FLUME STUDY OF PARTICLE-SIZE-DEPENDENT FILTRATION RATES OF A
SOLITARY ASCIDIAN: THE INFLUENCE OF BODY SIZE, FLOW SPEED, AND DRAG
Andrew N. Sumerel
A Thesis Submitted to the
University of North Carolina Wilmington in Partial Fulfillment
of the Requirements for the Degree of
Master of Science
Center for Marine Science
University of North Carolina Wilmington
2009
Approved by
Advisory Committee
Dr. Lynn A. Leonard
Dr. Martin H. Posey
Dr. Chris M. Finelli
Chair
Accepted by
DN: cn=Robert D. Roer, o=UNCW, ou=Dean of
the Graduate School & Research,
email=roer@uncw.edu, c=US
Date: 2010.01.21 14:49:23 -05'00'
___________________________________
Dean, Graduate School
TABLE OF CONTENTS
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
ACKNOWLEGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF CONSTANTS AND VARIABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Factors That Influence Suspension Feeding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Motivation For Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
MATERIALS AND METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Animals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Flume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Experimental Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Filtration Rate Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Drag Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Determination Of Additional Body Size Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
RESULTS AND DATA ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Relating Body Size Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Filtration Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Drag On Ascidians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Filtration Response To Increasing Body Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Filtration Response To Increasing Flow Speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
ii
Influence Of Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
iii
ABSTRACT
Ascidians are sessile, active suspension feeders, common in fouling communities around
the world. Active suspension feeders create their own feeding current to filter suspended
food-particles. Several factors can influence the filtration rates of active suspension feeders
including body size, food-particle size, flow speed and the force of drag. It is well established in
the literature that the relationship between filtration rate and body size of ascidians is allometric.
The effects of food-particle size on filtration rate vary for active suspension feeders, and
investigations into the effects of flow speed and drag on the filtration rates of active suspension
feeders are rare. Moreover, flow speed and drag effects have not been quantified for ascidians.
I have investigated the filtration rates of the solitary ascidian, Styela plicata, and found
interacting effects among all of the previously mentioned variables. Consistent with the
literature, I determined allometry with respect to body size, but my allometric exponents are
comparatively lower than those found in other investigations. This is because of the confounding
adverse effects of increasing flow speed, to which filtration rate responded in a non-linear,
unimodal fashion. The likely mechanisms for flow-dependent suppression of filtration rate
include deformation of internal feeding structures due to drag, and/or increased adverse pressure
gradients between the siphons as a result of drag or flow itself. Interestingly, maximum filtration
occurs at moderate flow speeds (~ 12 cm/s) when this ascidian filters particles in the range 1.25 to
6.03 µm. Maximum filtering of large particles (6.03 to 100 µm) occurs at low flow speeds (~ 0).
The most likely reason for this shift in maximum filtering of different size particles is enhanced
filtration of large particles at low speeds due to enhanced capture of large particles at the incurrent
region of the inhalant siphon. This also enhances the allometric exponent relating ‘large-particle’
filtration rate to body size.
iv
ACKNOWLEDGEMENTS
I would first like to thank Dr. Chris Finelli, Chair of my thesis advisory committee, for his
patience, generosity, and support through this endeavor, and for being extremely approachable and
available; a rarity among professors in my opinion. Additional thanks goes to the other members
of my committee, Dr. Martin Posey and Dr. Lynn Leonard for their further insight into this
research. I also wish to thank those in the Marine Biofluiddynamics and Ecology Lab including
Lou Muzyczek, Tiffany Lewis, Kelly Woods and Morgan Church, without whom, life would have
been more difficult. Additional thanks goes to Tse-Lynn Loh (and Lou again) for gracious help in
the field. I also greatly appreciate Dr. Joan Willey for her guidance and patience with me in
continuing to provide Teaching Assistantships as I worked through the Master of Science in
Marine Science program. Additionally, this research was funded in part by grants OCE-0751753,
OCE-0715271 and OCE-0715272 from the National Science Foundation. Finally, I am
continually grateful for my family DeLane, Glenda, Rebecca and Grandma for their endless
support, and for Ashley Bissette for her unending thoughtfulness and patience.
v
LIST OF TABLES
Table
Page
I.
Important Results From The Regressions Of Particle-size-dependent
Filtration Rate vs. Flow Speed And Body Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
II.
Comparison Of Allometric Exponents
In The Literature Relating FR To Body Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
vi
LIST OF FIGURES
Figure
Page
1.
Top and side cross-sectional drawing displaying structure of a typical ascidian . . . . . . . . . 1
2.
Suspected dependence of filtration rate on flow speed and body size . . . . . . . . . . . . . . . . . 5
3.
Theoretical dependence of drag on flow speed and body size . . . . . . . . . . . . . . . . . . . . . . . 6
4.
Schematic of the flume tank used in these experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
5.
Volume concentration vs. particle-size range (bin) showing an initial sample
(yellow) and a sample at four hours (red) for a particular biological trial . . . . . . . . . . . . . 12
6.
Allometric relationship between ash-free, dry mass and original frontal area . . . . . . . . . . 18
7.
Dependence of frontal area during flow on original area and flow speed . . . . . . . . . . . . . 19
8.
Response of a.) ‘small-particle’ b.) ‘large-particle’ and c.) total filtration rate
to increasing flow speed and frontal area during flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
9.
Drag coefficient vs. Reynolds number for ‘bluff-body’ wax ascidians
to determine drag correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
10.
Corrected drag as a function of flow speed and frontal area for wax ascidians . . . . . . . . . 24
11.
Corrected drag as a function of flow speed and frontal body area during flow
for S. plicata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
vii
LIST OF CONSTANTS AND VARIABLES
a . . . . . . . . . . . . . . . . . . . . . Empirically determined exponent in the potential power-law dependence
of drag coefficient on Reynolds number (unitless)
A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . King’s Law constant (V2)
b . . . . . . . . . . . . . . . . . . . . . . . . . . . Allometric exponent relating filtration rate to body size (unitless)
B . . . . . . . . . . . . . . . . . . . . . . . . . King’s Law constant (typically with units V2 s¼ cm-¼ or V2 s½ cm-½)
c . . . . . . . . . . . . . Empirical constant equivalent to body-size-dependent, filtration rate in still water
(units dependent on body size category)
CBo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Initial volume concentration during a biological trial (µL/L)
CBt . . . . . . . . . . . . . . . . . . . . . . . . . . . Volume concentration at time, t, during a biological trial (µL/L)
CD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The drag coefficient (unitless)
CDo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Initial volume concentration during a control trial (µL/L)
CDt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Volume concentration at time, t, during a control trial (µL/L)
CL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Volume concentration of ‘large’ particles (µL/L)
cr . . . . . . . . . . . . Empirical scaling constant relating drag coefficient to Reynolds number (unitless)
CS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Volume concentration of ‘small’ particles (µL/L)
CT . . . . . . . . . . . . . . . . . . . . . . . . . . Volume concentration across the entire particle-size range (µL/L)
CTBo . . . . . . . . . . . . . . . . Initial volume concentration of all particles during a biological trial (µL/L)
CTB4 . . . . . . . . . . . . . . . . Volume concentration of all particles at 4 h during a biological trial (µL/L)
CTDo . . . . . . . . . . . . . . . . . . . Initial volume concentration of all particles during a control trial (µL/L)
CTD4 . . . . . . . . . . . . . . . . . . . Volume concentration of all particles at 4 h during a control trial (µL/L)
viii
D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Force of drag on an object (Newtons)
DR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deposition rate (particles/h)
E . . . . . . . . E-value indicating degree of reconfiguration over a specific flow speed range (unitless)
F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Momentum flux (Newtons)
FR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Filtration rate (L/h)
FRL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Large-particle filtration rate (L/h)
FRo . . . . . . . . . . . . . . . . . . . . . . . . . Empirical constant equivalent to filtration rate in still water (L/h)
FRS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Small-particle filtration rate (L/h)
FRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total filtration rate across the entire particle-size range (L/h)
l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristic length (cm)
µ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluid kinematic viscosity (g cm-1 s-1)
n . . . . . . . . . . . . . . . . . . . . . . . Empirically determined King’s Law exponent of flow speed (unitless)
N . . . . . . . . . . . . . . . . . . . . . . Total number of 30 second, drag measurements during a trial (unitless)
Pd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltage from a constant temperature thermistor (V)
Re . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reynolds number (unitless)
ρ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluid density (g/cm3)
S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Body size (units dependent on body size category)
Sa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Area of an imaginary plane through which, fluid flows (cm2)
sc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Empirical scaling constant relating filtration rate to body size
(units dependent on body size category)
ix
Sd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Area of an imaginary plane downstream of a body (cm2)
Sdj . . . . . . . . . . . . . . . . . The jth area element of an imaginary plane downstream of an ascidian (cm2)
Sf . . . . . . . . . . . . . . . . . . . . . . Frontal area of an object projected normal to fluid flow direction (cm2)
SM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Body mass as wet mass, dry mass, or ash-free, dry mass (g)
SO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normally projected frontal area in still water (cm2)
SSD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Speed-specific drag (Newtons s2 cm-2)
Su . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Area of an imaginary plane upstream of a body (cm2)
t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time (h)
U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fluid flow speed (cm/s)
Ud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow speed downstream of a body (cm/s)
Udj . . . . . . . . . . . . . . The jth downstream mean flow speed estimate over a 30 second interval (cm/s)
Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow speed where maximum filtration occurs (cm/s)
Uu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow speed upstream of a body (cm/s)
Uuj . . . . . . . . . . . . . . . . . The jth upstream mean flow speed estimate over a 30 second interval (cm/s)
V . . . . . . . . . . . . . . . . . . . Volume of filterable seawater containing suspended particulate matter (L)
w . . . . . . . . . Descriptor related to the full-width at half-maximum of a Gaussian distribution (cm/s)
x
INTRODUCTION
Characterized by a diverse array of morphologies, including both solitary and colonial
forms, ascidians are sessile, active suspension feeders that live fixed to a substrate and pump water
through feeding structures to filter food particles. The basic structure of the solitary ascidian,
Styela plicata, is roughly cylindrical with outer skin known as the tunic (Fig. 1). There are two
openings, the inhalant and exhalant siphons, which permit water to enter and exit the body cavity
where particles are removed. Tentacles at the inhalant siphon opening serve to select food
particles of a certain size, mostly excluding large indigestible particles (Goodbody, 1974). The
inhalant siphon leads to the pharynx where lateral cilia, lining stigmatal openings of the branchial
basket (pharynx), pump water from the pharynx directly to the atrium from whence it is discharged
through the exhalant siphon (Fig. 1). The endostyle lines the entire inner branchial basket and
continuously secretes a mucus-net that captures food particles to be digested. Food particles are
trapped in the net and then passed on (with the entire net) to the esophagus by frontal cilia also
lining the endostyle (Fig. 1). In the esophagus, the food particles and net are digested, with
wastes finally entering the atrium as effluent and discharging via the exhalant siphon.
Figure 1: Top and side cross-sectional drawing displaying structure of a typical ascidian (Petersen, 2007)
Ascidians feed on suspended particulate matter including phytoplankton and large bacteria
(Petersen, 2007), and their diet depends in part, on the mucus net structure. The mucus net
consists of transverse and longitudinal filaments (10 to 40 nm diameter) resulting in rectangular
openings of 0.2-0.5 m by 0.5-2.2 m (Flood & Fiala-Médioni, 1981). Food-particles smaller
than the rectangular openings are not necessarily passed through to the atrium undigested. As
described by aerosol filtration theory (e.g. Rubenstein & Koehl, 1977), smaller particles can be
captured by the filaments via several different mechanisms including direct interception,
gravitational deposition, inertial impaction, Brownian diffusional deposition, and electrostatic
attraction; and are likely retained after deposition due to van der Waals forces between the particle
and sticky mucus filament (Rubenstein & Koehl, 1977; Shimeta & Jumars, 1991; Spielman, 1977;
Pich, 1966). For this reason, particles in the 1-2 m range are captured with about 70% efficiency
(Randløv & Riisgård, 1979). Particle retention studies have not been performed for sub-micron
particles, but it is believed that if these particles are retained, they do not constitute a quantitatively
important portion of ascidian diet (Petersen, 2007). Particles greater than 100 m can compound
mucus net overloading and often lead to expulsion of pseudofaeces through the siphons via
squirting (Robbins, 1984; Petersen, 2007).
Styela plicata is a common solitary ascidian with a roughly cylindrical or oblong
morphology. They are cloaked in an unstalked tunic that is typically described as tough,
thick, leathery (Fuller, 2007), warty and ridged (Howey, 1998). Interestingly, the tunic is
composed largely of cellulose compounds. For animals, this is common only to the tunicates
(Kimura & Itoh, 2007). Their color is typically grayish or tannish-white, with red or purple
stripes (usually four) on the siphons. They are abundant members of fouling communities
throughout the world’s oceans in temperate sub-tropical and some tropical climate zones, and they
2
can grow on the sides of floating docks and project outward into flow, horizontal to the water’s
surface with siphons typically oriented toward the water’s surface. S. plicata typically only live
for less than a year (Kott, 1972), although some investigators suspect they may live between 2 and
3 years (Lambert & Lambert, 1998). Their abundance makes them important animals for
ecological scientific inquiry.
The connection between life and environment is progressively made clearer through
studies of how feeding is affected by ambient hydrodynamic conditions. Such studies are rare for
ascidians, yet theory and studies of other active suspension feeders indicate that their filtration
rates should vary as a function of ambient flow speed, body size, and drag.
Factors That Influence Suspension Feeding
Ascidian feeding is very sensitive to a number of perturbing factors including temperature
and food-particle concentration (Petersen, 2007). Filtration rate can also depend on body size, a
term with variable meaning in the suspension-feeding literature used to describe one of several
related terms including body mass (wet mass, dry mass, or ash-free dry mass) and body-area
projected normal to flow (in still water or in flow). As body size increases, filtration rate also
increases as the allometric relationship,
Eq. 1
where FR is the filtration rate, sc is an empirical constant, S is body size, and b is a constant
(Randløv & Riisgård, 1979). The exponent b, has been empirically determined to vary between
0.38 (Holmes, 1973) and 1.08 (Klumpp, 1984) for various species of ascidian under various
experimental conditions. The 2/3 rule is used as the generally accepted comparison where b = 2/3
(0.667) for the relationship between filtration rate and body mass (Randløv & Riisgård, 1979;
Klumpp, 1984) determined from dimensional scaling of squared dimensions of surface area
3
responsible for filtration (branchial surface) and cubed dimensions of body volume
(Schmidt-Nielsen, 1997; Klumpp, 1984).
In addition to body size, filtration rate can depend on ambient fluid flow. No investigation
exists that explicitly concerns the relationship between ascidian filtration rate and varying ambient
flow speed, but there have been some flow studies for other active suspension feeders. The giant
scallop, Placopecten magellanicus, responded to increasing flow speed by increasing its filtration
rate to a peak with a subsequent decrease up to flow speeds of 45 cm/s (Wildish et al., 1992;
Wildish & Saulnier, 1993). Additionally, Wildish & Miyares (1990) found that the filtration rate
of the blue mussel, Mytilus edulis, rapidly decreased after 6 cm/s and leveled off to near-zero
above 25 cm/s. Filtration rates were not estimated for this mussel at flow speeds less than 6 cm/s,
but if it was determined that the filtration rate of this mussel increases at zero flow speed to values
observed at 6 cm/s, then its flow-dependent filtration rate would follow the same pattern observed
for the giant scallop. Wildish & Kristmanson (1997) generally refer to the entire response as
unimodal (peak function). The reasons for this general description are that there is no precise
theoretical mathematical relationship between flow speed and filtration rate of active suspension
feeders, and insufficient data prevent definition of the true form of the curve. Many mathematical
descriptions of peak functions exist. In the interest of simplicity, I prefer to describe the response
as the symmetrical Gaussian distribution such that filtration rate is a smooth, continuous
peak-function of flow speed so
Eq. 2
where, FRo is the filtration rate in still water, U is flow speed, Up is the position of the peak, and w
describes the width of the “bell” curve. Multiplying the right-side terms of Equations 1 and 2,
yields an estimate of filtration rate that is a function of both body size and flow speed
4
Eq. 3
shown in Fig. 2, where c = sc FRo.
Figure 2: Hypothesized dependence of filtration rate on flow speed and body size
Filtration rate increases directly with flow due to increasing particle flux across the feeding
appendage; but does not decrease to zero in still water because active suspension feeders create
their own feeding currents. At higher flow speeds, filtration rate is observed to be suppressed.
The ultimate reason for this is still unknown, but several hypotheses include particle overloading
(Wildish et al., 1992) due to overwhelming particle flux, the development of adverse pressure
gradients between inhalant and exhalant siphons in excessive flow (Wildish et al., 1992; Wildish
& Saulnier, 1993), and reconfiguration and body torsion due to drag, which could inhibit filtration
rate as described below.
Drag refers to force that resists the movement of a solid object through a fluid (or moving
fluid about a fixed solid object). It consists of frictional forces between the fluid and object's
surface and pressure forces, which act in a direction perpendicular to the object's surface. These
5
forces can be nearly impossible to resolve and can themselves depend on a large number of
variables. Therefore to limit the degrees of freedom, the typical model for the drag on a body is
described by Eq. 4, where drag depends largely on the square of the ambient fluid flow speed and
on the frontal body area, Sf, projected normal to flow (Vogel, 1981) so
Eq. 4
where D is drag, ρ is the density of the fluid, and CD is the drag coefficient. According to Vogel
(1981), the drag coefficient is a function of the Reynolds number, Re, where Re = ρlU/µ. The new
symbols here are l, the characteristic length of the object and µ, the dynamic viscosity. For the
purposes of this study, the characteristic length is considered the greatest length of the ascidian in
the direction of flow. The drag coefficient can be any function of Re, but typically for moderate to
high Reynolds numbers,
Eq. 5
where cr is an empirical constant and a is a number that may be constant or vary with Re.
Figure 3: Theoretical dependence of drag on flow speed and body size
6
Fig. 3 represents the ideal case where the drag coefficient is always constant (if Eq. 5 is true
for a body then this only happens when a = 0 or a = [ln CD/cr]/ln Re). This is largely true for what
Vogel (1984) refers to as a “bluff” body; a non-streamlined, non-flexible object. One might then
expect drag to behave differently for flexible bodies such as ascidians. Drag forces become a
factor at high flow speeds, and this could have the effect of suppressing (or even completely
inhibiting) filtration of flexible, active suspension feeders for several different possible reasons.
First, drag forces can alter a body’s orientation to flow. With regard to ascidians, drag can
perturb siphon orientation away from some ‘optimal’ feeding orientation. Knott et al. (2004)
found that flow directly into the inhalant siphon was most optimal for feeding. Inhalant siphons
oriented with the direction of flow resulted in greatly reduced feeding, and inhalant siphons
oriented perpendicular to flow showed the least feeding for Pyura stolonifera. Each of these
orientations were investigated at the same flow speed of 15.2 cm/s. It is unknown how the direct
influence of increasing flow on orientation will affect feeding, but it is possible that when siphon
orientation is sub-optimal, pressure differences increase between the inhalant and exhalant siphons
so that active suspension feeders (such as ascidians) must pump harder to process water containing
food (Wildish & Kristmanson, 1997; Knott et al., 2004). This scenario would not be energetically
efficient, and the ascidian could not compensate. Second, drag forces bend and deform flexible
creatures (reconfiguration), which may deform internal filtering structures and reduce the
efficiency of food-particle capture and processing (Shimeta & Jumars, 1991). In contrast,
reconfiguration could be beneficial where it facilitates shielding of external features responsible
for feeding (siphons) or bringing these features closer to the boundary layer where speeds are not
as harsh (Sponaugle & LaBarbera, 1991). This would allow some suppressed feeding as opposed
to none at all. Finally, it is also possible that drag forces can become so high that complete
7
dislodgement occurs, thereby ending feeding altogether. Thus, it may be that the more flexible
the organism, the better adapted they are to survive intense flow when dislodgement is likely
(Vogel, 1984; Koehl, 1984; Denny et al., 1985; Koehl, 1999).
Additionally, the response of filtration rates of active suspension feeders to varying flow
speed over a distribution of particle-sizes varies. This author is unaware of any studies with
regard to ascidians on this subject, but some exist concerning bryozoans. The bryozoans, Bugula
neritina and B. stolonifera, showed increased ingestion of large-particles and decreased ingestion
of small-particles around flow speeds of 10 to 12 cm/s while there was consistently higher
selection of large particles at both flow speeds (Okamura, 1990). Each of the relationships
mentioned previously are interrelated and underappreciated. Additionally, relationships among
filtration rate, selectivity, flow speed, body size, and drag have not previously been quantified for
ascidians. Quantifying and understanding these relationships is the intent of this investigation.
Motivation For Study
As inferred from the above discussion, quantitative uncertainty exists concerning
ascidians’ response of particle-size-dependent filtration rate to fluid flow, body size and drag.
Further understanding and quantification of these relationships is very important to theorists who
use hydrodynamic theory to explain aspects of the biology and behavior of suspension feeders.
Also, fouling due to ascidians has become an increasing nuisance for commercially
important marine cultures (Petersen, 2007). A better understanding of how ascidians behave in
different flow regimes may aid in reduction of fouling. It is possible that mussels can be given a
competitive advantage over ascidians by adjustment of factors (temperature, food concentration,
etc.) that affect feeding, because feeding response differs between mussels and ascidians
(Petersen, 2007). It is also possible that mussels (and other active suspension feeders) can be
8
given a competitive advantage over fouling ascidians in certain flow regimes. Knowledge of how
to reduce competitive pressure on commercially important species would be very valuable.
Of further value is the possible use of S. plicata as bioremediators (Draughon, 2009). As
coastal development has increased, natural habitats have changed and bacterial concentrations can
rise to unhealthy levels (Aslan-Yilmaz, 2004). Because bacteria are a significant portion of
ascidian diet, further understanding of the relationship between particle-size-dependent filtration
and flow regime could prove useful for the bioremediation effort.
Presented here are particle-size-dependent filtration rates of S. plicata as a response to
varying flow speed and body size. I also present indirect measurements of drag on each solitary
ascidian with varying flow speed and body size. These data provide a better understanding of
how ascidian feeding is affected by ambient hydrodynamic conditions.
9
MATERIALS AND METHODS
Animals
Specimens of Styela plicata were collected from floating docks in the Atlantic Intracoastal
Waterway (AIWW) near Wrightsville Beach NC (Latitude 34° 12' 31" N, Longitude 77° 47' 47"
W). Individual ascidians were gently removed from the dock surface using a putty knife, and
placed in plastic bags of ambient seawater for transport to the lab. Specimens were initially
selected based on their maximum end-to-end length at minimum body size (attained after being
gently disturbed in their habitat). Individuals were later grouped into a more formal body size
category based on projected body area. Upon arrival at the lab, each asidian was cleaned to
remove epibionts, blotted dry, and attached at the base to 6 cm by 8 cm Lucite Acrylic Sheet slides
(2 mm thick) with cyanoacrylate glue (Elmer’s Instant Krazy Glue). Mounting on slides was
necessary to facilitate immediate transfer to the flume for experimental use. Once secured in the
flume, the frontal body area of an ascidian was determined by photographing the individual
face-on in still water with a common digital camera (Samsung, 4.0 mega pixel, Digimax A402)
and measuring the area with commonly available image analysis software (Broken Symmetry
ImageJ, Vers. 1.4.3.67). Ascidians were grouped into three categories (for replication) based on
frontal area: small = 4.9 to 8.6 cm2, medium = 9 to 12.2 cm2, and large = 13 to 17.7 cm2.
Flume
Measurements of filtration and drag were gathered for varying size specimens of S. plicata
in a 16.4 L, laboratory paddle-flume tank (Fig. 4) at varying flow speeds. A Dayton gear motor
(Model 2H577A) rotated a paddle wheel on one side of the annular, open-channel flume (raceway
flume), and the rotation speed of the wheel was varied with a Dart Micro-drive II controller. The
paddles on the wheel move water unidirectionally around the flume from the paddle channel to the
observation channel. The flow speeds under consideration were approximately 3 cm/s, 15 cm/s,
and 21 cm/s as determined using an acoustic Doppler velocimeter (ADV; SonTek 16-Mhz
MicroADV) with the probe mounted in the center of the flume and sample volume located 5 cm
above the flume bottom (e.g. Finelli et al. 1999) . This flume is described in more detail in
Robinson et al. (2007) and Clarke et al. (2009).
Figure 4: Schematic of the flume tank used in these experiments (modified from Robinson et al., 2007)
Experimental Protocol
Prior to the beginning of each experimental trial, the flume was filled to a height of 10 cm
with seston-free artificial seawater (Crystal Sea) at a salinity of 35 ‰, and was constantly aerated.
An ascidian (mounted on a plastic slide) was transferred to the flume and secured to the bottom of
the flume channel with clear packing tape such that the inhalant siphon was oriented upward,
perpendicular to flow, and the exhalant siphon was oriented horizontal to the water’s surface, also
perpendicular to flow. The flume motor was started and allowed to come to speed. The ascidian
was allowed to acclimate to flow without feeding for at least 12 hours. There were 45 total trials
(3 different body sizes at 3 different flow speeds with 5 replicates), each with a corresponding
11
control trial using a simulated ascidian made from parafin wax (Boekel Tackiwax). Control wax
ascidians did not require the 12 hour acclimation period.
Filtration Rate Measurements
After acclimation, 3 g of cultured and preserved algae paste (Innovative Aquaculture
Products, LTD) was added to the flume. Filtration data were gathered over a four hour period by
determining seston clearance. At each predetermined time (0, 2, 4 hrs), three replicate 180 mL
water samples were obtained by syringe from the flume. Water samples were returned to the
flume after being analyzed with a Sequoia LISST Portable Laser Diffraction Particle Size
Analyzer. The LISST analyzer provides volume concentration of suspended particles (µL/L) in
32 logarithmically-increasing particle-size bins from 1.25 to 250 µm (Fig. 5). Because
food-particles larger than 100 µm are not ingested by ascidians, I truncated the particle
distribution to remove particles > 100 µm, resulting in 27 size bins.
Figure 5: Volume concentration vs. particle-size range (bin) showing an initial sample (yellow) and a sample at four
hours (red) for a particular biological trial
Chlorophyll analysis, using a Turner Trilogy Fluorometer and following the methods of
Welschmeyer (1994), showed that the concentration of Chl a always stayed above 12 µg/L during
12
an entire feeding period. This approach was necessary because filtration rates of ascidians do not
appear to vary with concentration above this amount (Petersen, 2007). The volume concentration
distribution of seston in the flume exhibited two distinct concentration peaks near 2 µm and near
22 µm (Fig. 5). Therefore for simplicity, the 27 particle ranges were grouped into two categories
such that the ranges around the first peak (1.25 to 6.03 µm) were considered the ‘small’ particle
group, and the ranges around the second peak (6.03 to 100 µm) were considered the ‘large’ particle
group. The area under an entire curve over the particle-size distribution is the total volume
concentration, CT. The area under a curve corresponding to the ‘small’ group is the
‘small-particle’ volume concentration, CS. The area under a curve corresponding to the ‘large’
group is the ‘large-particle’ volume concentration, CL. Filtration rates were obtained from the
volume concentrations as outlined by Coughlan (1969).
During a control trial, particles are assumed to only be deposited gravitationally in a
moving fluid such that the volume concentration decays exponentially (Coughlan, 1969; Fries &
Trowbridge, 2003), so
Eq. 6
where CDt is the volume concentration at time t, CDo is the initial volume concentration, and DR is
the deposition rate (particles per hour). Taking the natural log of both sides of Eq. 6, yields
ln
Eq. 7
which is the number of particles deposited by time t.
Organisms feeding at a constant rate will reduce successive ambient concentrations such
that the ambient concentration of food particles at any time decays exponentially (Coughlan 1969;
Peters 1984). Therefore, during a biological trial with both filtration and gravitational deposition
taking place, the volume concentration at time t is assumed to be
13
Eq. 8
where, CBt is the volume concentration at time t, CBo is the initial volume concentration, FR is the
filtration rate, and V is volume of filterable seawater in the flume. Figure 5 is an example where
CBo is represented in yellow and CBt is represented in red. Taking the natural logarithm of both
sides of Eq. 8, yields
ln
Eq. 9
and substituting Eq. 7 into Eq. 9 to account for gravitational deposition, the filtration rate for a
suspension feeding organism is
ln
ln
ln
Eq. 10
with units of liters per hour.
Since there were three different classes of volume concentration (CT, CS and CL), and
considering that each trial lasted 4.00 hours with V = 16.40 L, the total filtration rate, FRT, for
example is
4.10 ln
Eq. 11
with units of liters per hour where CTBo is the total, initial volume concentration during a biological
trial, CTB4 is the total volume concentration at four hours during a biological trial, CTD4 is the total
volume concentration at four hours during a control trial, and CTDo is the total, initial volume
concentration during a control trial. Filtration rates (‘small-particle,’ ‘large-particle’ and total)
were scatter-plotted (with SigmaPlot vers. 9.01) as a function of flow speed and each body size
category. Regression analyses were performed for the 3-dimensional plots, with regressions of
the surface described by Eq. 3.
14
Drag Measurements
Drag data were gathered using a procedure proposed by Vogel (1981). First, it is
necessary to introduce the concept of “momentum flux” of a fluid such that
Eq. 12
where F is the momentum flux of a fluid through an imaginary plane of area Sa, ρ is the density of
the fluid, and U is the velocity of the fluid. Notice that the momentum flux has units of force
(Newtons). Applying Newton’s Third Law, if a fluid exerts a drag on a body, then that body must
remove momentum from the fluid at a rate that balances its drag, or an incremental element of drag
is equal to change in momentum flux across incremental area elements upstream and downstream
of the body that is removing momentum so
Eq. 13
where dD is an incremental element of drag, dSu and dSd are the incremental area elements of
imaginary planes upstream and downstream of the body respectively, and Uu and Ud are the
respective upstream and downstream velocities of the fluid through their respective incremental
area elements. Applying the principle of continuity of an incompressible fluid (Vogel, 1981),
Eq. 14
such that Eq. 13 becomes
Eq. 15
and, integrating Eq. 15 yields the drag on a body such that
D    U d (U u  U d )dS d
Eq. 16
where D is drag,  is the density of seawater, Ud is the downstream flow speed, Uu is the upstream
flow speed, and dSd is the incremental area element of the imaginary plane downstream of the
body. Therefore, drag on a body can be measured indirectly by measuring flow speeds at
15
infinitely many points on an imaginary plane downstream of the body while simultaneously
measuring the corresponding flow speeds on an imaginary plane upstream of the body.
The wake of typical ascidians for each of the three body size categories were observed with
fluorescein dye (Sigma Chemical Co. A6877) to determine the position of the sampling plane
where a constant-temperature, thermistor flowmeter (LaBarbera & Vogel, 1976) was placed.
Using the thermistor, flow data was recorded for 30 seconds at a particular position in the
downstream sampling plane (Fig. 4). The thermistor was moved to different positions in the
sampling plane and the recording process repeated until an adequate array of measurements was
determined across the imaginary plane downstream of the ascidian. Another series of
corresponding measurements were made across an imaginary plane upstream of the ascidian in a
similar way until there were sufficient measurements to determine drag during a trial. Flow data
from the thermistor was recorded using a commercially available data logger (Campbell Scientific
CR10X).
Thermistor data was obtained from the data logger and reduced with common statistical
analysis software (SAS Vers. 9.1). The data consisted of, at most, 120 groups of voltage values
recorded every 0.25 seconds over 30 seconds. Using a calibration performed with the thermistor
and the SonTek ADV, the voltage values were transformed to flow speed values using King’s Law
(Brunn, 1996; Al-Deen et al., 1996; Al-Garni, 2007),
Eq. 17
where U is the flow speed, Pd is the voltage, A and B are constants, and n is a constant that is
usually considered to be ~ 0.5 but can depend on probe type, calibration method, and velocity
range (Al-Garni, 2007; Brunn, 1996). More generally, n has been observed to vary between 0.4
and 1.3 in air-flow studies (Al-Garni, 2007), but smaller exponents have been observed in
16
water-flow studies where n is usually in the range 0.25 to 0.3 for flow velocities less than 20 cm/s
and in the range 0.4 to 0.45 for flow speeds between 40 and 50 cm/s (Brunn, 1996). The constants
A, B and n in this study were determined from calibrations to be -1.0159, 2.1443, and 0.25
respectively for water temperatures above 18.0°C and -1.038, 1.9226, and 0.25 respectively for
water temperatures below 18.0°C. These King’s Law calibration constants lie in the reported
range for the velocities in this study. Because measurements were obtained at 120 or fewer points
on the plane (and not an infinite array of measurements), Eq. 16 was transformed to
N
D    U dj (U uj  U dj )S dj
Eq. 18
j 1
where N is the total number of 30 second measurements for each area segment Sdj behind each
ascidian, Udj is a downstream mean flow speed over the 30 second interval, and Uuj is an upstream
mean flow speed over the 30 second interval. The mean of flow values were then found over each
30 second interval and input into Eq. 18 along with  = 1.025 g/cm3 (Weast, 1967-1968) and Sdj =
0.25 cm2, which yields an adequate estimate of the drag on an ascidian of a particular body size at
a particular upstream flow speed, Uu = (1/N)Uuj.
Determination Of Additional Body Size Information
After each experiment, the height of the ascidian (from tank bottom) was measured during
flow. Because it was impossible to image the frontal area of the ascidian in flow, the ratio of final
height to initial height was used to ‘vertically shrink’ the original face-on picture (if the ratio was
less than one) in order to estimate frontal body area (also with ImageJ) during flow. In addition,
after experimental use, each ascidian was dried in an oven at 60ºC for 24 hours, then combusted in
a muffle furnace (550ºC for 3 hrs) to determine ash-free, dry mass (AFDM; range 0.15 and 1.05 g).
17
RESULTS AND DATA ANALYSIS
Relating Body Size Categories
The term, body size, is used with variable meaning in the suspension feeding literature. In
this study, ascidian body was estimated size using ash-free, dry mass (AFDM) and frontal body
area (both in still water and exposed to flow). These variables are closely related however, frontal
body area during flow, Sf, directly links body size in both filtration and drag estimates. There was
a strong power-law relationship between AFDM, SM, and original (i.e. in still water) frontal area
(R2 = 0.8066, P < 0.0001), where SM increases with original frontal area, SO, according to the
relation SM = 0.02420 SO1.304 (Fig. 6). This allometric exponent is not statistically different from
the value of 1.47 (t-test, P = 0.1538) obtained by Sherrard & LaBarbera (2005) for the solitary
ascidians, Corella inflata and Ciona savignyi.
Figure 6: Allometric relationship between ash-free, dry mass and original frontal area (R2 = 0.8066, P < 0.0001)
The relationship between original frontal area and frontal area during flow is more
complex with the additional influence of flow speed (Fig. 7 where the planar regression is
described by the equation Sf = 2.6938 + 0.8156SO – 0.1381U). The minus sign in this relationship
indicates that as speed increases, ascidians increasingly ‘lay over’ in flow so that siphon
orientation is initially perpendicular at slow flow but oriented (or nearly oriented) with flow at the
highest speeds. Intermediate speeds result in intermediate orientations. Fig. 7 also shows that
regardless of flow speed, frontal area in flow is nearly one-to-one with original frontal area.
Understanding these relationships between body size categories (and flow speed) is useful for
interpretation of filtration rate results.
Figure 7: Dependence of frontal area during flow on original area and flow speed (R2 = 0.8833, P < 0.0001)
Filtration Rates
Roughly the same filtration pattern was seen for all three body size categories. Therefore,
filtration rates are only presented as a function of flow speed and frontal area during flow because
drag is also dependent on precisely these variables. Four of the biological trials yielded slightly
negative filtration rates that were treated as zero filtration. Additionally, the choice of an
asymmetrical peak distribution (or other form of unimodal curve) over the simple symmetrical
peak distribution would have been inconsequential. In fact, a modified log-normal response of
filtration rate to increasing flow speed was only a slight improvement of fit to ‘large-particle’
19
filtration while also a slightly worse fit to ‘small-particle’ and total filtration. The resulting
surface fits for ‘small-particle’ and total filtration rates yielded R-squared values less than 0.3.
This is consistent with increased variation in the data for those scatter plots. Better fits occurred
for ‘large-particle’ filtration rates (R2 ≈ 0.6). For both total and large-particle filtration, there was
a highly statistically significant relationship (P < 0.01) between dependent and independent
variables. This relationship was not statistically significant for small-particle filtration, although
the P-value for the regression was less than 0.1. Specific R-squared values and P-values are given
in Table I.
Figure 8: Response of a.) ‘small-particle’ b.) ‘large-particle’ and c.) total filtration rate to increasing flow speed and
frontal area during flow
20
Total filtration rate (FRT) seems to be largely driven by large-particle filtration rate (FRL)
with some slight modification from small-particle filtration rate (FRS). Therefore FRT, like FRL,
decreases with increasing flow speed, but FRT decreases less rapidly. The plotted data show a
continual decrease of FRT and FRL with flow speed, which differs from the expected unimodal
curve (Fig. 2). However if the Gaussian curve is a good representation of FR, then there are
insufficient data to show the peak which would likely exist near the slow flow speed. Such is the
case since the peak was constrained to be positive as seen in Table I. A unimodal response to
flow speed is seen for FRS, with a peak near the moderate flow speed. Specific peak values are
reported in Table I where σp is the standard error of the peak value.
Particle selectivity is evident in Fig. 8. Upon comparison of the larger FRL values to the
consistently smaller FRS values, Styela plicata appears to select large particles more than small
particles at each flow speed. Flow appears to have differing effects on filtration of different size
particles and can best be described by the peak position. As flow increases from slow to moderate
speeds, large-particle filtration drops dramatically while small-particle filtration increases slightly.
Both large- and small-particle filtration appears to be suppressed at high flow speeds.
The relationship between FR and body size is consistent regardless of how body size is
defined (AFDM vs. projected area in still water or in flow). The allometric exponents that
describe the relationship between FR and the three measures of body size are reported in Table I
where σb is the standard error of the exponent, b. In general, the allometric exponent, b, is lower
for small-particle filtration and total filtration rates, than for large-particle filtration rates.
Moreover, values of b are also lower for the relationship between FR and SM than for the same
relationship using projected area to measure body size. This can be partially explained by the
relationship between AFDM and projected area (SM = 0.02420 SO1.304).
21
Table I: Important Results From The Regressions Of Particle-size-dependent Filtration Rate vs.
Flow Speed And Body Size
Body Size Category
FRS
AFDM
FRL
FRT
Original
FRS
frontal
FRL
area
FRT
Area
FRS
during
FRL
flow
FRT
R2
P-value*
b ± σb**
Up ± σp***
0.152
0.579
0.270
0.0779
< 0.0001
0.0045
0.267 ± 0.188
0.579 ± 0.180
0.305 ± 0.182
11.9 ± 1.4
~0
2.83 ± 9.16
0.160
0.585
0.286
0.0653
< 0.0001
0.0030
0.436 ± 0.278
0.812 ± 0.253
0.511 ± 0.254
12.3 ± 1.5
~0
3.36 ± 9.00
0.145
0.567
0.254
0.0905
< 0.0001
0.0070
0.365 ± 0.280
0.745 ± 0.257
0.361 ± 0.267
12.8 ± 1.7
~0
2.83 ± 11.6
*Probability that a random distribution will produce similar results as described by Eq. 3
**Allometric exponent (and associated standard error) of body size as it relates to filtration rate
***Flow speed where peak filtration occurs and the associated standard error
Drag On Ascidians
S. plicata are not bluff bodies. Therefore, drag on the organism does not increase
precisely with the square of flow speed. Vogel (1984) introduced a way of comparing the drag
coefficients of flexible organisms to those of bluff bodies. If drag is divided by the square of flow
speed, Eq. 4 becomes
Eq. 19
where SSD is what is known as speed-specific drag. Recall that for a bluff body, CD is typically
constant, and a plot of SSD versus U will yield a horizontal line. However for a flexible body, a
plot of SSD versus U should show deviations from the horizontal ‘base’ line of a bluff body. This
‘additional variation’ with flow speed appears in the drag coefficient because Eq. 5 is often true for
flexible bodies, and substituting Eq. 5 into Eq. 19 with Re = ρlU/µ, then
Eq. 20
and in short, SSD is proportional to Ua. For the purposes of comparison between flexible bodies,
Vogel (1984) expressed the exponent, a using the variable E, because Eq. 5 might not always be
22
true for a body depending on flow regime and the body itself. These E-values are usually
negative and therefore an indication of how well a flexible body can reduce the rate of increase in
drag as speeds increase. Further variation in SSD due to body area can be accounted for by simply
plotting the log of drag coefficient versus the log of Reynolds number. The slope of the resulting
trend will be the exponent a, the E-value.
Surprisingly, an E-value of -1.8 for the non-flexible wax ascidians was determined in the
control trials. Because CD consistently decreased with increasing Reynolds number in the
controls (Fig. 9), I suspected that there was an apparent drag-dampening effect due to my method
and apparatus that would also be present in the biological trials. Therefore a correction factor of
9.4 x 10-7 Re1.8 was multiplied to the control drag data, and fit Eq. 4 to the
corrected control data (Fig. 10) yielding a drag coefficient estimate of 0.98 ± 0.05.
Figure 9: Drag coefficient vs. Reynolds number for ‘bluff-body’ wax ascidians to determine drag correction
(R2 = 0.67, P < 0.0001)
23
Figure 10: Corrected drag as a function of flow speed and frontal area for wax ascidians (R2 = 0.86)
The Reynolds number correction was determined for bluff bodies where the characteristic
length does not vary with flow speed. Therefore, the Re correction could not be applied to the
biological drag data until determination of what I termed the ‘bluff Reynolds number.’ The bluff
Re is the Reynolds number a flexible object would have if it remained upright in flow so as not to
change its characteristic length. After the bluff Re correction, drag on ascidians appears to
increase somewhat linearly with the projected frontal area during flow, and drag increases with
less-than-the-square of flow speed as expected (Fig. 11). Fitting D
estimate of -0.43 ± 0.20 for the range 1000 < Re < 10000.
24
SfU2+E, yielded an E-value
Figure 11: Corrected drag as a function of flow speed and frontal body area during flow for S. plicata
(R2 = 0.83, P < 0.0001)
25
DISCUSSION
I have presented measurements of drag and particle-size-dependent filtration rates for the
ascidian Styela plicata as responses to varying body size and ambient flow speed in a flume.
Below I discuss in further detail the possible reasons why drag may be producing the expected
results and how these findings compare to those of other investigations of suspension feeders.
Filtration Response To Increasing Body Size
Reports of relationships between ascidian filtration rate and body mass are consistently
allometric. Those exceptions not listed in Table II include the case of Draughon (2009) who
found no relationship between filtration rate and total wet mass of Styela plicata, and the study by
Petersen & Svane (2002) which showed no relationship between filtration rate and total dry mass
of a conglomerate of species (Clavelina lepadiformis, Ciona intestinalis, Corella
parallelogramma, Ascidia virginea, Boltenia echinata, Molgula manhattensis, and Pyura
tessellata). Petersen & Svane (2002) suggest the lack of correlation to be due to their particular
methods concerning mass determination. Additionally, differences in tunics among species could
increase variation of total mass. The lack of correlation found by Draughon (2009) cannot yet be
commented on for need of further details from the author including materials, methods and
analysis. Allometric exponents in Table II approximately equal to one are surprising and
considered to be due to a lack of low-mass specimens (Klumpp, 1984) or due to non-isometric
growth of the tunic compared with total mass (Randløv & Riisgård, 1979). Holmes (1973)
determined small allometric exponents in still water, and higher exponents in running water (with
the exception of some small exponents in running water for Ascidiella aspersa). The flow speed
of the running water regime cannot be precisely determined from Holmes’ data but is likely no
more than 5 cm/s (estimate from volumetric flow). The low exponents were suspected to result
from animal disturbance. This could be true for some of the results for Ascidiella aspersa, but the
higher exponents in running water could be an indication of increased filtration from increased
seston flux.
Table II: Comparison Of Allometric Exponents In The Literature Relating FR To Body Mass
Species
Pyura
stolonifera
Ascidia
atra
Ciona
intestinalis
Animal Food-particle
size range
size range
Allometric
exponent
0.1-19 g
0.3-13 g
10-160 g
6-50 µm
No feeding
0.7
1.08
0.87*
0.05-0.18 g
4.8-8 µm
0.68
Ciona
intestinalis
Ascidiella
aspersa
Ascidiella
aspersa
0.03-0.4 g
1-7 µm
0.84
Styela
clava
0.1-1.0 g
Styela
plicata
1.2-1.9 g
7-8 µm
0.415
0.617
0.646
0.934**
Styela
plicata
0.15-1.05 g
1.25-6.03 µm
6.03-100 µm
1.25-100 µm
0.267
0.579
0.305
0.04-0.8 g
0.1-0.4 g
0.1-1.0 g
Methods/conditions Source
Indirect, flow-through
mL/min for g dry mass
Indirect, flow-through
cm3/min for g wet mass
Indirect, static
mL/min for g dry mass
Indirect & direct, static
mL/min for g dry mass
1.05
8-12 µm
0.45
0.383-0.607
Indirect, static
Direct, flow-through
mL/min for g dry mass
Indirect, static
Direct, flow-through
mL/min for g dry mass
Indirect, static
L/h for g dry mass
Indirect, flume
L/h for g ash-free,
dry mass
Klumpp
(1984)
Hecht
(1916)
Petersen &
Riisgård
(1992)
Randløv &
Riisgård
(1979)
Holmes
(1973)
FialaMédioni
(1978)
Present
study
*Determined by Randløv & Riisgård (1979)
**Calculated from the data of Fiala-Médioni (1978)
The allometric exponent of 0.579, relating ‘large-particle’ filtration to body mass, is not
statistically different from the expected value of 0.667 (t-test, P = 0.629). Estimated allometric
exponents for small-particle filtration and total filtration were both significantly different than
0.667 (t-test, Small: P = 0.0388; Total: P = 0.0526). Indeed there is much variation in reported
exponents in Table II, and some suggest that this variation not only reflects the differences among
27
species but also reflects differences in experimental methods used to determine allometry
(Klumpp, 1984; Randløv & Riisgård, 1979; Riisgård, 2001). The reason for my low exponents
would be that the allometric fit to varying body size is across the entire range of flow speeds, most
of which tend to lower filtration rate. When the confounding influence of flow speed on the
relationship between body size and FR was removed by calculating b for only the slow flow
treatments, estimates of 0.519 for small particles, 0.646 for large particles, and 0.416 for total were
obtained. These values are much closer to the expected 0.667; an indication that flow speed has a
strong influence on the allometric filtration response to body size.
Filtration Response To Increasing Flow Speed
Particle-size-dependent filtration rates are clearly suppressed at high flow speeds.
Particle overloading due to increased particle flux is an unlikely suppression mechanism, because
this should be associated with increased siphon closure and squirting during intense flow, which
was not observed. Also, no additional mucus strings were observed in the flume, which is also
indicative of increased squirting. In fact, very little fecal matter was observed after the ascidians
had acclimated to intense flow. This observation may indicate decreased digestion of material
from the AIWW, although it is also possible for fecal matter to break up at high flow speeds. A
more plausible explanation may be the development of adverse pressure gradients across the
siphons during excessive flow.
The Gaussian function of flow speed as a description of filtration rate, although arbitrary,
proved to be quite useful. Interestingly, maximum filtration of small particles occurs at higher
speeds (Up ≈ 12 cm/s) than does filtration of larger particles (Up ≈ 0 cm/s). I suspect enhanced
filtration of large particles occurs at low speeds due to enhanced capture of large particles at the
incurrent region of the inhalant siphon. This particle-size effect also enhances the allometry of
28
FRL with body mass as seen in Table II. Further, higher R-squared values for the surface fits to
FRL indicate the influence of flow speed on filtration of large particles is far greater than filtration
of small particles. Whether this change in particle-size-dependent filtration is due to active
selection by the animal or changing particle dynamics in changing flow regimes, the result is that
the total filtration response to increased flow gradually decreases over a wide range of speeds so
that feeding remains somewhat steady until flow speeds become too great.
Few studies investigate the response of filtration rate to increasing flow speed, so
additional studies are discussed below describing the response of growth rate to increasing flow
speed. The most commonly studied suspension feeders are bivalves and bryozoans.
Bivalves
The bay scallop, Argopecten irradians, showed similar responses of growth to increasing
flow speed. Kirby-Smith (1972) found that growth rate falls off rapidly from ~ 0.5 cm/s to 12.5
cm/s after which, nearly no growth occurs. In another study, this bay scallop’s growth rate
appears to increase steeply from 0 to 1 cm/s and then fall off gradually from 1 to 15 cm/s (Cahalan
et al., 1989). Eckman et al. (1989) determined that growth rate decreased steadily from 0 to 17
cm/s after which, there was minimal growth. In contrast, the growth rate of the oyster,
Crassostrea virginica, increased steadily within the flow range under investigation (0 to 7 cm/s),
but is suspected to be inhibited with increasing flow speed at some point after 7 cm/s (Lenihan et
al., 1996). The growth rate of the giant scallop, Placopecten magellanicus, appeared to increase
steadily between flow speeds of 0 and 5 cm/s, after which growth rate dramatically fell off up to
speeds of 18 cm/s (Wildish et al., 1987). Additionally, filtration rates of this giant scallop
appeared to fall off steadily between flow speeds of 10 to 80 cm/s (Wildish et al., 1992; Wildish &
Saulnier, 1993) depending on seston concentration, which led Wildish et al. to suspect that
29
inhibited growth is due to inhibited filtration. This may also be true of S. plicata based on the
current investigation and personal observations along the floating docks of the AIWW. Where
docks are parallel to flow and vary in distance from shore, the average size of S. plicata decreases
with increasing distance from shore. The increased distance corresponds to increased flow speed
(as determined by a Nortek Vector ADV) along the docks. Most of the natural flow speeds,
created between tides, were replicated in the lab where filtration was inhibited in high flow.
Supposing there is also a strong connection between filtration rate and growth rate for S. plicata,
inhibited growth rate does not necessarily place a limit on body size. However, since S. plicata
typically only live for nearly a year, inhibited growth rate could limit body size before natural
mortality. It is therefore likely that body size is limited along the outer docks by an
as-yet-undetermined mechanism (or mechanisms, discussed later) that limits filtration and thus
growth and/or drag forces that lead to dislodgement.
Bryozoans
Bryozoans are active suspension feeders that are usually colonial. Membranipora
membranacea showed steadily decreasing potential growth rate (temporal difference in circular
area where radii were considered maximum distance from ancestrula to colony edge) over the flow
speed range 0 to 16 cm/s (Eckman & Duggins, 1993). The encrusting cheilostome Parasmittina
jeffreysi exhibited decreased growth rate between 4 cm/s to 18 cm/s, consistent with the findings of
Eckman & Duggins (1993), but showed an increase around 24 cm/s (Genovese & Witman, 1999).
If the response of filtration rate to flow speed is responsible for the response of growth rate to flow
speed, this would be one of the only anomalous findings.
Concerning particle-size selectivity with increasing flow speed, Okamura (1987) observed
Bugula neritina ingested more large particles than small particles at slow flow (1 to 2 cm/s), and
30
while this pattern of selection did not change, ingestion of large particles decreased and ingestion
of small particles increased around flow speeds of 10 to 12 cm/s. This observation concurs with
the present study for S. plicata, but Okamura also found the opposite for a smaller species of
bryozoan, B. stolonifera. This species ingested more small particles than large particles at slow
flow, but at higher flow speeds, more large particles were ingested. Okamura suggested the most
likely explanation for this anomaly is a switch from ciliary pumping to increased tentacular
activity for the smaller species. These results were observed when bryozoans were fed
single-sized latex beads during a trial. However, when fed evenly mixed solutions of the
different-sized beads, both species showed increased ingestion of large-particles and decreased
ingestion of small-particles around flow speeds of 10 to 12 cm/s while there was consistently more
selection of large particles at both flow speeds (Okamura, 1990). In addition to different feeding
structures and behavior between colonial bryozoans and solitary ascidians, one possible
explanation for the difference between Okamura’s observations and those in this study is that I
suspect large-particle filtration was greatly enhanced at slow flow speeds for S. plicata by
enhanced capture of large particles at the incurrent region of the inhalant siphon, whereas
Okamura observed no significant deposition of particles at either flow speed.
Influence Of Drag
At this point, it is necessary to separate the influence of drag on FR with increasing body
size and increasing flow. Allometry dominates the filtration response to increasing body size at
all flow speeds, but the height of the curve (as determined by the exponent, b) decreases in a flow
dependent manner. This indicates that scope for increasing filtration rate in larger ascidians is less
in higher flow than in slow flow. The influence of drag on FR, specifically with increasing flow,
is more unfavorable (squared speed relationship to drag as opposed to a linear body size relation).
31
Therefore, drag could likely be responsible for the flow-dependent suppression of filtration in the
following ways. Ascidians were clearly reconfigured in flow as a result of drag forces.
Deformation of internal feeding structures is possible as the ascidian is bent, and this could reduce
filtering efficiency. Reconfiguration also implies alteration of siphon orientation. Knott et al.
(2004) found that model ascidians utilized ambient flow to filter more-so at the orientation with
flow (laid-over) than at an upright orientation, perpendicular to flow. Further, this reliance on
passive flow was shown to increase feeding in Pyura stolonifera (Knott et al., 2004). This finding
is contrary to my results where feeding was increasingly suppressed from upright to laid-over
orientations. However, because the orientation investigation of Knott et al. was performed at a
single flow speed, and during this study, orientations were altered by varying flow, it is still
unclear whether changing siphon orientation from upright to laid-over will increase adverse
pressure gradients between the siphons or if the development of adverse pressure gradients is a
result of simultaneously increasing flow and laying over.
E-values describing flexibility of organisms in flow are rare in the literature. The
flexibility of S. plicata compares best with that of a streamlined body in the same Re range (-0.5;
Vogel, 1984). Other marine organisms in the same Re range are seemingly more flexible. The
sea pen, Ptilosarcus gurneyi, was determined to have an E-value of -1.14 (Best, 1988), and
E-values of -1.28 and -1.66 were respectively determined for the hydroid, Abietenaria rigida
(Harvell & LaBarbera, 1985), and two species gorgonian, Pseudopterogorgia acerosa and P.
americana (Sponaugle & LaBarbera, 1991). Nevertheless, it is reasonable that streamlined
bodies are better adapted to ambient conditions than bluff bodies, and this adaptation may afford S.
plicata some advantage over non-flexible suspension feeders (Vogel, 1984; Koehl, 1984; Denny et
al., 1985; Koehl, 1999).
32
Summary
The particle-size-dependent filtration rates of S. plicata are allometric with respect to body
size and unimodal with respect to flow speed. Allometry with body mass is well established in
the literature, and the allometric exponents reported in this study are comparatively lower than
those found in other investigations. This was shown to be due to the confounding adverse effects
of increasing flow speed. The likely mechanisms for flow-dependent suppression of filtration
rate include deformation of internal feeding structures due to drag, and/or increased adverse
pressure gradients between the siphons as a result of drag or flow itself.
Interestingly, maximum filtration occurs at moderate flow speeds (~ 12 cm/s) when this
ascidian filters particles in the range 1.25 to 6.03 µm. Maximum filtering of large particles (6.03
to 100 µm) occurs at low flow speeds (~ 0). The most likely reason for this shift in maximum
filtering of different size particles is enhanced filtration of large particles at low speeds due to
enhanced capture of large particles in the incurrent region of the inhalant siphon.
These findings will be very useful to those interested in bioremediation since peak
filtration of bacterial-size particles appears to occur at different flow speeds than peak filtration of
particles the size of large phytoplankton. These experiments could be carried out again in more
depth to gain a better understanding of the precise flow speeds where peak particle-size-dependent
filtration occurs. Additionally, investigations into the relationship between filtration rate and
growth rate with flow should also be performed for this ascidian and other suspension feeders.
Optimal filtering conditions may differ in flow regime for fouling ascidians and other suspension
feeders. If true, this knowledge could aid those who commercially culture marine organisms.
The connection between life and environment is progressively made clearer through
studies of how feeding is affected by ambient hydrodynamic conditions. Further understanding
33
of the feeding response to those conditions has been gained with additional regard to food-particle
size and interactions among each of the biological and hydrodynamic variables.
34
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