NSF-REU PROJECT AT UIC

Nadiya KlepClemson University, SCDavid Pelot, UICDr. Yarin, UIC August 2,2013

Spreading of Herschel-Bulkley fluid using lubrication approximation

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OUTLINE: Purpose and applications

Background

Sample preparation

Methods of data collection

Data

Results

PURPOSE AND APPLICATION

Small Angles <2˚• Bearings• Screw extruder

Larger angles (5 ˚+)• Construction***

• Grout, mortar, joint compound

• Foods • Industrial processing

• Spreading of• Jams• Frosting• Peanut

butters• Etc.…

• Personal care products• Creams• Hair jells

BACKGROUND:

Source: www.substech.com

Source: Schlichting, Boundary-Layer Theory,McGraw-Hill,Inc,1987.

Small angles in a nutshell:• small angle between the two surfaces.• convective acceleration• viscous forces predominate over inertial forces • Navier–Stokes equations becomes simpler:

• With the use of boundary conditions :at y = 0, u = U at x = 0, p = p0

at y = h, u = 0 and at x = l, p = p0

• and the fact that volume flow must be a constant:

From this the equation for velocity (:

Where:

• Backflow occurs in areas of increasingpressure near the stationary wall

V0

2

0

y H dp y yu = V 1 - - 1 -

H 2μ dx H H

dpdx

 = 12μ(V0

2 H2  − QH3 )p ( x )  =  p0  + 6 μV 0∫

0

xdxH2  − 12 μQ∫

0

xdxH3

SAMPLE PREPARATION:

Source: Noveon Source: wikipedia.com

2. Neutralized with NaOH 3. Stress yield fluid: Herschel-Bulkley 1. 1.5% Solution of Carbopol

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CARBOPOL VISCOSITY

0.1 1 10 1001

10

100

1000 Vane Visc

Shear rate (1/s)

Vis

cosi

ty (

Pa·

s)

Power Law: fluids=µ Newtonian=non-Newtonian =µeff : eff. viscosity

METHODS OF DATA COLLECTION: Apparatus to mimic the wedge: High-speed camera Phantom video player MatLab OriginPro graphing

DATA AND ANALYSIS

Source: Schlinchting, Boundary-Layer Theory,McGraw-Hill,Inc,1987.

𝐹 𝑛=∫0

𝑙

𝜎𝑛𝑛𝑑𝑥

cos (𝛼)

2

0

y H dp y yu = V 1 - - 1 -

H 2μ dx H H

2 2nn n xx xy yyσ = n σ = sin (α) σ + 2sin(α)cos(α)σ + cos (α)σ

LLLLLLLLLLLLL L

RESULTS:

At larger larger amount of fluid under wedge

faster reverse flow

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00

5

10

15

20

25

30

35

40

x

0H

-0.20.00.30.50.81.0

f) 20 ˚, 1300um, 0.167m/s

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00

10

20

30

40

50

60

70

80

0H

x

-0.2

0.0

0.3

0.5

0.8

1.0

e) 20˚, 600um, 0.167m/s

0.0 0.2 0.4 0.6 0.8 1.00

3

6

9

12

15

18

x

0H

-0.2

0.0

0.3

0.5

0.8

1.0

d) 10 ˚ , 1500um, 0.167m/s

RESULTS:

At same as h1 increases Force decreases

-1 1 3 5 7 9 11 13 150

4

8

12

16

20

a

c

d

f

Time t, sec

Forc

e F

(N)

Ho=23 h1 =600um

Ho=34 h1=800um

Ho=15 h1=1500um

Ho=40 h1=1300um

RESULTS: At same h1 increases Force, F (N) decreases

Ho=23 h1=600umHo=34 h1=800um

Ho=87 h1=600um

0 2 4 6 8 10 12 14 16 180

2

4

6

8

10

12

14

16a

c

e

Time t, sec

Forc

e F,

N

0 2 4 6 8 10 12 14 16 180

4

8

12b

d

f

Time t, sec

Forc

e F,

N

Ho=10 h1=1500um

Ho=18 h1=1500um

Ho=40 h1=1300um

RESULTS: At same h1 & as V0 (U) increases

Force increases

0 2 4 6 8 10 12 140

1

2

3

4

5

6

7

8

9 g

h

e

f

TIme t, sec

Forc

e F,

N

V=0.167m/s

Ho=80 h1=650umV=0.24m/s

Ho=35 h1=1500um

Ho=87 h1=600um

Ho=40 h1=1300um

SUMMARY OF RESULTS

Trial (Fig. 5)

Angle (deg)

H1 (mm)

Velocity (m∙s-1)

Force (N)

Viscosity (Pa∙s)

a 5 0.60 23 0.167 19.1 4.7

b 5 1.50 10 0.167 15.0 5.9

c 10 0.80 34 0.167 13.5 11.4

d 10 1.50 18 0.167 7.9 8.3

e 20 0.60 87 0.167 8.1 20.2

f 20 1.30 40 0.167 6.8 19.5

g 20 0.65 80 0.240 9.8 17.2

h 20 1.50 35 0.240 9.7 20.0

VISCOSITY

1

10

100

1000

0.1 1 10 100

Vis

cosi

ty (

Pa

·s)

Strain rate (1/s)

Max shear rate was calculated to be: 300s-1 : Viscosity: 0.6PasMin shear rate was calculated to be: 3s-1 : Viscosity 30 Pas

Questions?

Thank you to: NSF grant # 1062943 Dr. Yarin David Pelot Everyone in Dr. Yarin’s group Professors Takoudis and Jursich Everyone involved with the REU program at UIC