Supplementary information - Polymer conformation during ...Supplementary information - Polymer...

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Supplementary information - Polymer conformation during flow of viscoelastic solution in a porous media Durgesh Kawale a,b,c , Gelmer Bouwman b , Shaurya Sachdev b Pacelli L. J. Zitha a , Michiel T. Kreutzer b , W. R. Rossen a , and Pouyan E. Boukany b* a Department of Geosciences and Engineering, Delft University of Technology, Stevinweg 1, Delft, The Netherlands; b Department of Chemical Engineering, Delft University of Technology, Van der Maasweg 9, Delft, The Netherlands; c Dutch Polymer Institute (DPI), P.O. Box 902, 9600 AX, Eindhoven, The Netherlands. * E-mail: [email protected] 1. Two movies, SM-1 and SM-2 are included in the supplementary information. Both these movies show one instance of DNA chain (marked with dotted circle) approaching the pillar. The DNA chains coil at the tip of DZ and as it enters the DZ it stretches and rotates in a direction perpendicular to the flow. ˙ γ app = 3.3s -1 , C s = 0 mM NaCl, Wi = 290.98, Ma = 0.95, Re 1. 2. Table S1, we summarize the mean DNA fractional extension, μ and skewness, s. 3. In fig. S1 we show the stead-shear rheology of 0.2gL -1 PAA solutions at 22 C in DI water ( C s = 0 mM) and in presence of salt ( C s = 6 mM). 4. In fig. S2 we show the results from pressure drop measurement across the periodic array. In fig. S2a the standard deviation (std) of the ΔP fluctuations in the microfluidic device. The sampling period for Newtonian fluid flow is 120 s and for polymer solution flow is 600 s. All three solid are obtained by fitting power law equation of type y = ax b through experimental data. For Newtonian data, regression is performed over all data points. For polymer solution data, regression is performed for data beyond ˙ γ app = 10s -1 . The onset point is obtained as the intersection of polymer solution lines with the Newtonian data lines. In fig. S2b, the apparent viscosity as calculated by Darcy’s law is shown. Error bars are calculated based on std(ΔP). 5. In fig. S3 we show the probability distribution of DNA orientation angle, θ as Wi number increases. The DNA samples were located inside the DZ. 6. Fig. S4 shows schematic explaining the molecular parameters extracted from DNA-imaging. The end-to-end vector, - R is measured manually using ImageJ. The DNA extension, h - R i is the magni- tude of - R , whereas the DNA orientation angle, θ is the angle of - R . θ is 0 in the direction of flow (x-axis), whereas it is 90 in the direction perpendicular to the flow (along the microfluidic device width, y-axis). 7. Fig. S5 shows the velocity field for flow of the 200 ppm PAA solution (in DI Water) through pillared array at ˙ γ app = 0.07s -1 (Wi = 5.8). We can see the dead zone formation in the left figure. The velocity field appears not to be time dependent. Details of the PIV calculations are - the PIV vector calculation was performed using LaVision DaVis 8.4.0 (LaVision inc, England). The background noise was subtracted by subtracting the average intensity of the raw images (in time) 1 Electronic Supplementary Material (ESI) for Soft Matter. This journal is © The Royal Society of Chemistry 2017

Transcript of Supplementary information - Polymer conformation during ...Supplementary information - Polymer...

Page 1: Supplementary information - Polymer conformation during ...Supplementary information - Polymer conformation during flow of viscoelastic solution in a porous media Durgesh Kawalea;b;c,

Supplementary information - Polymer conformation during flow ofviscoelastic solution in a porous media

Durgesh Kawalea,b,c, Gelmer Bouwmanb, Shaurya Sachdevb Pacelli L. J. Zithaa, Michiel T. Kreutzerb,W. R. Rossena, and Pouyan E. Boukanyb∗

aDepartment of Geosciences and Engineering, Delft University of Technology, Stevinweg 1, Delft, The Netherlands;bDepartment of Chemical Engineering, Delft University of Technology, Van der Maasweg 9, Delft, The Netherlands;cDutch Polymer Institute (DPI), P.O. Box 902, 9600 AX, Eindhoven, The Netherlands.∗ E-mail: [email protected]

1. Two movies, SM-1 and SM-2 are included in the supplementary information. Both these moviesshow one instance of DNA chain (marked with dotted circle) approaching the pillar. The DNAchains coil at the tip of DZ and as it enters the DZ it stretches and rotates in a direction perpendicularto the flow. γ̇app = 3.3s−1, Cs = 0mM NaCl, Wi = 290.98, Ma = 0.95, Re� 1.

2. Table S1, we summarize the mean DNA fractional extension, µ and skewness, s.

3. In fig. S1 we show the stead-shear rheology of 0.2 gL−1 PAA solutions at 22 ◦C in DI water (Cs =0mM) and in presence of salt (Cs = 6mM).

4. In fig. S2 we show the results from pressure drop measurement across the periodic array. In fig. S2athe standard deviation (std) of the ∆P fluctuations in the microfluidic device. The sampling periodfor Newtonian fluid flow is 120 s and for polymer solution flow is 600 s. All three solid are obtainedby fitting power law equation of type y = axb through experimental data. For Newtonian data,regression is performed over all data points. For polymer solution data, regression is performed fordata beyond γ̇app = 10s−1. The onset point is obtained as the intersection of polymer solution lineswith the Newtonian data lines. In fig. S2b, the apparent viscosity as calculated by Darcy’s law isshown. Error bars are calculated based on std(∆P).

5. In fig. S3 we show the probability distribution of DNA orientation angle, θ as Wi number increases.The DNA samples were located inside the DZ.

6. Fig. S4 shows schematic explaining the molecular parameters extracted from DNA-imaging. Theend-to-end vector,

−→R is measured manually using ImageJ. The DNA extension, 〈−→R 〉 is the magni-

tude of−→R , whereas the DNA orientation angle, θ is the angle of

−→R . θ is 0◦ in the direction of flow

(x-axis), whereas it is 90◦ in the direction perpendicular to the flow (along the microfluidic devicewidth, y-axis).

7. Fig. S5 shows the velocity field for flow of the 200 ppm PAA solution (in DI Water) throughpillared array at γ̇app = 0.07s−1 (Wi = 5.8). We can see the dead zone formation in the left figure.The velocity field appears not to be time dependent. Details of the PIV calculations are - thePIV vector calculation was performed using LaVision DaVis 8.4.0 (LaVision inc, England). Thebackground noise was subtracted by subtracting the average intensity of the raw images (in time)

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Electronic Supplementary Material (ESI) for Soft Matter.This journal is © The Royal Society of Chemistry 2017

Page 2: Supplementary information - Polymer conformation during ...Supplementary information - Polymer conformation during flow of viscoelastic solution in a porous media Durgesh Kawalea;b;c,

Table S1: DNA fractional extension mean, µ and skewness, s at the DZ tip (coil) and closeto pillar (stretch).

Cs = 0mM Cs = 6mM

Coil Stretch Coil Stretch

γ̇app = 3.3s−1 µ = 0.18±0.12 µ = 0.30±0.15 µ = 0.09±0.02 µ = 0.15±0.07s = 3.08 s = 0.69 s = 0.84 s = 1.00

γ̇app = 33s−1 µ = 0.21±0.04 µ = 0.53±0.18 µ = 0.11±0.03 µ = 0.22±0.1s = 0.14 s = 1.04 s = 0.38 s = 1.21

Table S2: Summary of DNA fractional extension inside DZ, local De and DNA velocity inside DZ. Thestandard deviation of Deloc and vDNA values is based on an ensemble of 20 individual DNA trackingvelocimetry measurements, whereas the standard deviation of DNA fractional extension is based on thenumber of DNA molecules measured as shown in fig. 5c

DNA fractional extension (-) Deloc (-) vDNA (µms−1)

0.15±0.07 0.59±0.28 78.48±27.430.22±0.10 4.76±1.45 497.19±174.170.30±0.15 15.55±5.00 19.28±5.240.53±0.18 735.60±250.20 573.29±202.09

from each raw image. The pillars were then masked out using geometric masks. Vector wereobtained using multipass FFT based cross correlation with window sizes from 64x64 px (50%, 2pass) to 16x16 px (50%, 3 pass). Spurious vectors were removed using a median filter. Sub-pixelinterpolation was done using a 3 point Gaussian estimator. Final presented results are average of100 instantaneous vector fields (average in time). The peak standard deviation in velocity is around5.25×10−5 ms−1 (at zones with high velocity). Calibration was done with pillar diameter. Theother derived parameters were based on the average velocity field using in built functions.

8. Fig.S6 shows the ratio of the polymer apparent viscosity to the steady shear viscosity calculated atthe apparent shear rate, ηapp plotted against the Wi number.

9. Table S2 shows the DNA fractional extension inside DZ, local Deborah number, Deloc and theDNA velocity, vDNA inside the DZ.

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10−3 10−2 10−1 100 101 102

10−2

10−1

100 (b)

Shear rate, γ̇ (s−1)

Viscosity,η(P

as)

Cs = 0mMCs = 6mM

Figure S1: (b) Steady-state shear rheology of 0.2 gL−1 PAA solutions at 22 ◦C in DI water (Cs = 0mMNaCl, filled-circle symbol) and in presence of salt (Cs = 6mM NaCl, filled-square symbol). The solidline is a Carreau model fit (eqn. ??) to the shear rheology.

10−1 100 101 102

10−1

100

101

γ̇Cs=6mMonset

= 15.8 s−1

γ̇Cs=0mMonset

= 9.5 s−1

(a)

Apparent shear rate, γ̇ (s−1)

std(∆

P),

(mbar)

Cs = 0mM

Cs = 6mM

Newtonian

10−1 100 101 102

10−3

10−2

10−1

(b)

Apparent shear rate, γ̇ (s−1)

Apparentviscosity,ηapp(P

as)

Cs = 0mM

Cs = 6mM

Figure S2: (a) Standard deviation (std) of the ∆P fluctuations. The dotted curve is fitted to the data. (b)The apparent viscosity as calculated from Darcy’s law. The solid lines are spline fit to the data, shown asa guide to the reader’s eye. Error bars are based on std(∆P).

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Wi = 1.57Cs = 6mM

γ̇app = 3.3 s−1

N = 78

0 90 1800.00

0.02

0.04

0.06

Angle, |θ| (◦)

pdf

Wi = 15.67Cs = 6mM

γ̇app = 33 s−1

N = 32

0 90 1800.00

0.02

0.04

0.06

Angle, |θ| (◦)

pdf

Wi = 290.98Cs = 0mM

γ̇app = 3.3 s−1

N = 56

0 90 1800.00

0.02

0.04

0.06

Angle, |θ| (◦)

pdf

Wi = 2909.85Cs = 0mM

γ̇app = 33 s−1

N = 41

0 90 1800.00

0.02

0.04

0.06

Angle, |θ| (◦)

pdf

Figure S3: Probability distribution of DNA orientation angle, θ as Wi number increases. N is the numberof samples measured and all the samples are located inside the DZ.

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Flow direction(Along micro�uidic device length)

End-to-end vector

DNA chain

x

y

θPerp

endi

cula

r to

�ow

dire

ctio

n(A

long

mic

ro�u

idic

dev

ice

wid

th)

Orientation angle

Figure S4: Schematic showing DNA chain end-to-end vector, ~R and the orientation angle, θ.

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|V |(m/s)0.00030.000270.000240.000210.000180.000150.000129E -056E -053E -050

0.00025 m/s

|V|(m/s)0.00030.000270.000240.000210.000180.000150.000129E-056E-053E-050

0.00025 m/s

(a)

(b) (c)

100 m

100 m

100 m

Figure S5: (a) Streamline snapshots and the (b-c) the velocity field calculated by PIV at Wi = 5.8 orγ̇app = 0.07s−1. The fluid is 200 ppm PAA in DI water. Flow direction is from right to left. (c) shows azoomed-in image of the velocity field in the DZ.

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10−2 10−1 100 101 102 103 10410−1

100

101

Wi

ηapp

ηSh

Cs = 0mM

Cs = 6mM

Figure S6: Figure showing ratio of the apparent viscosity, ηapp and the steady-shear viscosity, ηSh at theapparent shear rate, γ̇app as a function of the Wi number.

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