John%20Abbott

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MTE-AMA
Elongating Bubble in an Accelerating Extensional
Flow

• John Abbott
• Mathematics in Industry Workshop 06/16/2008

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Outline

• Introduction to Corning!
• Brief Problem Statement
• Background, Introduction, and Context
• Pictures
• References Previous work
• Restatement of Problem
• Extensions, further work which might be possible

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Corning Incorporated

• RD labs celebrating 100th year anniversary
• Corporate member of IMA at Univ. of Minnesota
• Emphasis on innovation and new products
• Light bulb worked with Edison, all incandescent
  light bulbs in the world are made by the high
  speed ribbon machine developed by Corning
• Glass for Cathode Ray TVs (CRTs) color TVs
• Silicones spun off to Dow-Corning (private
  company)
• Fiber glass insulation spun off to
  Owens-Corning Fiberglas
• Optical Fiber low cost, low attenuation optical
  fiber for telecommunications
• Precision glass for LCD flat panel displays
• Extruded Ceramics for catalytic converter
  substrates
• Specialty glass ceramics (mirror blank for
  Hubble telescope)

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Environmental Products

• Corning makes ceramic substrates catalytic
  converters for cars

The substrate is made by extruding wet ceramic
through a die with hundreds of holes the holes
need to be uniform. In drilling the holes the
drills used to wear out..
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Display Large Glass Sheets for LCD displays

• Corning invented a process for making sheet glass
  where the glass flows over two sides of a weir,
  so that the final sheet has two pristine surfaces.

0.7mm thick
Gen 8 2160x2460mm Gen10 3000x3000m
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Optical Fibers

• One of Cornings big businesses
• is optical fiber essential to the internet.

The combustion synthesis process used to make
pure SiO2 was developed by Franklin Hyde at the
Corning RD labs, the same fellow who invented
silicones. The same process is used to make
windows for the space shuttle and the glass for
the Hubble space telescope. GeO2 SiO2 optical
fibers TiO2 SiO2 low thermal expansion
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Optical Fiber
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Outline

• Introduction to Corning!
• Brief Problem Statement
• Background, Introduction, and Context
• Pictures
• References Previous work
• Restatement of Problem
• Extensions, further work which might be possible

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Problem Statement

• How is a single spherical bubble or seed
  stretched as it moves down the tapering root
  during a high speed optical fiber draw process?
• The leading tip of the bubble sees an
  exponentially increasing velocity (and
  extensional rate). How (if at all) does the
  shape differ from the distortion in either simple
  shear flow or simple extensional flow.

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Outline

• Introduction to Corning!
• Brief Problem Statement
• Background, Introduction, and Context
• Pictures
• References Previous work
• Restatement of Problem
• Extensions, further work which might be possible

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Blisters in volcanic magma
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Experimental measurement of bubble shapes
Rust, Manga 2002
An optical fiber airline has a large aspect ratio
l/a
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Previous Analysis (Hinch Acrivos papers)

• 11 Hinch, E.J., and Acrivos, A., Long slender
  drops in a simple shear flow, Journal of Fluid
  Mechanics Vol. 98 Issue 2 (1980) pp. 305-328.
• Some differences between simple shear flow and
  simple extensional flow

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Previous Analysis (Howell Siegel papers)

• 15 Howell, P.D., and Siegel, M., The evolution
  of a slender non-axisymmetric drop in an
  extensional flow, Journal of Fluid Mechanics
  Vol. 521 (2004) pp. 155-180..
• Both Howell-Siegel and Hinch-Acrivos predict the
  pointed ends to the elongating bubbles which is
  seen in practice.

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Generic Draw Model use Huang/Miura/Wylie where
possible.

• 9 Huang, H., Miura, R.M., and Wylie, J.J.,
  Optical Fiber Drawing and Dopant Transport,
  submitted to SIAM J. Applied Math 2008
• www.math.yorku.ca/Who/Faculty/hhuang/preprints/Dop
  antFinal.pdf

Because of cylindrical geometry 2D plot does not
show cross-sectional area.
Where log R vs. z is convex, heat is going into
blank. Where log R vs. z is concave, heat is
coming out.
log R
dT/dz0 determines inflection
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Velocity U(z) and extension rate dU/dz
We can approximate u(z) by something convenient
exponential heating, exponential cooling.
(du/dz)
log u(z)
z
z
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Input to problem

• Need assumed V(z) and dV/dz.
• Blank shape D(z), velocity V(z), and temperature
  T(z) all need to be consistent.
• JSA to provide base model.

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Outline

• Introduction to Corning!
• Brief Problem Statement
• Background, Introduction, and Context
• Pictures
• References Previous work
• Restatement of Problem
• Extensions, further work which might be possible

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Problem Statement

• How is a single spherical bubble or seed
  stretched as it moves down the tapering root
  during a high speed optical fiber draw process?

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Outline

• Introduction to Corning!
• Brief Problem Statement
• Background, Introduction, and Context
• Pictures
• References Previous work
• Restatement of Problem
• Extensions, further work which might be possible

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Thank you!