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Authors: Simon Dennington, Ponkrit Mekkhunthod, Martin Rides, David Gibbs, Maria Salta, Victoria Stoodley, Julian Wharton and Paul Stoodley
Published 4 September 2015 • © 2015 IOP Publishing Ltd • Surface Topography: Metrology and Properties, Volume 3, Number 3
Frictional drag from the submerged hull surface of a ship
is a major component of the resistance experienced when moving through
water. Techniques for measuring frictional drag on test surfaces include
towing tanks, flow tunnels and rotating discs. These large-scale
methods present practical difficulties that hinder their widespread
adoption and they are not conducive to rapid throughput. In this study a
miniaturized benchtop rotating disc method is described that uses test
discs 25 mm in diameter. A highly sensitive analytical rheometer is used
to measure the torque acting on the discs rotating in water. Frictional
resistance changes are estimated by comparing momentum coefficients.
Model rough surfaces were prepared by attaching different grades of
sandpaper to the disc surface. Discs with experimental antifouling
coatings applied were exposed in the marine environment for the
accumulation of microbial fouling, and the rotor was capable of
detecting the increased drag due to biofilm formation. The drag due to
biofilm was related to an equivalent sand roughness.
fouling is the undesired accumulation of living organisms on ships'
hulls and other manmade structures when these are immersed in the sea.
Such fouling builds up inexorably on untreated ships' hulls and greatly
increases frictional drag resulting in higher fuel consumption with an
inevitable corresponding increase in carbon dioxide gas emissions. The
economic consequences are severe, but difficult to quantify. The overall
cost associated with hull fouling for the US Navy's mid-sized DDG-51
class destroyer fleet (22% of the navy's wetted hull area) was estimated
by a unique study in 2010 to be $56M per year (Schultz et al, 2011). A recent study (Eyring et al, 2010)
suggest that oceangoing ships consumed between 200 and 290 million
metric tons of fuel in the year 2000, therefore at a present fuel cost
of approximately $600 per tonne, each 1% increase in fuel consumption of
the world's fleet equates to an expenditure of more than $1 billion.
The attachment of marine organisms to ships' hulls also facilitates
their translocation around the globe, and unwanted 'alien' species
transported in this way can threaten biodiversity and cause real
economic damage when they become established in new habitats. The costs
of controlling the invasive zebra mussel in North America have been
close to $1 billion over 10 years (De Poorter et al, 2013).
antifouling paints are used on ship hulls below the waterline to combat
the attachment of marine organisms. Traditional toxic antifouling
paints containing biocidal ingredients (such as copper oxide and
approved organic biocides) have proven very effective at preventing the
attachment of fouling organisms. Non-toxic foul release coatings (FRC)
are increasingly being used to avoid the problematic release of biocides
into the marine environment. FRC have low energy ('non-stick') surfaces
that macro-fouling organisms such as barnacles and algae (seaweed) have
difficulty in adhering strongly to, so that these loosely-attached
organisms are removed by hydrodynamic forces when a ship reaches an
operational speed of around 10 knots (Swain, 1999).
However, attached microbial fouling deposits known as biofilms, more
commonly referred to as 'slime' by ship owners, form readily on FRC and
are not removed even when a ship is under way at 30 knots (Candries et al, 2001). The composition of marine biofilms has been reviewed (Salta et al, 2013) and shown to consist largely of diatoms and bacteria, with pennate diatoms such as Navicula sp., Nitzschia sp. and Licomophora
sp. dominating the biofilm. The increase in frictional drag due to even
moderate biofilm coverage is considerable and has been estimated at 5%
to 25% after 40 days and 240 days service respectively (Townsin, 2003). Simple and rapid methods of measuring the drag due to biofilm are required.
the actual speed reduction of ships in service due to frictional drag
is difficult, owing to the many challenges of collecting performance
data and the lack of suitable controls. Therefore small-scale comparison
methods using representative test surfaces must be used. Schulz
(Schultz and Myers, 2003) has compared three of the most common testing methods, namely towing tank tests, flow tunnels and rotating discs.
tank tests operate by measuring the resistance to flow of a flat plate
that is dragged through a large tank of water at speeds that simulate a
moving vessel; the towing tank at the United States Naval Academy
Hydrodynamics Laboratory described by Schultz (Schultz and Myers, , 2003) operates at up to 7.6 m s-1
(14.8 knots) velocity. To reach this speed and to enable sufficient
data to be gathered the length of the tank is 115 m. Towing tank tests
are complex to carry out and each run is time-consuming and expensive.
flow tunnels the test surface is held static and water flows rapidly
over it in a closed circuit system. The flow tank described by Schultz
and Myers (2003) accepted test pieces 1.8 m in length with water flow velocity up to 6 m s-1
(11.7 knots). The velocity profile of the water flow over the surface
was measured by laser Doppler velocimetry. The large size of the test
plates is not conducive to testing expensive or difficult to apply
coatings or other surface modifications.
disc methods are a simpler alternative to towing tanks and flow tests
for characterizing the drag properties of test surfaces (Holm et al, 2004).
Discs are easily rotated in a tank of water, and high velocities,
similar to those associated with ships, are attainable in a relatively
compact apparatus. Rotation is by electric motor and the moment of force
acting on the disc is measured by an in-line torque meter.
Hydrodynamics are not well characterized since the flow varies across
the surface. Cylindrical tanks are most commonly used but vortex flow is
rapidly established in open cylinders without baffles. Tanks may need
to be fully filled and enclosed to prevent the loss of water during high
speed rotation and this complicates data analysis. Measurements are
dependent on the geometry of the specific test rig.
Typical rotating disc rigs described in the literature used discs with diameters 23 cm (Schultz and Myers, 2003) to 30 cm (Nelka, 1973).
These discs are rotated by an electric motor in cylindrical reservoirs
containing volumes of water estimated at 20 L and 1000 L respectively.
Tight fitting lids are required to prevent water being ejected from
smaller reservoirs by rapidly rotating discs. Many of the handling
issues associated with large rotating discs can be eliminated by a
reduction in scale of the apparatus. However the drag forces generated
on miniature discs are very low, which introduces unique measurement
difficulties. We proposed the use of a sensitive rotational rheometer to
measure the drag forces acting on discs of 25 mm diameter. Analytical
rheometers are sensitive down to the µN m range of torque and
have been previously used for measuring the frictional force on standard
discs rotating in aqueous drag-reducing polymer solutions (Kim et al, 2001).
Small circular test coupons with varying surface conditions can be
attached to the viscometer spindle and rotated in water at high angular
velocities to measure the torque due to friction. Test coupons can be
fabricated from a variety of materials, and experimental coatings may be
applied to them by all standard methods including spin coating. We
propose that multiple coated discs can be exposed simultaneously to
marine fouling conditions by field exposure, giving the possibility of
rapid throughput testing. For calibration purposes discs could have
sandpaper of various grit sizes attached to their surface in order to
establish the relationship between angular velocity and torque for
different surface roughness in a similar manner to that of the Moody
diagram which relates pressure drop (expressed as the non-dimensional
friction factor) to flow velocity (expressed as the non-dimensional
Reynolds numbers) for flow through rough pipes (Shockling et al, 2006). In this way the degree of marine fouling could be expressed in terms of an effective roughness length scale.
coupons were developed for antifouling sea exposure trials, fabricated
from a 7.5 mm thick slice of 25 mm diameter rod made of black Delrin®
(Du Pont) polyoxymethylene (POM or acetal) engineering thermoplastic.
The high tensile strength and rigidity of POM combined with its low
water absorption give the test coupons good dimensional and hydrolytic
stability. An M3 screw thread was tapped into the centre of the rear
side of each plastic coupon enabling attachment to a threaded rheometer
spindle and fixing by an M3 nylon bolt in each well of the multiwell
holder for ocean exposure.
Self-adhesive waterproof sandpaper
discs of different roughness grades were fixed to the face of test
coupons for calibration purposes. Circular discs with the same diameter
as the test coupons were cut from commercial sandpaper sheets having a
pressure-sensitive adhesive backing. To ensure that precise dimensions
and a smooth edge were obtained, these discs were precision cut by a
laser cutter (Laserscript LS6840, HPC Laser). The grades of red
aluminium oxide sandpaper used were P240 (Faithfull Tools) and P120,
P100, P80, P60 (Draper). Surface roughness of the discs was assessed by
non-contact laser profilometry using an Alicona Infinite Focus Standard
focus variation optical profiling microscope (Alicona Imaging GmbH). The
roughness parameter used is Sa, the arithmetic average of the 3D
roughness profile measured over a 20 mm zig-zag track made up of 10
continuous profile lines.
Experimental polymer coatings were
applied to the face side only of discs by evaporation of polymer
solutions. Poly(methyl methacrylate) (PMMA, mol. wt. 120 000,
Sigma-Aldrich) was dissolved in toluene (low sulphur, Fisher Scientific)
by stirring at 50 °C under nitrogen for 30 min to give a solution
containing 30 wt% PMMA with viscosity 1770 mPa s at 25 °C (Brookfield
CAP-2000+ cone and plate viscometer, cone no. 6 at 225 rpm).
Approximately 2.2 g of polymer solution was spread onto a disc and the
solvent was allowed to evaporate under ambient conditions, leaving a
film of polymer approximately 120 µm thick. The amount of
polymer applied was determined gravimetrically and the film thickness
calculated knowing the density of the polymer.
Two compounds with
potential activity against marine microbial fouling were investigated.
These were cis-2-decanoic acid (Carbosynth),which is a short chain fatty
acid (FA), and a proteolytic enzyme derived from pineapples, bromelain
(BR) (Sigma-Aldrich). These compounds were dissolved and dispersed,
respectively, in the PMMA solution and the two coatings were applied to
discs, using the same procedure as the pure PMMA, to give films
containing 2.4 wt% of each additive.
water contact angle on coatings applied to the test coupons was
measured using a Kruss DSA100 goniometer and drop shape analysis
software. Droplets of deionized water 1 µL in volume were
placed on the surface of each test piece, centred 3 mm from the edge,
using a motor-driven Hamilton syringe at 100 µL min-1.
The droplets (6 duplicates for each surface) were photographed 10 s
after placement, at ambient temperature and humidity, and the software
algorithm 'tangent 1' was used to determine the contact angle.
to be exposed to fouling conditions in the sea were held in 25 mm
diameter recesses in a flat poly(tetrafluoroethylene) (PTFE) plate by M3
nylon bolts screwed into the tapped hole for the rheometer mounting,
with the surface of each disc held flush with the surface of the PTFE
plate (figure 1).
The plate with 12 coupons attached was immersed horizontally in the sea
at a depth of 1.5 m from the seawater surface from 24th August 2012 to
3rd September 2012 (9 days) at the National Oceanography Centre
Southampton (NOCS), latitude 50°53'28N longitude 1°23'38W. After sea
exposure a small amount of biofilm had formed on the surface of the
coupons, more easily visible on the white PTFE holder which showed a
patchy distribution of green/brown biofilm (figure 1).
The patchy appearance of biofilms on the holder could indicate grazing
by fish, and measures to prevent this will be taken in future. There is
no fouling growth on the sides of the coupons as these are protected
within the holder, allowing the surface roughness alone to be compared
to equivalent sandpaper roughness grades. The coupons were recovered and
those intended for rheometer drag testing were stored immersed in
artificial seawater (ASW), in a container placed on wet ice to prevent
further growth or deterioration.
Figure 1. PTFE holder (377 mm × 70
mm) with 25 mm diameter sample coupons mounted. Before immersion
(above), fouled after immersion (below). The brown appearance of the
edges of the coupons before immersion is an optical artefact.
rheometer type AR-G2 (TA Instruments) with a magnetic thrust-bearing
was adapted for measuring the ultra-low torque on sample discs rotating
in water. According to the instrument manufacturer, the torque
measurement range of this rheometer for 'steady shear' measurements is
0.01 µN m to 200 mN m with a resolution of 1 nN m. An M3
screw-threaded stainless steel connector rod, passing through the
rheometer, was screwed into the threaded hole in the rear face of a
disc, thereby clamping it to the rotating part of the instrument. The
rheometer body was then lowered to immerse the disc in water. Any air
bubbles trapped below the horizontal test face of the disc were removed
by suction using a glass Pasteur pipette with the tip bent upwards in a
U-shape. A cylindrical reservoir (Fisher, tall form 600 mL glass beaker)
filled with water to a depth of 7 cm was evaluated but rejected for use
as a reservoir as significant vortex flow was established even at
moderate angular velocity, leading to water being ejected from the
container. Discs could however be rotated in a cubic clear acrylic
reservoir with 9.4 cm sides (internal measurement) and water depth 7 cm
at up to 300 rad s-1 (2865 rpm) without causing splashing or
significant vortexing, and this system was adopted for all tests. This
was approximately the largest square reservoir that could be fitted into
the space available, limited by the structure of the instrument. The
gap between the lower surface of the disc and the floor of the cube was
fixed at 1 cm after initial trials to determine the effect of gap size
on flow patterns and torque sensitivity. Flow patterns were visualized
by adding neutral buoyancy polymer beads of two contrasting colours,
blue and orange (Cospheric LLC, Santa Barbara, CA, USA) and photographed
using a digital camera (Olympus C-5050) at a shutter speed of 1/30 s.
For recording torque data the disc angular velocity was increased
linearly from standstill to 300 rad s-1 over 60 s and
rotation was maintained for 30 s at the highest speed before decreasing
to zero angular velocity linearly over 60 s.
The moment or torque coefficient (Cm) of a rotating disc is a dimensionless number defined by (Granville, 1982):
where M is the torque acting on the whole disc, ? is the density of the fluid, r is the radius of the disc and ? is the angular velocity.
k is a constant for the system
For a disc rotating in a constrained volume of fluid, a mean
tangential swirling or vortex flow may be induced, which reduces the
effective angular velocity of the disc. To compensate for this a 'swirl
factor' () may be determined (Granville, 1982) with value 0 < < 1
relating the conditions to those obtaining in an unenclosed volume of
fluid. The effective angular velocity then becomes ? . This calibration was not performed by us ( = 1),
due to the structure of the instrument making measurements with larger
reservoirs not possible, and only the relative changes in torque due to
drag were considered.
Torque (M) over the angular velocity (?) range between 200 and 300 rad s-1 was plotted against ?2
for each disc condition. In this turbulent flow regime the drag shows a
close to quadratic angular velocity dependence and the data could be
fitted to a straight line having slope Values of Cm in this velocity range were compared to indicate the effect of different surface roughness conditions.
The flow pattern in the cubic water reservoir with a 25 mm diameter blank Delrin disc rotating at 275 rad s-1, made visible by the motion of blue and orange neutral density beads during a 1/30 s exposure, is shown in figure 2. There was minimal vortexing around the shaft, and turbulent flow with good mixing throughout the volume of water.
Figure 2. Flow patterns with neutral density beads, blank 25 mm diameter disc at 275 rad s-1, exposure 1/30 s.
configuration was used to measure the torque generated on blank 25 mm
diameter Delrin discs rotating in ASW. The angular velocity was
increased from standstill to 300 rad s-1 over 60 s while the
torque was continuously recorded. The slope of the torque against
angular velocity increases regularly with no chaotic change that would
indicate a transition from laminar to turbulent flow regimes, while at
angular velocity =200 rad s-1 the torque can be taken as varying linearly with the square of the rotational velocity (figure 3). Therefore torque data in the rotational range of 200–300 rad s-1 (1910–2865 rpm) were used for calculation of the momentum coefficient. The rotational Reynolds Number varies from 3.0 × 104 to 4.5 × 104 over this velocity range.
Figure 3. Torque data for blank 25 mm diameter Delrin discs (average of 5 runs). (Left) raw data showing torque as a function of ? . (Right) data was linearized by plotting torque against (?)2 demonstrating a 2nd order power law relationship above ? = 200 rad s-1 (4 × 104 rad2 s-2).
rheometer set-up was calibrated using each size of disc by measuring
the torque on coupons with discs of self-adhesive sandpaper attached.
The mean torque (M) acting on replicate discs for each sandpaper grade was plotted against ?2 (figure 4) over the angular velocity range ? greater than or equal to 200 rad s-1. Linear regression gave the slope (= k Cm) which yields the dimensionless, Cm when divided by the appropriate value of k (table 1). For 25 mm diameter discs in ASW with density 1025 kg m-3, k = 1.564 × 10-7 kg m2.
Figure 4. Torque versus ?2 for 25 mm diameter Delrin discs with sandpaper-covered surface.
Coefficient of momentum derived by linear regression.
Note: SD (n) = sample standard deviation (number of samples) and p-value from two-tailed t-test comparing Cm with sandpaper to that of blank disc.
The torque data for the P80 and P100 grade
sandpaper surfaces were very close to each other, and the measured Sa
values confirmed that the two grades had a similar surface roughness of
38.4 µm and 38.7 µm respectively. In figure 5
the coefficient of momentum is plotted against the measured surface
roughness derived from two duplicate discs, with a linear trendline
Figure 5. Coefficient of momentum versus measured surface roughness.
The value of Cm calculated from the torque data can be fit to the surface area roughness (Sa) of the sandpapers by the linear relation:
It is noted that the disc geometry is complex, and Cm
is influenced not only by the test surface but also the 7.5 mm depth
perimeter of the disc, the disc's upper surface and also the immersed
length of the rotating rod to which the disc is attached. These
additional surfaces presumably complicate the analysis beyond that of
the analysis by Granville.
The water contact angle of the clean polymer-coated disc surfaces is given in table 2.
Water contact angle and standard deviation of the polymer-coated disc surfaces.
The presence of the 120 µm thick PMMA-based coatings on the discs gave a small increase of approximately 4% in Cm
compared to the uncoated discs. This increase could possibly be due to
the increased thickness or weight contributed by the coating rather than
to any change in surface roughness. It was not possible to measure the
actual surface roughness of the coated discs using optical profilometry
owing to intense light reflection from the clear, glasslike surfaces.
Visually the surfaces appeared smooth.
The Delrin discs recovered
after 9 days of exposure in the sea had a light covering of microfouling
(slime) visible to the naked eye, as did the PTFE holder. The covering
on the holder was patchy, indicating possible predation by fish grazing
on biofilm. Representative fouled coupons were air-dried and sputter
coated with gold and the fouling organisms were examined using a
scanning electron microscope (SEM) (JEOL JSM-5600LV) (figure 6).
Figure 6. SEM
micrographs of the PMMA surface (top left), PMMA + FA (top right) and
PMMA + BR (bottom). The surfaces were colonized with pennate diatoms
having various frustule morphologies, including Amphora sp. and Navicula
sp. On the PMMA + FA short bacterial rods were also present but they
were not seen in all locations on the surface. There was little
difference in the thickness (considering dehydration) but the PMMA + BR
appeared to have the densest covering composed mainly of diatoms.
The measured Cm values for the clean discs and the fouled discs is given in table 3
along with the equivalent sandpaper roughness (Sa) calculated from the
25 mm disc regression equation. The equivalent roughness values are
plotted in figure 7 where the dotted line indicates the mean equivalent roughness (3.79 µm) of the clean discs.
Cm and Sa for clean and biofilmed coupons.
Note: FA = fatty acid, BR = bromolein, SD = sample standard deviation and p-value from paired one-tailed t-test comparing duplicate fouled coupons with duplicate clean coupons.
Figure 7. Equivalent sandpaper roughness of experimental antifouling coatings.
moving through a resistive medium experience an opposing force which is
related to their velocity in either a linear or quadratic fashion
depending on the Reynolds number (Re) (Timmerman and van der Weele, 1999). Thus, a small sphere falling through a viscous liquid under the force of gravity (at very low Re) experiences drag linearly proportional to its velocity as described by Stokes law.
where Fd is the drag force, µ is the dynamic viscosity of the liquid, R is the radius of the sphere and ? is the velocity of the sphere.
A sphere moving through a fluid at high velocity resulting in turbulent flow (i.e. at high Re) will experience drag varying as the square of the velocity according to Rayleigh's equation
where Fd is the drag force, ? is the density of the fluid, v is the speed of the object relative to the fluid, A is the cross-sectional area and Cd is the drag coefficient—a dimensionless number.
similar relationship also holds for fluid flow in pipes, where the head
loss (or pressure drop) is proportional to the square of the velocity
in turbulent flow according to the Darcy formula (Massey, 2012). We observed that the torque acting on our rotating discs varied as the square of the angular velocity at speeds >200 rad s-1. The motion of neutral density beads indicated
turbulent flow patterns with a stable Taylor-like vortex pair having an
axis of rotation parallel to the plate. Owing to the choice of a cubic
rather than cylindrical container no splashing and only minimal
vortexing of the water occurred, even at maximum rotational velocity.
This simplifies the experimental procedure and may reduce the need for
an empirical 'swirl factor' when calculating the momentum coefficient.
Holm et al (Holm et al, 2004) used the percentage change in the frictional resistance coefficient (Cf)
of a rotating disc to measure the drag penalty due to accumulated
biofilms on experimental FRC. The similarity-law characterization method
developed by Granville (1978, 1982) was used to derive the roughness functions (?B versus k*)
from the measured momentum coefficients and the roughness functions
were converted to frictional resistance coefficients through Granville's
iterative process based on the similarity of the boundary layers of
rough and smooth walls. A Reynolds number corresponding to a 100 m flat
plate was chosen as being representative of the length of a ship for
this conversion. Our attempts to use the similarity index did not result
in a good relationship with surface roughness. It is unclear whether
this is due to the geometry of the discs or to the fact that we were not
fully in the turbulent regime. We have therefore chosen to use the
percentage change in (Cm) to compare frictional drag penalties. Cm is a simple parameter to calculate and was found to be constant over the range of angular velocities studied (200–300 rad s-1). However the absolute value of Cm is dependent on the geometry of the measurement system of disc and shaft.
drag due to different grades of sandpaper attached to disc surfaces
could be correlated with their measured surface roughness as determined
by optical profilometry. The most relevant measure of surface roughness
was Sa, which showed a linear relation with Cm. The
value of Sa extrapolated from the linear sandpaper calibration curves
for the blank 25 mm discs was close to the roughness measured by optical
profilometry (3.8 µm compared to 1.4 µm).
The derived relation of Cm
to measured surface roughness for a fixed disc rotor geometry enables
unknown surface textures (e.g. from marine fouling) to be related to
equivalent standard sandpaper roughness values. The use of a FA and an
enzyme (BR) as experimental antifouling agents was a first attempt at
assessing the rheometer methodology for detecting antifouling active
coatings. After sea exposure all fouled discs except for one duplicate
of the FA-containing PMMA coating showed greater sandpaper equivalent
roughness compared to the clean state of the discs, and the mean
increase over all discs was significant (p = 0.015, paired one-tailed t-test).
The apparent degree of microfouling on discs with the same coating
varied greatly between the two duplicates exposed. This is to be
expected in any biological growth experiment. Duplicate exposures are
clearly inadequate to assess the degree of biofilm fouling accumulated,
and the results presented here are purely to demonstrate that the method
is capable of detecting and quantifying small changes in surface
roughness due to biofilm.
Interestingly, both BR-containing
coatings showed the heaviest microfouling coverage. One speculative
explanation is that the protease activity might have digested naturally
occurring proteins in the water providing amino acids at the surface
possibly stimulating growth. For future studies, in addition to
increasing the sample number, it is also important to confirm
bioactivity of the active agent when incorporated into a coating as well
as characterizing the release kinetics.
The increase in drag due
to even the thickest biofilm observed in this exposure series was only
comparable to the finest grade 240 sandpaper, with an equivalent
sandpaper roughness of approximately 12 µm. The thickness of
the biofilm appeared much greater than this by visual inspection, but
the discrepancy could be due to the patchiness of the biofilm coverage.
The low equivalent roughness could also be connected with the
viscoelasticity of the biofilm and this interesting possibility will be
explored in further work.
The small scale of the test will limit
its use largely to fouling by microbial slime and it will not be
suitable for assessing the drag due to larger organisms or colonies of
organisms such as sea squirts, barnacles, etc whose size scale and
pattern distribution is larger than the discs themselves. In this
respect the small discs may only be appropriate for assessing the
potential efficacy of coatings to reduce or prevent microbial slime in
the early stages of exposure. The analytical rheometer is sufficiently
sensitive to measure the minute changes in drag due to a thin
accumulation of microbial fouling, and we are currently working on using
optical coherence tomography and other methods to quantify the fouling
layer so that we can make better interpretation between the change in
drag and the amount of biomass.
method described here is simple and rapid to carry out. The small size
of the discs and the low volume of water required to rotate them in
(<1 L) eliminates the handling problems associated with large disc
rotors while producing data of comparable utility. The lack of vortexing
and swirling of the water in a cubic container increases confidence in
the data obtained and may eliminate the need for considering an
empirical swirl factor.
Calibration using discs bearing known
sandpaper textures was straightforward, and allows comparison of fouled
disc surfaces with those of known surface roughness. Calibration results
apply to a specific measurement geometry and disc diameter only. An
important consideration is the sensitivity of the analysis to variables
in the experimental set-up. Temperature and density of the water in the
tank are easily controlled in the laboratory and have only minor effects
on torque. A potential source of variation is the fact that the torque
is proportional to the radius of the disc raised to the fifth power.
This means that the value of Cm is extremely
sensitive to small changes in effective disc radius, e.g. such as would
be caused by fouling adhering to the edge of the disc.
rheometer used was found to be capable of registering the increased drag
due to a thin covering of microfouling developed over only 9 days sea
immersion on a small sample disc. It could also differentiate between
the amounts of microfouling accumulated on different experimental
antifouling coatings. A coating containing dispersed BR enzyme appeared
to foul more than a blank coating or one containing a short chain FA,
however duplicate disc exposures of the potential antifouling coatings
gave highly varying results for the amount of biofilm accumulated. This
is to be expected for any biological process, and multiple discs should
Future work will compare these data with those
obtained from a conventional large disc rotor rig and ultimately with
those from a flat plate in a towing tank. The aim will be to
mathematically relate the hydrodynamic drag measured in the different
test systems to each other using a scaling factor analysis.
authors gratefully acknowledge financial support from the EPSRC grant
EP/J001023/1 (Green Tribology), the National Physical Laboratory, the
Knowledge Transfer Partnership between the University of Southampton and
Haydale Limited (Technology Strategy Board Project 508710), and the
University of Southampton Engineering Sciences MSc programme. Data
supporting this study are openly available from the University of
Southampton repository at http://dx.doi.org/10.5258/SOTON/379269.