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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
Bodega Marine Laboratory and Section of Evolution and Ecology, University of California at Davis, Bodega Bay, CA 94923, USA
* Author for correspondence (e-mail: mcferner{at}ucdavis.edu)
Accepted 15 September 2008
 |
Summary |
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 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Key words: functional morphology, structural flexibility, elastic modulus, filtration, leakiness, low Reynolds number, cylindrical arrays, biomechanics
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INTRODUCTION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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).
Recognizing their ecological significance, numerous researchers have examined
flow effects on particle capture by these animals (e.g.
Koehl and Strickler, 1981;
Leonard et al., 1988;
Hunter, 1989;
Patterson, 1991;
Lacoursière and Craig,
1993; Larsson and Jonsson,
2006) (reviewed by Wildish and
Kristmanson, 1997). The traditional point of departure for
understanding the mechanics of particle capture has been hydrosol filtration
theory, commonly applied to idealized collector arrays composed of perfectly
rigid cylinders (Rubenstein and Koehl,
1977; LaBarbera,
1984; Shimeta and Jumars,
1991). A key index emerging from this conceptualization is
`leakiness', a measure of filter efficacy quantified as the proportion of
water passing through an externally held feeding array, relative to the flow
impinging on it (Cheer and Koehl,
1987). Based on many studies (e.g.
Hansen and Tiselius, 1992;
Loudon et al., 1994;
Koehl, 1995;
Mead and Koehl, 2000), much is
now known about how leakiness varies as a function of geometry and collector
Reynolds number (Re=Ud
/µ; a measure of the relative
importance of inertial and viscous forces in a flow past a collector, where
U is an appropriate velocity scale, d is the collector
diameter, is the density and µ is the dynamic viscosity).
Despite these advances, notable gaps remain in understanding even the most
basic features of suspension feeding. One important omission has been a
systematic appreciation for the consequences of deformation. The structural
flexibility of appendages of real animals enables them to deflect in flow,
creating deviations from the idealized case. For example, filter bending can
reduce imposed forces and expand the range of flow conditions under which
feeding is possible (Patterson,
1984; Harvell and LaBarbera,
1985; Sponaugle and LaBarbera,
1991). Deflection can also have negative effects because the area
of a filter array facing flow is diminished by bending.
To begin to isolate the consequences of structural flexibility for filter
function, we examined leakiness through simple but deformable physical models
composed of multiple cylindrical elements. These artificial filters extended
away from a solid surface, mimicking the situation faced by animals that hold
filter arrays away from the substratum or from their own support structures.
Because we wanted to distinguish effects of filter bending from other factors,
we focused on relatively low cylinder Re (
10–5
to 10–3, with U set equal to the free-stream
velocity outside local boundary layers adjacent to animal bodies or the
seafloor). Reynolds numbers of suspension feeders extend across a much broader
range (<10–6 to >10)
(Vogel, 1994), but the higher
end of this range is characterized by leakiness values that depend strongly on
hydrodynamic processes that interact with other factors
(Koehl, 1995;
Loudon and Koehl, 2000). Our
results, derived for the more easily interpreted range of lower Re
conditions, indicate clearly that the bending of feeding appendages can
strongly influence filter leakiness and the capacity for particle capture.
Effects of collector deflection at low Re may apply to a variety of
suspension-feeding animals that experience flows as slow as 0.1 mm
s–1 and possess small filtering structures (0.1–10
µm diameter), including flagellated protozoans, cladocerans, bryozoans and
serpulid polychaetes, among others (e.g.
Turner et al., 1988;
Scardino et al., 2008).
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MATERIALS AND METHODS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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;
Leonard, 1992), and
incorporating model materials of a range of flexibilities
(Table 1). We then considered
ensuing filter deformations within the following generalized framework. Taking
as a starting point the simplified case of flow past a single, perfectly rigid
cylinder far from a solid surface, there are five variables that influence the
magnitude of force (F) imposed on the cylinder. These variables are
, U, µ, d and the length of the cylinder,
L. This suite of parameters can be combined using techniques of
dimensional analysis (e.g. Fox and
MacDonald, 1985) to produce the relationship:
 | (1) |
, U, µ and the distance, x, of the attachment
point of the cylinder from the upstream edge of the surface
(Schlichting, 1979). This
situation creates a positional effect defined by the parameter
x/d, leading to the equality:
 | (2) |
/L, which quantifies the lateral deflection of the
cylinder's tip () relative to its length. A dimensional analysis of the
bending process, coupled with Eqns
1 and
2, leads to the expression:
 | (3) |
U2) (henceforth = B).
B is the nondimensional stiffness, equal to the modulus (E)
divided by twice the dynamic pressure of the flow
(Fox and MacDonald, 1985).
|
In more complex geometries beyond solitary cylinders, including multiple
cylinders in arrays, additional dimensionless parameters become important.
They include the ratio of gap width between cylinders to cylinder diameter,
the ratio of the width of a multiple-cylinder array to cylinder diameter, and
(in the case of laboratory experiments) ratios of tank or other apparatus
dimensions to cylinder diameter. In situations where cylinders protrude from
rough surfaces into turbulent regions of benthic boundary layers, two further
parameters arise (the ratio of roughness height to cylinder diameter, and
another Reynolds number based on U*, the so-called
`friction velocity') (Eckman and Nowell,
1984).
We focused on a subset of the full parameter space spanned by the governing
variables identified above. For each of three values of collector Re
between approximately 10–5 and 10–3, we
tested cylinder aspect ratios, L/d, of 50 and 100. Given the
dimensional analysis described above, the use of Reynolds numbers based on
free-stream velocities, rather than `face velocities' incident on the filter
array, simplified the approach. However, we acknowledge that this convention
[also used by other researchers (e.g. Cheer
and Koehl, 1987)] interferes in some circumstances with easy
interpretation. Values of E have not been measured for intact
suspension-feeding appendages, yet natural polymer composites that make up
these structures have elastic moduli on the order of 0.1–100 GPa
(Wegst and Ashby, 2004). In
aquatic environments characterized by relative velocities of
10–4–1 m s–1, it follows that actual
values of B range from approximately 105 to
1016 for most suspension feeders, but we restricted experiments to
the upper end of this range to avoid a disproportionate emphasis on
consequences of extreme bending. We held the parameter x/d
constant in all experiments. We considered only one ratio of gap width to
cylinder diameter, one ratio of array width to cylinder diameter, and single
ratios of apparatus dimensions to cylinder diameter. These restrictions
obviously limit our ability to generalize across the full breadth of
conditions occurring in nature, so we focused on phenomena that are likely to
be general across a wide choice of cylinder arrays, emphasizing qualitative
results that ensued from the quantitative measures we undertook using specific
filter sizes and geometries.
|
), filter
structures inherently operate in close proximity to other solid surfaces (e.g.
bodies, neighbors or substratum) and our intention was to compare filter
performance in the context of biologically reasonable geometries. Dynamic
viscosity of the syrup was measured with a digital viscometer (Brookfield
Engineering Labs, Model HBDV-E, Middleboro, MA, USA) and density was
calculated by weighing a known volume. The syrup was thoroughly mixed 10 days
prior to experiments so that large entrained air bubbles, which would have
interfered with model visualization, had time to float to the surface and be
removed. A nearly uniform suspension of small bubbles [mean (± s.d.)
diameter=123 (±33) µm; N=100] remained trapped in the
syrup, rising only exceptionally slowly (<2 mm day–1) and
thereby serving as tracer particles for flow visualization (see Filter
leakiness, below).
Model filter arrays
Scale models of organism filter arrays were constructed using four parallel
and vertically oriented, cylindrical rods spaced evenly in a row perpendicular
to the direction of motion. Cylinders were inserted into predrilled holes in
the central region of a transparent acrylic sled (230 mm long, 160 mm wide, 5
mm thick) that rested on the fluid surface. The longest axis of the sled was
aligned with the direction of motion, and the leading and trailing edges of
the sled were curved upward to facilitate travel across the fluid surface.
Filter arrays were centered on the sled at a distance of 56 mm (35
cylinder diameters) from the leading edge, and all cylinders had a diameter
(d) of 1.59 mm. The cylinders extended either 159 or 79.5 mm into the
flow (referred to as `slender' and `stout' arrays, respectively, where
L is cylinder length). The gap between adjacent cylinder edges was
7.95 mm (5d), yielding a total array width of 30.2 mm (19d)
for all filters.
Each array contained cylinders composed of one of the following materials:
stainless steel (type 316), brass (alloy 260), Garolite-G10 (glass-cloth
laminate plastic), Garolite-XX (paper-based laminate plastic), or nylon (6/6).
Materials were selected to represent the natural range of structural
flexibility found in materials composing biological fibers, hairs and setae of
real animals (Wegst and Ashby,
2004). The elastic modulus (E) of each model material was
measured using three-point bending tests conducted on an Instron materials
testing device (Model 3345, Norwood, MA, USA).
Filter deformation
Relative fluid motion through and around the filter arrays was generated by
towing the model filters through the syrup using a micro-stepping motor
(Oriental Motor Company, Model RK564AA, Torrance, CA, USA) driven by
motion-control software (National Instruments, NI-Motion v.1.2). Filters were
towed at each of three velocities (U=0.3, 3.0, or 30 mm
s–1). After filter elements reached a steady state, the
filters were photographed through the walls of the tank using a 35 mm camera
(Nikon D70s, 60 mm lens). The spatial coordinates of each filter array (in
both side and end views) were recorded under conditions of no motion and at
all tow velocities, in order to determine the extent of streamwise bending of
the array, lateral compression or narrowing of the array, and the resultant
projected filter area as viewed from directly upstream.
Filter leakiness
Fluid motion between individual filter elements was measured by quantifying
displacements of suspended tracer particles relative to the filter over time,
a technique known as particle tracking velocimetry. Overhead images were
collected by mounting the 35 mm camera directly above the sled and focusing it
on a plane located at a known distance below the base of the filter array.
Trials were run in the dark and fluid motion at the target height was
illuminated with a light sheet (5–7 mm thick) produced by shining a
synchronized flash (Nikon Speedlight SB-800) through a 1-mm slit at the
upstream end of the tank. As before, the sled was towed at the chosen test
velocity until filter elements reached steady-state deflection. Four
successive images then were collected at regular intervals during each trial
to allow sufficient particle displacement for velocity determination. In
experiments with slender filter elements (L/d=100), images
were collected at 10, 30, 50, 70, 90, 110, 130 and 150 mm from the filter
base. In experiments with stout filter elements (L/d=50),
images were collected at 10, 30, 50 and 70 mm from the filter base. The order
of the three tow velocities was determined randomly for each light sheet
position. Replicate trials (three per condition) were collected on different
days and this same protocol was applied to filter arrays composed of each of
the five materials examined in the study, resulting in 540 total experimental
trials.
Images were calibrated to convert from pixels to actual dimensions for each combination of filter material, aspect ratio and measurement height (ImageJ 1.37). Coordinates of cylinder locations were recorded and particles for tracking were selected in frame one from those located within in the narrow sector between adjacent cylinders (Fig. 2). Flow past highly bent cylinders was sometimes deflected vertically, carrying particles out of the imaging plane. To avoid positional ambiguity associated with such vertical movements, only particles that were illuminated through all four frames were tracked and used in estimating velocity. Total horizontal (streamwise) displacement was calculated for each particle and divided by the time interval between the first and fourth frames to obtain particle velocities.
|
Two distinct leakiness quantities were calculated for each model filter. Estimates of `planar' leakiness were obtained at each of multiple discrete distances from the filter base by dividing (at each distance) the spatially integrated velocity profile across the width of the array by the product of array width (without deformation) and free-stream velocity. This proportionality equaled the amount of fluid that actually passed through the filter in a plane at a given distance from the base, normalized by the amount of fluid that would have passed through the same space (i.e. the region spanned by the undeformed filter) if the filter were absent. Replicate estimates of planar leakiness were averaged for each filter material and within each combination of velocity and vertical position. Taking each set of planar leakiness values (one value for each of a series of distances from the base of the filter array), the `whole-model' leakiness was then computed for the entire array in order to account for the proximal-to-distal variation in planar leakiness along the length of the filter. Note that the whole-model leakiness was estimated by averaging the values of planar leakiness across all measurement distances out to L, including those beyond the reduced height of the bent array. This convention effectively normalized the amount of fluid passing through the bent array by the amount of fluid that would, in the absence of the filter, pass through the region spanned by it in its undeflected configuration (as opposed to the amount of fluid that would, in the absence of the filter, pass through the smaller region spanned by it in its bent configuration). Such values of whole-model leakiness thereby captured effects of both decreases in fluid passage through the array and array deformation, when providing an index of overall filter performance.
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RESULTS |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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=1456±27 kg m–3; N=9), but
unavoidable changes in room temperature caused modest variation in dynamic
viscosity [µ=118±19 Ns m–2 (N=13) for
trials with arrays of slender filter elements (L/d=100);
µ=161±5 Ns m–2 (N=10) for trials with
arrays of stout filter elements (L/d=50)]. These conditions
resulted in average Re values of 5.1x10–6,
5.1x10–5 and 5.1x10–4, although
for simplicity's sake these experimental conditions are referenced using
order-of-magnitude designations (i.e. Re of 10–5,
10–4 and 10–3). The elastic moduli of the
cylinder materials (mean ± s.d.; N=4 of each material) spanned
a more than 100-fold range in stiffness (stainless steel, 176.50±1.97
GPa; brass, 127.61±0.14 GPa; Garolite-G10, 21.03±1.25 GPa;
Garolite-XX, 8.00±0.07 GPa; nylon, 1.37±0.05 GPa) and yielded
average B values of 1.0x109 to
1.4x1015 across conditions.
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/L)] of the cylinders averaged across all
four filter elements in an array varied from 0.1 to 2.9 deg. for the most
rigid material (E177 GPa), and from 3.7 to 70.4 deg. for the
most flexible material (E1 GPa). This streamwise bending
decreased vertical filter height, as viewed from upstream, by as much as 0.5%,
1.1%, 7.1%, 21.8% or 68.2%, for filters ranging from least to most flexible.
The oblique orientation of deflected filter elements also changed the
cross-sectional shape of elements penetrating a given horizontal plane (e.g.
Fig. 2E), increasing the amount
of element surface bordering the planar flow. The two outer filter elements
bent farther than the inner elements, probably because the outer elements
experienced faster relative velocities and thus higher drag (e.g.
Fig. 2E). The latter
differential bending was detectable in many of the filter materials and flow
conditions but was maximal in the flexible arrays exposed to higher-velocity
flows.
|
8 GPa,
distance from the filter base=0.7 L).
The two effects outlined above, streamwise bending and cross-stream
narrowing, together caused a substantial decrease in total projected filter
area (Fig. 5). Relative to
stationary arrays, filter deformation reduced projected area by as much as
1.0, 4.0, 20.7, 46.0 or 72.1%, for models ranging from least to most flexible.
Filter area was similar among arrays composed of all five materials when flow
velocities and Re were lowest. In the intermediate Re
condition, only the most flexible array (E1 GPa) deformed
appreciably, and in the highest Re condition the observed reductions
in filter area were inversely correlated with material stiffness. For the most
flexible array (E 1 GPa) in the highest Re condition,
streamwise bending dominated the reduction in projected area because extreme
bending restricted the vertical filter span to only three measurement
distances from the base (e.g. Fig.
3C; Fig. 4C).
Planar leakiness
Planar leakiness averaged across the width (three gaps) of each array
varied systematically with distance from the array base, Re, and
elastic modulus (Fig. 6).
Maximum planar leakiness associated with any of the test conditions was only
0.17 because of pronounced velocity retardation in the boundary layer over the
sled and substantial flow diversion around the filter arrays, as would be
expected for low Re conditions. All filters exhibited comparable
leakiness for planes immediately beneath the sled where the local angle of
cylinder deflection was negligible. The general increase in leakiness with
distance from the array base was attributed to the velocity gradient
established over the sled, which led to faster relative flow speeds in planes
farther from the sled.
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128, 177 GPa), filter
leakiness was dependent on current speed, with the greatest leakiness
occurring in the highest Re flow
(Fig. 6A,B). This positive
trend in planar leakiness with increasing Re was reversed for filters
composed of the other three materials (E1, 8, 21). In these more
flexible arrays, leakiness was reduced in fast flows. This reversal was most
apparent in the highest Re condition where strong streamwise bending
prevented filtration far from the filter base in the two most flexible arrays
(E1, 8), producing leakiness values that were effectively zero
for the most distal measurement planes
(Fig. 6D,E). Further examination of planar leakiness revealed a subtler effect of cylinder bending that was independent of changes in filter area. For any given filter array and distance from the filter base, one might expect that variations in planar leakiness would correspond to variations in array width. This expectation held for model filters that experienced relatively little deflection, but when streamwise bending was more pronounced, observed reductions in planar leakiness were modified. We evaluated this trend by calculating a `renormalized' value of planar leakiness that controlled for the influence of changing array width. For every combination of filter material, tow velocity and distance from the base, values of renormalized planar leakiness were obtained by dividing the spatially integrated velocity profile across the width of the array by the product of narrowed array width (i.e. accounting for deformation) and free-stream velocity. The resultant estimates of renormalized planar leakiness were then plotted as a function of distance from the array base for all filter materials and Re conditions (Fig. 7). If changes in array width alone had accounted for the previously observed reductions in planar leakiness through more flexible filters (Fig. 6), then renormalized planar leakiness values should have been identical for all filters operating at a given Re, regardless of their material stiffness. This default outcome, however, did not occur. Instead, additional reductions in water flow between filter elements arose in association with the oblique orientation of deflected elements, probably as a result of the combination of vertical diversion of flow around a bent filter array (resulting in lower horizontal velocities impinging on the filter) and increased resistance to flow through the filter due to more element surface bordering each gap (cf. elliptical cross sections in Fig. 2E).
Effects of element flexibility on renormalized planar leakiness also appeared to intensify with increasing Re and filter deflection (Fig. 7B,C). However, careful inspection revealed an experimental artifact associated with extreme levels of element bending due to our method of flow visualization. Beyond a certain distance from the filter base, the substantial reductions in renormalized planar leakiness associated with filter deformation became relatively less pronounced. This shift can be explained by the observation that bent cylinders within an array did not stabilize at precisely the same height. Particularly at large distances from the base of a flexible array, bending of the outer elements exceeded that of the inner ones (e.g. Fig. 2E) and resulted in vertical separation of elements that caused the absolute distance between adjacent elements to become greater than the observed (horizontal) separation when looking straight down on the filter array. This vertical separation of filter elements changed the three-dimensional flow patterns such that measured fluid motion through the `observed gap' became greater than expected.
Effects of aspect ratio
Additional tests using arrays of shorter and proportionally thicker
(stouter) filter elements (L/d=50) of the same materials
showed a similar but less pronounced pattern than the slender arrays
(Fig. 8). Maximum planar
leakiness (through the most rigid filters) was 0.13, representing a 14%
reduction from the maximum leakiness through the slender arrays. Planar
leakiness near the base was similar among model filters (0.03) but the
increase in leakiness with distance from the base was suppressed by filter
deformation, although this effect was weaker than that observed for the
slender arrays. Relative to average maximum leakiness through the rigid
filters, leakiness at the most distal measurement plane decreased by 16% and
11% for stout arrays in which E8 and 21 GPa, respectively,
representing a milder consequence of bending than was observed in slender
arrays (e.g. Fig. 6C,D). In the
highest Re, the most flexible stout array (E1 GPa)
deformed enough to prevent filtration far from the filter base, consequently
reducing leakiness relative to the lower Re conditions
(Fig. 8E), but again this
reduction in leakiness was far less than that in slender arrays where more
than 50% of the filter span was effectively eliminated by bending
(Fig. 6E).
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Whole-model leakiness
Whole-model leakiness, computed by integrating planar leakiness across the
full height of the filter array (Fig.
9), illustrated the overall effect of structural flexibility for
filter function. One critical trend was the different behavior of rigid
versus flexible filters, especially for the slender arrays. In
general, whole-model leakiness of rigid filters (E128, 177)
increased with Re. In our study, average whole-model leakiness
through the most rigid arrays of slender elements (L/d=100)
increased by 24% between Re of 10–4 and
10–3, compared to an increase of only 5% between Re
of 10–5 and 10–4
(Fig. 9A). In marked contrast,
the three more flexible arrays exhibited the opposite trend in whole-model
leakiness. For instance, the most flexible slender array (E1)
exhibited a dramatic, 41% decline in leakiness between Re of
10–5 and 10–4 and an additional decrease of
60% between Re of 10–4 and 10–3.
The effect was similar, although somewhat muted, in the second most flexible
(E8) and intermediately flexible (E21) arrays.
These filter arrays experienced decreases in leakiness of 55% and 10%,
respectively, between the intermediate and high Re conditions. The
most pronounced reductions in leakiness resulted primarily from effective
shortening of the filters, which led to zero filtration at fixed distances far
from the filter base in the two most flexible arrays
(Fig. 6D,E).
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128, 177) in the highest Re condition was 0.08 for
stout arrays versus almost 0.12 for slender arrays. Given that
cylinder diameters, gap widths, array width, and fraction of projected area
occluded by filter elements were equivalent among the most rigid filter
arrays, observed reductions in leakiness through the stout arrays can be fully
attributed to their lower position in the boundary layer formed over the tow
sled. |
DISCUSSION |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Patterns of whole-model (integrated) leakiness also demonstrate that filter
flexibility can alter the relationship between filter leakiness and
Re, particularly in arrays composed of slender elements. Prior
studies of leakiness through rigid filter arrays have found that leakiness
increases gradually over Re from 10–5 to
10–3, in contrast to filters operating at slightly higher
Re where leakiness is very sensitive to Re
(Cheer and Koehl, 1987;
Koehl, 1995). However, data
presented here suggest that deformation of feeding appendages may incur a cost
of reduced leakiness across a range of low Re, potentially altering
expectations of when critical transitions in filter function may occur. Our
results also suggest the need to re-evaluate the notion that slender (as
opposed to stout) elements in filter arrays always ensure greater leakiness,
given that this trend may disappear in the presence of substantial deformation
(compare case for E1 GPa at the highest Re condition in
Fig. 9A,B). Such neglected
aspects of filter function may require some adjustment to existing perceptions
regarding linkages between morphology and ecology in suspension feeders.
Experimental considerations
Although strong trends are apparent in the results above, some care should
also be applied in their interpretation. Findings are relevant to
low-Re conditions representative of suspension feeders on the small
end of the size spectrum, and quantitative values underlying the overall
qualitative patterns may apply rigorously only to specific geometries.
Examples of organisms that operate at Re 10–5
whose filter structures resemble those studied here include nanoplanktonic
flagellates (e.g. Actinomonas mirabilis; L/d
60; g/d 5; x/d 20)
(Fenchel, 1982). Suspension
feeders that function at Re 10–4 include
cladocerans (e.g. Penilia avirostris, with L/d
45; g/d 6; x/d 15)
(Turner et al., 1988). There
are many organisms that feed at Re 10–3 and use
filters analogous in shape to those of this study (e.g. Euphausia
superba, with L/d 60;
g/d 4; x/d 10)
(McClatchie and Boyd,
1983).
Complete effects of reduced filter area also may not be evident in our
analysis because flow was measured though a finite number of horizontal
planes. We were therefore forced to assume that leakiness through interior
portions of arrays where flow was not quantified (i.e. regions between
measurement heights) could be reasonably approximated by interpolation.
However, contributions to leakiness from the extreme upper, and sometimes
lower, portions of each filter were not represented. Material imperfections in
individual filter elements also may have contributed to variability in the
leakiness calculations, as they occasionally caused slight non-uniformities in
bending. These inconsistencies likely resulted from asymmetries introduced
during manufacture of the model elements, although analogous effects could
also play a role in the bending trajectories of actual animal feeding
appendages. We further note that although observations of invertebrate
suspension feeders reveal that bending of their particle capture apparatus is
common, quantitative evaluations of the moduli of these structures are
generally unavailable. For our purposes, we assumed that the stiffnesses of
suspension-feeding structures are similar to those of the `building-block'
materials from which they are composed, and for which there are data. For
example, skeletal components such as chitin and keratin have elastic moduli of
1–100 GPa, and structures reinforced with calcium carbonate have elastic
moduli less than 100 GPa (Wegst and Ashby,
2004). Assuming stiffnesses across this range, the materials we
employed in our experiments corresponded to biologically relevant ranges of
nondimensional stiffness (B). However, it is also possible that some
suspension feeders produce particle capture apparatuses that diverge from
values of B used in our experiments.
Filters in the natural environment
Leakiness patterns presented here reveal new insights into the function of
filters operating in steady flows at very low Re (e.g. in pelagic
environments or in tidal currents where changes occur over timescales of
hours). Our findings may be less applicable to flows associated with rapidly
evolving waves or turbulence, such as those found in intertidal or shallow
subtidal habitats (Gaylord,
1999; Gaylord,
2000; Gaylord,
2008). In these latter environments, filter deformation and its
implications for particle capture could be either suppressed or intensified
depending on the combined effect of fluid reversals and vortex attachment or
shedding. During periods of accelerating or decelerating flow, for example,
the bending trajectories of even moderately flexible filters might lag behind
flow reversals and thus damp fluctuations in relative velocities. Some
microhabitats where benthic suspension feeders settle will also experience
velocity bursts as the effects of turbulent eddies penetrate all the way to
the seafloor (Cantwell, 1981;
Dade, 1993). Individuals living
in topographical microhabitats where velocity transients are common could
experience disproportionate consequences of filter deflection. We also note
that the bending of biological filters may influence the function of
array-like structures in organisms beyond marine suspension feeders.
Low-Re filters are employed for respiration, propulsion and olfaction
in a wide variety of freshwater and terrestrial invertebrates (see e.g.
Loudon and Koehl, 2000;
Sunada et al., 2002;
Barta and Weihs, 2006).
Deformation-induced effects on leakiness probably play paramount roles in
these organisms as well.
Conclusions
Our results concern leakiness, and not particle encounter or capture (e.g.
Palmer et al., 2004), and
therefore do not address the full suite of factors driving food acquisition by
mechanisms of hydrosol filtration. However, fluid transmission through a
filter array is one of the fundamental gatekeepers for particle capture. Here,
we show that structural flexibility can compromise leakiness across a range of
low Re conditions. Detrimental effects of filter deformation on
leakiness generally increase with Re and are offset in some cases for
stouter filter elements. Such consequences of material properties and element
shape for filter leakiness are likely to have important implications for
suspension feeders of a variety of morphologies. Future studies should examine
effects of flexibility across a greater spectrum of filter geometries and at
higher Re, and should examine other steps in the feeding process
(encounter and retention). Such work will facilitate the development of more
comprehensive predictions of how food acquisition varies with collector
morphology, flow conditions, and particle size and concentration.
LIST OF SYMBOLS
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Acknowledgments |
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References |
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TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Barta, E. and Weihs, D. (2006). Creeping flow around a finite row of slender bodies in close proximity. J. Fluid Mech. 551,1 -17.[CrossRef]
Cantwell, B. J. (1981). Organized motion in turbulent flow. Annu. Rev. Fluid Mech. 13,457 -515.[CrossRef]
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