Ever Upwards: The rise and rise of fluids in optical capillaries

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Ever UpwardsThe rise and rise of fluids in
optical capillaries
Andrew Danos
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Photonic Crystal Fibres

• Anti-Resonating Reflecting Optical Waveguide
  (ARROW)
• All holes filled with optical fluid
• Bandgap Omitted Waveguide (BOW)
• Inner ring filled only

NL-3.0-870-02 (3mm hole diameter)
SC-5.0-1040 (1.6mm hole diameter)
ESM-12-01 (3.7mm hole diameter)
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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
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The Problem

• Require a method to keep fluid away from free end

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The Problem

• Filled channels act as waveguides themselves
• No BOW effect, since light is not being carried
  in the fibre
• n2 lt n1 allows total internal reflection q2 gt
  90
• Fibre effectively becomes an array of
  independent, high loss waveguides

q2
q1
n2
n1
www.timbercon.com/Total-Internal-Reflection.html
n1sinq1 n2 sinq2
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The Fluids

• Oils with precisely engineered refractive index
• Referred to by their index
• Wide range available
• Requested fluid properties datasheets from
  manufacturer

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The Idea

• Fluid is drawn up fibre by its surface tension

• Fluid properties
• Surface tension (g) Nm-1
• Density (r) kgm-3
• Viscosity (h) kgm-1s-1

r
Upward force on fluid column 2prg
L
Downward force on fluid column mg
(Volume)rg (pr2L)rg
2g
http//www.physics.usyd.edu.au/helenj/PHYS1902/Fl
uids3.pdf
Equilibrium at L But this is FAR too long for
us 70cm
rgr
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The Solution

• Time capillary infiltration so that fluid doesnt
  reach the end

?
finite time
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It Should WorkIn Theory

• Washburn (1921) gives
• PA atmospheric pressure difference 0 since
  fibre open at both ends
• Ph hydrostatic pressure 0 at examined L
• Pc capillary pressure
• 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

2gcosq
r
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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
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A Bit of Maths

• Cancelling
• Integrating with L(0)0 (ie, the fluid starts
  at the bottom)

D diameter of fibre channel 2r
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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

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Verification
filled pattern
scatters off fibre
laser
unfilled pattern
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Pattern Change

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Setup
diode laser
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Setup
focusing lens
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Setup
positionable fibre and fluid mount
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Setup
sample fibre (white) testing half cm increments
over 4 cm fluid reservoir (yellow)
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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
  Washburns under assumption that cosq 1

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Results Index Matching in SC-1040

• 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

Squaring both sides gives relationship between L
and t
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Results

• Took results from a range of fibre and fluid
  types
• Confirms Washburn for both fluid and capillary
  property dependences

Increasing capillary radius
Fluids SC-1040 NL-870 ESM
Index matching (1.4587) ? ? ?
1.46 ?
1.48 ?
1.62 ?
1.63 ?
Changing fluid properties
actual fibre/fluid combination used for filled
fibres
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Problem Solved

• It is the empirical constant relating t and L
  that is useful for accurately filling fibres
• even if it cant be determined exactly from fluid
  and fibre properties
• And now it works, so Im told

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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

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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(1-3), p326-330