NSF-REU P ROJECT AT UIC Nadiya Klep Clemson University, SC David Pelot, UIC Dr. Yarin, UIC August...
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Transcript of NSF-REU P ROJECT AT UIC Nadiya Klep Clemson University, SC David Pelot, UIC Dr. Yarin, UIC August...
NSF-REU PROJECT AT UIC
Nadiya KlepClemson University, SCDavid Pelot, UICDr. Yarin, UIC August 2,2013
Spreading of Herschel-Bulkley fluid using lubrication approximation
Source: www.alibaba.com
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
Source: www.pharmainfo.net
Source: www.alibaba.com
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