical dependence of the capillary ratchet on the beak's wetting properties, thus making clear the vulnerability of capillary feeders to surface pollutants."

Capillarity Phenomena

Figure 1: A shore bird feeding via capillarity. Its beak oscillates at a few hertz, thereby driving the drop caught between its beak up towards its mouth.

This paper investigates the use of capillary forces by shorebirds to drive water droplets up their beaks against gravity. A first approximation to this behaviour was replicated in the laboratory by wetting a stainless steel wedge with silicon oil (which fully wets the mechanical beak). As was first observed by Hauksbee in 1712 (! - Philos. Trans 27, 395), the drop of oil is spontaneously driven towards the vertex of the wedge. This is a result of the pressure difference between the two ends of the capillary bridge created by the water droplet in the beak. The air pressure on the open end of the beak is lower than the pressure in the drop; there is a pressure drop across the opposite water-air interface which overcompensates for the first pressure difference (because the interface closer to the vertex of the wedge is more curved than the interface on the open side). A net pressure therefore drives the droplet up the wedge.

Figure 2: (A) Schematic of the experiment using a mechanical beak (ie. a stainless steel wedge) with a drop of partially wetting fluid in between the wedge. (B) Motion of the leading and trailing edges of the drop in the mechanical beak. <math>\alpha</math> is the opening angle of the wedge.

In the true-to-life case, however, water does not fully wet the bird's bill: there is contact angle hysteresis, which impedes the spontaneous motion of the drop up the beak. This is the reason for the "tweezering motion" observed in shore birds. The drop is "pumped" up the bill via capillary forces arising from the difference in advancing and receding contact angles. To simulate this circumstance, a drop of water is inserted into the mechanical beak on which it has a contact angle hysteresis of <math>45^o</math> (advancing contact angle: <math>20^o</math>, receding: <math>65^o</math>). The wedge is made to oscillate at a nominal frequency <math>\omega</math>. The drop is seen to "ratchet" up the beak towards the apex of the wedge is a slip-like motion. When the wedge is being closed, both the ends of the drop spread, but the edge closer to the apex begins to move before the opposite edge and it moves farther. The opposite is true when the wedge is being opened (ie. The "trailing edge" moves up the beak first and further than the "leading edge".) The result is net movement of the drop up the beak. Unfortunately, there is no more quantitative investigation beyond the graph shown in figure 2.

Figure 3. Different capillary driving regimes determined by the opening angle <math>\alpha</math>. The most efficient shore birds can pump up a drop into their mouths in this fashion in as few as 3 oscillations of the beak (circled number "3").

It is important to note that the capillary force which overcomes gravity and ultimately propels the bird's food into its mouth is <math>F_{p} = \gamma W \delta cos(\theta)</math> and it is therefor no surprise that there needs to be a moderate surface tension for this feeding method to work. Pollution in the form of oily contaminants to these birds' habitat could have the rather non-obvious effect of preventing them from feeding by lowering the surface tension of the water.