Efficient water- soluble drag reducing star polymers with
improved mechanical stability
David P. Cole1, Ezat Khosravi 1, Osama M. Musa2
1
Department of Chemistry, Durham University, Durham, DH1 3LE, United Kingdom
2
Ashland Specialty Ingredients, Bridgewater, New Jersey, 08807, United States
Correspondence to: E. Khosravi (E-mail: ezat.khosravi@durham.ac.uk)
SUPPORTING INFORMATION
Hydrolysis of PtBA
Figure S1: 400 MHz-1H NMR spectrum of; a) Star-PtBA2 before hydrolysis (in CDCl3); b) Star-PAA2
following hydrolysis (in D2O).
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Testing of drag reduction efficiency
A test rig owned by Ashland Inc. (Fig. S2) was used to measure the %DR of polymer
solutions. %DR describes the change in flow rate of a polymer solution when compared with
a pure solvent control sample. The rig is used routinely by Ashland to determine the %DR of
commercial products. It allows a simple and effective method to calculate %DR of a dilute
polymer solution experienced during pipe flow. The rig comprises a pressure chamber into
which the polymer solution is loaded and pressurised using nitrogen gas. The solution is
released in to the Teflon tube (l = 219 cm, d = 0.4 cm) and collected in a measuring cylinder.
To calculate %DR, the time is recorded for a known volume of dilute polymer solution (500
ml) to travel through the length of pipe. The flow rate is compared with a pure water control
sample.
Figure S2: Drag reduction rig
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The drag reduction test rig is represented schematically in Figure S3. An example procedure
for the determination of %DR of a dilute polymer solution is detailed below. A data set
recorded for a Praestol (PAM) sample is used to demonstrate the procedure to convert the raw
data to %DR values.
Figure S3: Schematic representation of drag reduction test rig.
General procedure
A pure water control sample was first tested as follows:
1. Valve 1 (V1) (Fig. S3) was opened and water (600 ml) was loaded to the pressure
chamber via the funnel; the chamber was sealed by closing V1.
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2. V2 (leading to the nitrogen line) was opened and the chamber was pressurised to 10
Psig.
3. V3 was opened and a small amount of water (≈ 100 ml) was run through the pipe
into the measuring cylinder. This allowed fine tuning of the pressure (via the gauge)
and loaded the pipe with sample in order to accurately measure the time for 500 ml
of sample to be dispensed.
4. V3 and V2 were closed and V1 opened to return the water to the chamber. V1 was
closed and the chamber was re-pressurised (V2 opened).
5. V3 was opened and a stopwatch was used to measure the time taken for 500 ml of
water to flow in to the measuring cylinder.
6. The remaining water was then evacuated from the pipe and reloaded in to the
chamber.
7. The measurement was repeated at 10 Psig before the same procedure was conducted
at a pressure of 20 and 30 Psig. The average time for 500 ml of liquid to flow in to
measuring cylinder at each pressure is shown in Table S1.
Table S1: Average time for transfer of 500 ml of water at increasing pressure.
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Following the blank water measurement, a dilute polymer solution was prepared by
adding a stock solution (0.5 wt%, volume dependent on required dose) via syringe to a
flask containing tap water (600 ml). The flask was shaken thoroughly for 1 min to allow
complete mixing of polymer solution. The procedure described above was repeated for
the polymer solution. Following measurement at 10, 20 and 30 Psig, the solution was
fully evacuated from the pipe and further stock solution was added to increase the dose.
The process was repeated with increasing dose until all required doses had been tested.
The raw data set for a Praestol sample is shown in Table S2.
Table S2: Average time for transfer of 500 ml of Praestol polymer solution at a range of pressures and
increasing dose.
Calculation of %DR
Following the measurements taken for pure water and the polymer solution, %DR was
calculated as follows:
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1. The time for the transfer of 500 ml of polymer solution at each dose and pressure was
converted to flow rate using Equation S1. This information, for each pressure at a dose of
1.25 ppm, is summarized in Table S3.
Flow rate (Q) =
volume (500 ml)
time (s)
(Equation S1)
Table S3: Flow rate for Praestol, dose = 1.25 ppm at increasing pressure.
2. Reynolds number (Re) for each dose and pressure (dependent on the flow rate, pipe
dimensions and solution properties) was then calculated using Equation S2. This gives a
measure of turbulence in each system.
Re =
4Q
d μρ
where  
d 2
ζ
(Equation S2)
d = inner diameter of tube (0.4 cm), Q = flow rate (ml s-1), ρ = solution density ≡ 1, ζ =
solution viscosity in Poise (1 cP = 0.01 P). For these dilute systems ρ and ζ assumed to be
equal to pure water.
A friction factor (F), a measure of the friction a fluid experiences as it flows through a
pipe, was also calculated for each polymer solution at increasing pressure using Equation
S3. Re and F is summarized for a dose of 1.25 ppm at each pressure in Table S4.
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F =
d 5 P2
32 L ρ Q 2
(Equation S3)
ΔP = pressure drop from the pressure chamber (10, 20 or 30 Psig) to 0 Psig at end of pipe
(convert pressure from Psig to pressure in dynes cm-1 by multiplying by 68985), L =
length of tube = 219 cm, ρ = density ≡ 1
Table S4: Summary of Re and F at each pressure for Praestol dose = 1.25 ppm
3. Re was then plotted vs F and the equation of the trendline was calculated (Fig. S3).
Figure S4: Plot of Re vs F for Praestol dose = 1.25 ppm with equation of trendline included.
This equation (F = 0.119Re-0.289) allowed Re to be standardized and F could be calculated at
three specifically chosen Re values (Table S5). This is important as Re varies for every
solution, even at the same pressure, depending on the exact solution properties. It is necessary
to determine F at a specific Re value in order to directly compare with the control water
sample.
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Table S5: F calculated at specific Re for Praestol dose = 1.25 ppm.
4. Steps 1-4 were then used to determine F for pure water (at Re = 1.0, 1.5 and 2.0 x 104).
The %DR at each Re was calculated from the difference between F of the polymer
solution and pure water sample (Equation S4). The %DR at each Re is summarized for
dose = 1.25 ppm in Table S6.
 (F (polymer solution)

%DR = 100  
100 
F (pure water)


(Equation S4)
Table S6: Summary of %DR at increasing Re for Praestol dose = 1.25 ppm
5. The same analysis (Steps 1-5) was repeated for each increasing dose (2.5-10 ppm) and is
summarized in Table S7. From this data a graph was then plotted demonstrating the
change in drag reduction with polymer dose (Fig. S4).
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Table S7: Summary of %DR for Praestol, calculated at each dose and Re.
Figure S5: Change with %DR with polymer dose for Praestol at three Re values.
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Raw Measurements for mechanical stability testing
Figure S6: Change in flow rate over consecutive runs through the test rig for Star-PAA2, including raw data.
Figure S7: Change in flow rate over consecutive runs through the test rig for Linear-PAA, including raw data.
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Figure S8: Change in flow rate over consecutive runs through the test rig for Praestol, including raw data.
Figure S9: Change in flow rate over consecutive runs through test rig for PEO-8M, including raw data.
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