First published online October 31, 2008
Journal of Experimental Biology 211, 3563-3572 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.018010
Flexibility foils filter function: structural limitations on suspension feeding
Matthew C. Ferner* and
Brian Gaylord
Bodega Marine Laboratory and Section of Evolution and Ecology, University
of California at Davis, Bodega Bay, CA 94923, USA
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Fig. 1. Schematic of low Reynolds number tank used for visualizing flow-through
model filters. An array of four cylindrical filter elements, oriented
vertically, was fixed to a sled that was towed through viscous syrup using a
computer-controlled linear drive. This motion produced relative flow through
the model filter analogous to currents passing through feeding appendages of
suspension feeders. Overhead images of flow between filter elements were
collected with a camera focused on a thin light sheet projected through the
end of the tank. Longest dimension of the tank measured 1.25 m, for scale.
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Fig. 3. Side view of deflected filter arrays (L/d=100) showing
that streamwise bending reduced effective filter height to an extent that
depended on the elastic modulus of the filter elements. Models were towed at
different velocities to produce relative flow at approximate Re of
(A) 10–5, (B) 10–4 and (C)
10–3. Filter elements were anchored in a flat sled at the
fluid surface and extended vertically into the fluid when at rest. Plotted
positions represent an average of the bending trajectories of inner and outer
elements within each array, digitized from photographs (three replicate runs
per flow speed). Measured deflections and distances from the filter base were
normalized by the height, L, of a stationary array. Arrow indicates
direction of flow through filters.
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Fig. 4. Cross-stream width of flexible filter arrays (L/d=100)
decreased with distance from the base, illustrating filter narrowing due to
flow diversion around the models at approximate Re of (A)
10–5, (B) 10–4 and (C)
10–3. Measured array widths were normalized by the width of a
stationary array and distances from the filter base were normalized by the
height, L, of a stationary array.
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Fig. 5. Projected area of filter arrays (L/d=100) as a function
of Re. Decreased filter area at higher Re was due to a
combination of streamwise bending and cross-stream narrowing of flexible
arrays. Measured areas were normalized by the area of a stationary array.
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Fig. 6. Planar leakiness of slender-element filter arrays
(L/d=100) versus distance from their base at
approximate Re of 10–3 (solid circles),
10–4 (open circles) and 10–5 (solid
triangles). Data for filters of different materials are presented in order of
increasing flexibility from A to E. Instances where planar leakiness equals
zero indicate severe bending of the filter array that prevented filtration at
that height. Distances from the filter base were normalized by the height,
L, of a stationary array.
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Fig. 7. Renormalized planar leakiness (i.e. calculated relative to instantaneous
rather than idealized array width) versus distance from the base of
filter arrays (L/d=100) operating at approximate Re
of (A) 10–5, (B) 10–4, and (C)
10–3. Divergent trajectories evident in B and C illustrate
changes in leakiness that were independent of variation in array width.
Distances from the filter base were normalized by the height, L, of a
stationary array.
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Fig. 8. Planar leakiness of stout-element filter arrays (L/d=50)
versus distance from the base at approximate Re of
10–3 (solid circles), 10–4 (open circles)
and 10–5 (solid triangles). Data for filters of different
materials are presented in order of increasing flexibility from A to E. The
case where planar leakiness equaled zero in E indicates severe bending of the
filter array that prevented filtration at that height. Distances from the
filter base were normalized by the height, L, of a stationary
array.
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Fig. 9. Whole-model leakiness versus Re for arrays of filter elements
having an aspect ratio of (A) L/d=100 and (B)
L/d=50. The diverging pattern in A illustrates the
susceptibility of slender-element arrays to flexibility-related reductions in
leakiness, an effect that became more pronounced in faster flows. Consequences
of structural flexibility were reduced in stout-element arrays (B), but a
diverging pattern was still apparent in the highest Re condition.
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© The Company of Biologists Ltd 2008
177 GPa). Leakiness was calculated by dividing the
spatially integrated velocity profile across the width of the array (shaded
regions) by the product of undeformed array width and free-stream velocity
(bounding box). (E) Composite representation of fluid motion through a
flexible filter array (E