Ever Upwards:
The rise and rise of fluids in optical capillaries
Andrew Danos
Photonic Crystal Fibres
NL-3.0-870-02
(3mm hole diameter)
SC-5.0-1040
(1.6mm hole diameter)
ESM-12-01
(3.7mm hole diameter)
• Anti-Resonating Reflecting Optical Waveguide (ARROW)
– All holes filled with optical fluid
• Bandgap Omitted Waveguide (BOW)
– Inner ring filled only
Making BOW Fibre
• Apply a UV curing glue to fibre ends to seal target channels
– Delicate and prone to catastrophic failure, but not impossible
– Previously filled by pumping from reservoir
• Unable to fill reliably by this method
– Fluid escaping free end makes unable to couple
Sealed ESM
Sealed SC-1040
The Problem
Require a method to keep fluid away from free end
The Problem
• Filled channels act as waveguides themselves
• No BOW effect, since light is not being carried in the fibre
q2
q1
n2
n1
www.timbercon.com/Total-Internal-Reflection.html
n1sinq1 = n2 sinq2
• n2 < n1 allows total internal reflection: q2 > 90°
• Fibre effectively becomes an array of independent, high loss
waveguides
The Fluids
• Oils with precisely
engineered refractive index
– Referred to by their index
– Wide range available
• Requested fluid properties
datasheets from
manufacturer
The Idea
Fluid is drawn up fibre by its surface tension
r
L
Fluid properties:
• Surface tension (g)
• Density (r)
• Viscosity (h)
N·m-1
kg·m-3
kg·m−1·s−1
Upward force on fluid column
= 2pr·g
Downward force on fluid column
= mg = (Volume)rg
=(pr2L)rg
http://www.physics.usyd.edu.au/~helenj/PHYS1902/Fluids3.pdf
2g
Equilibrium at L = rgr
But this is FAR too long for us: ~70cm
The Solution
• Time capillary infiltration so that fluid doesn’t
reach the end
⇒
finite time
“It Should Work…In Theory”
• Washburn (1921) gives
PA = atmospheric pressure difference = 0 since fibre open at both ends
Ph = hydrostatic pressure ≈ 0 at examined L
2gcosq
Pc = capillary pressure =
r
e = coefficient of slip ≈ 0 (material property)
q = contact angle between glass and fluid ≈ 0 on large scale test
• Equation has recent experimental support on cm, nm scale
and regarding contact angle, but not on mm scale
Contact Angle
• Should expect contact angles to be different in
different glass/fluid combinations
gsv = solid surface free energy (tabulated)
glv = liquid surface free energy (surface tension)
gsl = solid/liquid interfacial free energy (not tabulated)
q = contact angle
q
A Bit of Maths
• Cancelling
• Integrating with L(0)=0
(ie, the fluid starts at the bottom)
D = diameter of fibre channel = 2r
Verification
• Measure time taken for fluid to reach given L
• Time measurement is easy
– use a stopwatch
• Length is more difficult
– exploit change in scattering pattern between filled
and unfilled fibre to know when fluid has passed
Verification
filled pattern
scatters off fibre…
laser…
unfilled pattern
Pattern Change
Setup
diode laser
Setup
focusing lens
Setup
positionable fibre and fluid mount
Setup
sample fibre (white): testing half cm increments over 4 cm
fluid reservoir (yellow)
Results
• Record time for first sign of pattern change and
end of change at each L
– Gives data of form (L,t1,t2)
• Plot
against L and get a linear relationship
• Washburn predicts the gradient:
– Then compare experimental gradient with
Washburn’s under assumption that cosq = 1
Results: Index Matching in SC-1040
60
y = 1190.5x
R² = 0.9953
Square root of time (s½)
50
For L against
( in S.I units)
Experimental gradient =1190
(solid line, fitted to data points)
Theoretical gradient =1163
(dashed line)
Indicates that cosq = 0.955
• q = 17.25°
•
40
30
•
20
10
•
0
0
0.01
0.02
0.03
0.04
0.05
Length (m)
3000
Time (s)
2500
2000
Squaring both sides
gives relationship
between L and t
1500
1000
500
0
0
0.005
0.01
0.015
0.02
Length (m)
0.025
0.03
0.035
0.04
0.045
Results
• Took results from a range of fibre and fluid types
– Confirms Washburn for both fluid and capillary property dependences
Increasing capillary radius
Fluids
Index
matching
(1.4587)
SC-1040
✓
NL-870
✓
ESM
✓
1.46
✓
1.48
✓
1.62
✓
1.63
✓
actual fibre/fluid combination
used for filled fibres
Changing fluid
properties
Problem Solved
• It is the empirical constant relating t and L that is
useful for accurately filling fibres
– even if it can’t be determined exactly from fluid and fibre properties
• And now it works, so I’m told
ESM ARROW vs. hybrid sample , n=1.62 capillary fill
0
ESM ARROW
ESM 1 ring filled
Transmission (dB)
-10
-20
-30
-40
600
700
800
900
1000
Wavelength (nm)
1100
1200
Acknowledgements
Made possible by:
• Dr. Jeremy Bolger: lab manager and direct supervisor
• Dr. Boris Kuhlmey: leading theoretician
• Prof. Ben Eggleton: CUDOS director
• Dr. Eduard Tsoy
• Dr. Helen Johnston
• Prof. Dick Hunstead: TSP coordinator
References
1. Washburn, E (1921) ‘The Dynamics of Capillary Flow’, The
Physical Review, 17(3)
2. Chebbi, R (2007) ‘Dynamics of Liquid Penetration into
Capillary Tubes’, The Journal of Colloid and Interface
Science, 135(1), p255-260
3. Tas, N et al. (2004) ‘Capillary Filling of Water in Nanotubes’,
Applied Physical Letters, 85(15), p3274-3276
4. Xue, H et al. (2006) ‘Contact Angle Determined by
Spontaneous Capillary Rises with Hydrostatic Effects;
Explanation and Theory’, Chemical Physics Letters, 432(13), p326-330