Team of Brazil
Problem 07
Drawing pins
reporter:
Ibraim Rebouças
Team of Brazil
Problem 07:
## Title
Drawing Pins
Problem 07
Drawing pins
A drawing pin (thumbtack) floating on the
surface of water near another floating object is
subject to an attractive force. Investigate and
explain the phenomenon. Is it possible to
achieve a repulsive force by a similar
mechanism?
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Bad Saulgau, 20th – 29th July, 2012
2
Team of Brazil
Problem 07:
## Title
Drawing Pins
Contents
Theoretical introduction
• Surface tension
• Viscosity
• Capillarity
• Horizontal Forces
•
•
•
Attraction and repulsion
Dimensionless parameters
Time of approach
• Interaction energy
Experiments
• Tests
• Comparison between theory and experiments
Conclusion
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Bad Saulgau, 20th – 29th July, 2012
3
Team of Brazil
Problem 07:
## Title
Drawing Pins
Surface tension
Definition:
Is a property of fluids caused by intermolecular forces,
and tends to minimize the surface area to minimize his
energy.
∆p
Υ
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Surface tension table
Liquid
Temperature
°C
Surface
tension,
γ
Acetic acid
20
27.6
Acetic acid
(40.1%) +
Water
30
40.68
Acetone
20
23.7
Ethanol
20
22.27
Glycerol
20
63
Isopropanol
20
21.7
Mercury
15
487
Methanol
20
22.6
n-Octane
20
21.8
Water
25
71.97
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Drag force
We have a drag force caused by the viscosity of the fluid.
Viscous
Force
Adjustment
parameter
Radius of the
shape
6
Absolut
viscosity (Pa.s)
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Velocity
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Problem 07:
## Title
Drawing Pins
Capillarity
The interaction between contacting surfaces of a liquid and a
solid that distorts the liquid surface from a planar shape.
Considering water as the fluid, we can classify the particles in:
Hydrophilic particle
Hydrophobic particle
Hydrophilic: attract the water molecules
Hydrophobic: repels the water molecules
Hydrophilic particle
Hydrophobic particle
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Meniscus – kinds of forces
Attractive
Force
Attractive
Force
Repulsive
Force
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Bad Saulgau, 20th – 29th July, 2012
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Vertical forces
2
Capillary
forces
Pressure
Force
Atmospheric
pressure
%&
Atmospheric
pressure
'
12
Weight
sin
=
345
cos
( sin
2
)
sin
)
*+ ,- ) Δ*/ 0
6
) 789 :;
5
6346 < ) 789 :;
<
7895 :;
5
At the equilibrium
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Horizontal forces
Liquid F
/
arctan h′L
Gas
Contact point
The interaction energy is given by the Nicolson’s superposition approximation:
/ sin
Bound number
>?
D
)2 (@A B B C'
>
Bessel
function
D
Capillary length
)2 (
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
(
@ Δ*
E
C
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Dimensionless parameters
Bound number
N
BM
W ∈ 1,2
*V
*+
2N ) 1 1
) QRS
3
2
@A ≅
1
cos T
6
Radius of the
semi sphere
/ sin
≅
@A
Contact angle
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Attraction and repulsion
D
Attraction cases
SZ[
\0
\0
SZ[
\0
SZ[
^0
Or
SZ[
^0
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
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11
Team of Brazil
Problem 07:
## Title
Drawing Pins
Attraction and repulsion
D
Repulsion cases
SZ[
^0
\0
SZ[
^0
SZ[
\0
Or
SZ[
^0
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
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12
Team of Brazil
Problem 07:
## Title
Drawing Pins
Space function for small L
For small values of L, the Bessel function can reduced to:
C
≪1 `
a
1
Using Torricelli's equation:
)2 (@A B B
D
'
We get:
0
b b
d
'
c
a
2( @A B B
)
3 e
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Bad Saulgau, 20th – 29th July, 2012
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Experiment 1: Two pins in water - attraction
1
2
3
4
1
5
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Experiment 1: Two pins in water - attraction
Position in function of time
1
2
3
4
1
5
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Experiment 1: Two pins in water
i 0.0003W
k2lmno 0.0728 rse
: 38°
Temperature: 20u
Radius: 24.62 mm
h: 0.00103 m
1
2
c
3
f. hii
4
E
/ sin
5
E
0.00616
Source of errors
Rule and conversion: v0.5ee
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
@A
²
@A ≅ 74
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Experiment 2: Water with surfactant
1
2
The phenomena
does not occur, because
the surfactant break the
surface tension, and the
force became 0, according
to the theory.
a
3
D
4
5
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
)2 (@A B
(→0
→0
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Experiment 3: distance vs. time of approach
1
2
3
4
Distance (cm)
Time of approach(s)
1.09
0.82
1.95
9.81
1.36
2.17
1.54
2.95
1.37
1.33
0.76
0.92
Source of errors:
•
Measure of the distance
and conversion
•
•
•
Imprecisions:
Time: v0.05S
Conversion and
measurement: v0.5ee
5
There’s no pattern.
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Bad Saulgau, 20th – 29th July, 2012
18
Team of Brazil
Problem 07:
## Title
Drawing Pins
Experiment 4:Repulsion
The phenomenon
1
2
3
4
5
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Bad Saulgau, 20th – 29th July, 2012
19
Team of Brazil
Problem 07:
## Title
Drawing Pins
Experiment 4:Repulsion
Position X Time (Repulsion)
1
The pin stop
3
4
5
Position (mm)
2
8
6
4
2
0
-2 0
-4
-6
-8
-10
Precision: ±0.5 mm
1
2
3
4
5
Initial impulse
Time (s)
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Experiment 5: Two pins in glycerin
3.50
1
3
4
5
3.00
Position (mm)
2
Position X Time
2.50
2.00
1.50
Pin A
1.00
Pin B
0.50
Precision: ±0.5 mm
0.00
0
1
2
Time (s)
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
3
4
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Problem 07:
## Title
Drawing Pins
Conclusion
The movement
Repulsion
Viscosity
Time of approach
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
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Team of Brazil
Problem 07:
## Title
Drawing Pins
References
•
•
•
•
•
•
G. K. Batchelor, An Introduction to Fluid Dynamics Cambridge U.P.,Cambridge, 1967.
Fluid Mechanics 4th ed - F. White
D.D. Joseph, J. Wang, R. Bai, and B.H. Yang, 2003. Particle motion in a liquid film rimming the
inside of a partially filled rotating cylinder. J. Fluid. Mech., 496, 139-163.
P. A. Kralchevsky, K. D. Danov, Interactions between Particles at a Fluid Interface, In:
Nanoscience: Colloidal and Interfacial Aspects, V. M. Starov, Ed.; CRC Press, New York, 2010;
Chapter 15, pp. 397-435.
P. Singh and D.D. Joseph, 2005. Fluid dynamics of floating particles. J. Fluid Mech., 530, 31-80.
Capillary interactions between particles bound to interfaces, liquid films and biomembranes Peter A. Kralchevsky a,b, Kuniaki Nagayamaa,U
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Bad Saulgau, 20th – 29th July, 2012
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Thank you!
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Bad Saulgau, 20th – 29th July, 2012
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Appendix A
• Brownian motion
Particle
Fractal
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Bessel function
• There’s no analytical solution for the equation in no asymptotic cases.
²{
z²
z²
{
z
) z)
z
Order
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Bad Saulgau, 20th – 29th July, 2012
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Team of Brazil
Problem 07:
## Title
Drawing Pins
Software used to data collect and analysis
• Tracker Physics Video analysis V 4.62
• Origin Pro 7.0
• Corel Draw X5
Team of Brazil: Bárbara Santiago, Guilherme Moreira, Ibraim Rebouças, João Gabriel Faria and Liara Guinsberg
Reporter: Ibraim Rebouças
Bad Saulgau, 20th – 29th July, 2012
27