Using Settling Velocity to Model Particle Stickiness in a Mesocosm

1
Using Settling Velocity to Model Particle
Stickiness in a Mesocosm
L. Alex Kahl, Oscar Schofield Coastal Ocean
Observation Laboratory, Environmental Biophysics
and Molecular Ecology Laboratory
Institute of Marine Coastal Sciences, Rutgers
University, New Brunswick, NJ USA
ABSTRACT
CONCLUSIONS
RESULTS
The probability of adhesion of two particles upon
collision, particle stickiness (sticking
efficiency, ?), is one of the principle factors
affecting the interaction and subsequent flux of
particles in the ocean. However, parameterization
and accurate estimation of particle stickiness is
difficult. Conventional determination of particle
stickiness relies on changes in the Particle Size
Distribution (PSD) through the use of a
horizontal Couette device having
well-characterized shear. This technique requires
that the velocity of the fluid within the Couette
device be much larger than the range of possible
settling velocities of the interacting particles.
Under low energy levels in a mesocosm experiment,
the effects of the loss of particles due to
settling will affect the PSD such that such that
current models for directly estimating particle
stickiness are incomplete. We conducted mesocosm
experiments, with phytoplankton monocultures, in
a 1500 liter rotating annular flume. The annular
flume has near laminar flow and our mesocosm
experiments were conducted with a mean shear of
0.0946/s. Variability of compared estimates of
mesocosm particle stickiness as determined in
both a Couette device and directly from the flume
could not be explained using traditional models.
This variability can be explained by loses from
the PSD due to the settling of particles. Our
experiments show that the vertical loss of
particles in the low shear mesocosm is an
important factor that contributed to the
variability of our direct estimates of particle
stickiness. To improve direct estimates of
particle stickiness in mesocosm experiments, we
have developed a model that utilizes measurements
of the PSD and the settling velocity of particles
within the mesocosm. Our model is derived from
the basic equations for algal cell aggregation as
presented in Jackson 1990. Initialization of
the model with the PSD and average particle
settling velocity produces reasonable estimates
of particle stickiness, compared to previously
published values. The use of our model, when
combined with the low shear of our mesocosm
allows for estimates of particle stickiness with
minimal exposure of fragile marine particles to
the high energy levels inherent in conventional
techniques.
The mesocosm bloom remained healthy for
approximately 14 days Figure 4a. Once the bloom
began to decline, our model estimated two peaks
in algal cell sticking efficiency. One peak
occurred at day 16 and another peak occurred at
day 27. The modeled sticking efficiency during
and between these peaks ranged from 0 to 0.88
Figure 4c. In both cases, an increase in
sticking efficiency was followed by an increase
in aggregation of algal cells. Between days 22
and 24, the increase in algal cell aggregation
propagated downward from 20 cm to 2 cm above the
bottom of the flume Figure 4b. Because the
shear in the flume is primarily caused by the
counter-rotating top, aggregate re-suspension
and/or externally forced break-up during
sedimentation was not observed and was assumed to
be minimal. Additionally, because aggregated
algal cells settle at a higher rate than do
individual cells, the majority of algal cells
near the shear-generating top of the flume are
likely to be individual cells.
Until now, In situ and laboratory estimates of
sticking efficiency, or ?, on phytoplankton have
been made using a combination of both specialized
shearing devices and particle size counters.
Previous techniques have utilized levels of shear
much higher than is observed in much of the ocean
Figure 6. Such methods are convenient because
they allow estimations of ? to be made while only
accounting for the fluid shear collision
function. However, aggregation over the worlds
oceans is highly dependent on differential
sedimentation. Annular flumes allow a novel
method for testing our model of sticking
efficiency. This is particularly important
because our model incorporates the differential
sedimentation collision function. One
short-coming of our method is that the water
column depth of our annular flume is less than
one half of a meter. This relatively short
settling path length prevents the formation of
larger aggregates. For example, the level of
energy in our experiment was comparable to the
levels observed by Riebsell 1991, 1992 and
Kiørboe 1998. However, we did not observe algal
cell aggregates of similar to size to their
(Riebesell and Kiørboe) field measurements. While
the oceanic particles have many meters over which
differential sedimentation collisions may occur,
our experiment only allowed for 42cm of
differential sedimentation interactions. Similar
observations depicting the role of differential
sedimentation as a major coagulation mechanism
have also been observed at density
discontinuities MacIntyre, 1995.
Particle sticking efficiency or , ?, is the ratio
of successfully adhesive particle collisions to
the total number of particle collisions which
result from physically mediated interactions
Equation 1. Historically, ? is difficult to
measure and quantify. Quantitatively, ? acts as a
probability coefficient for each collision
function. Despite its importance in coagulation
models, accurate estimation and parameterization
of ? is quite elusive in systems that are both
physically and biologically mediated
In the form of Equation 2, we can solve for ? by
directly measuring each of the terms in the
numerator, and modeling each of the terms in the
denominator. The ratio of measured changes in the
Particle Size Distribution (PSD) to modeled
changes in the PSD is the mean sticking
efficiency of the particles under observation.
INTRODUCTION
While the physics of particle interactions have
been well defined for more than a century, the
affect of biological processes in such
interactions is ill-defined. One of the most
important arenas of biologically and physically
mediated particle interactions is the aggregation
and sedimentation of algal cells or
phytoplankton. Sedimentation of algal aggregates
is a major component of the global carbon cycle.
As a result of the significance of aggregation to
the global carbon cycle, an accurate estimate of
the fundamental mechanisms governing algal cell
aggregation is necessary for improving our
understanding of global carbon fluxes. The
least-well understood component of bio-physical
oceanic particle aggregation is the sticking
efficiency of the particles. The sticking
efficiency, or stickiness, of algal cells is a
direct result of cellular exudation.
Parameterization of algal cell sticking
efficiency is difficult because of its dependence
on cellular processes Alldredge, 1995 Passow,
1995 Prieto, 2002. Previous estimates of
sticking efficiency vary by more than an order of
magnitude Dam, 1995. Additionally, all previous
estimates of algal cell sticking efficiency have
been made under moderate to high shear
conditions.
Figure 4
To solve for the denominator, we modified
Jacksons 1990 sectional method to find a
numerical solution for the PSD that would result
from all abiotic, particle interactions, without
loss due to settling. Each term of the numerator
was determined experimentally. In the numerator,
the change in the PSD over time and the growth
rate were both determined using the measured PSD.
The settling term was determined by calculating
the volume balance between three discrete depths.
Our volume balance calculations followed the
method of Jackson et al. 2005 and utilized
empirically derived algal cell density data
Waite and Nodder, 2001.
? algal stickiness i, j algal cells of size i
and j n number of bins in PSD dt time between
measurements C concentration of algal cells w
vertical velocity of algae ? specific growth
rate z vertical distance ? used to account
for same size algae collision and removal from
size bin

• Sticking efficiency, is driven by a combination
  of biological and physical factors and is
  extremely variable during a phytoplankton bloom
  (a range of 0-0.88 was observed). Values
  increased as the bloom began to decline.
• Increasing particle sticking efficiency is
  followed by an increase in the number of
  aggregates in the water column.
• Sticky aggregates sink quickly, and the remaining
  cells tend to have a lower sticking efficiency.
  Therefore ? can vary on the timescale of a day.
• Differential sedimentation may play a larger role
  in algal cell aggregation kinetics than
  previously thought. This significantly impacts
  experimental methods that are used to measure ?.

EXPERIMENTAL SET-UP
THEORY
We used a rotating annular flume Images 56
with an outer diameter of 3.99 meters. The flow
within the annular flume is driven by a counter
rotating top, relative to the bottom. The channel
of the flume is 30 cm wide. During the
experiment, the flume had a water depth of 42cm.
To simulate a phytoplankton bloom in the annular
flume, we grew a batch culture of Thalassiosira
pseudonana in 1500 liters of f/10. The mean
irradiance in the flume during the experiment was
1.036x1020 Quanta/m2/sec (172.1 ?E/m2/sec). The
flume temperature was maintained at 170.3 C via
a titanium heat exchanger located in the
counter-rotating top of the flume. The flume flow
was characterized using a 2-axis Laser Doppler
Velocimeter (LDV) Image 1.
Particle coagulation models are based on physical
principles that have been well-tested and
verified since von Smoluchowskis formulations of
particle interactions von Smoluchowski, 1917
during the early part of the 20th century. The
application of a physics-based particle
coagulation model to cellular aggregation
Jackson, 1990 has proven to be a reasonable
approximation of a phenomenon that is in large
part controlled by biological processes. The
processes directly responsible for cellular
aggregation are 1) particle size, 2) fluid shear
(?), 3) sticking efficiency of cells (?) and 4)
organism growth rate (?). Subsequently, each of
these factors are included in Jackson, and others
Ackleh, 1997 Ruiz, 2002 cellular aggregation
model. Two of these three parameters (?, ?) are
biologically mediated in models of algal cell
aggregation.
There are three mechanisms of particle
interaction governing the behavior of algal cell
aggregation. Brownian motion, fluid shear, and
differential sedimentation. Each of these
mechanisms can be represented mathematically by a
collision function, also known as an interaction
kernel. Schematically, a collision function (?)
represents the probability of an interaction
mechanism of a particle (of size i) with a
particle (of size j). Following Hunts 1980
dimensional analysis of each of the three
collision functions, differential settling is the
principle mechanism of particle interaction
within our mesocosm (Fig. 1). In our model, we
follow the assumption of Jackson 1990 that one
collision function dominates the interaction
between two particles. Another assumption made in
modeling of coagulation is that the collision
function defines the interaction between no more
than 2 particles at a time
After the sticking efficiency peaked, the number
of individual cells decreased due to the
formation of larger algal cell aggregates
Figures 5a-d. Accordingly, there was an
increase in algal cell aggregates as indicated by
the increase in volume at larger ESDs. The
formation of algal cell aggregates had the effect
of decreasing the slope of the PSD. Prior to the
major decline of the bloom between days 5 and
25, the mesocosm bloom remained optically dense
Images 3 4. As the bloom declined, and the
PSD began to shift towards fewer but larger
particles, algal cell sedimentation was apparent
Images 5 6. The transition from the visually
disparate conditions of Images 3 and 5 occurred
between days 24 and 27 Figures 5a 5b.
Using the LDV, we measured flow velocities at 207
points across the flume channel. Flow velocity
was measured in the directions vertical and
along channel. Our 207 points were spaced at a
maximum distance of 1cm in the center of the
flume channel, and at a minimum distance of 2 mm
near the flume walls. Due to instrument
limitations, we were only able to use the LDV to
determine fluid shear up to 25 cm above the flume
bottom Figure 3. The mean shear of the flume
cross section shown in Figure 3 is 0.09 s-1.
Compared to previous lab studies, we were able to
achieve a low shear rate Figure 6.
Additionally, the principle location of shear
generation in the flume is from the
counter-rotating top. As a result, physical
disaggregation of downward settling algal flocs
is unlikely.
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Our model assumes that the initial particle
diameter has an approximate diameter of 5?m
because this is equal to the Equivalent Spherical
Diameter (ESD) of our model species (the diatom
Thalassiosira pseudonana). Figure 1 depicts the
collision function for interactions occurring
between a primary particle (our model organism)
range of sizes of secondary particles. In the
environment of our mesocosm, differential
sedimentation is the dominant collision function
during coagulation. Due to increasingly similar
settling velocities, the differential
sedimentation collision function is minimized as
the difference between the size of the two
particles decreases. However, when fluid shear is
the dominant collision function in a coagulation
model Figure 2, differential sedimentation
dominates interactions between particles of
increasingly disparate sizes. Due to the size of
our model organism, Brownian motion collision
functions are not significant.
The annular flume was sampled by hand once daily
(except two multi-day gaps) at 3 depths. The
flume was sampled using a thin piece of PVC with
3 mounted 50 ml Falcon tubes Image 2. The
falcon tubes were modified such that both ends of
the tube require a cap. The tubes were mounted on
the PVC such that they always sampled at 2 cm, 20
cm, and 40cm above the flume bottom. Due to the
fragile nature of algal aggregates, extreme
caution was taken during extraction of the
samples from the flume. Upon removal from the
flume, the PSD was characterized using a Beckman
Coulter Counter Multisizer II with a 100?m
orifice tube. Additionally, the number of
individual cells was determined by vigorously
shaking a sub-sample from each depth and
characterizing the subsequent PSD. The
disaggregated cell counts were used to estimate
1) the specific growth rate of the culture and 2)
the number cells bound within aggregates. As a
measure of culture health, photosynthetic
efficiency of PSII was measured with a Fast
Repetition Rate Fluorometer (FRRF).
Additionally, in the days after each peak in
sticking efficiency, there was an increase in the
bulk photosynthetic efficiency of PSII (Fv/Fm)
Figure 4a. The two increases in Fv/Fm that each
followed periods of peak sticking efficiency,
likely occurred for two different reasons. Indeed
both increases in Fv/Fm occurred due to the
removal of more sticky, less healthy cells from
the water column. However, the first increase was
a result of the remaining, non-aggregated
Thalassiosira pseudonana cells relatively high
Fv/FM. Conversely, the second increase in Fv/Fm
was due to succession of our diatom bloom by
another phytoplankton species of smaller ESD
Figures 5b-d.
ACKNOWLEDGEMENTS
The authors would like to thank the Office of
Naval Research and the National Science
Foundation for their support. We also thank Kay
Bidle, Paul Falkowski, Zoe Finkel, Matt Oliver,
and Tuo Shi for their ideas and feedback. And
special thanks to Stan Cho, and Char Fuller,
John Hencken, Bryan Kirk, Elizabeth Leonardis,
Andrew Mutz, Piotr Nawrot, Hugh Roarty, and Kevin
Wyman for their help during the experiment.