Transcript Corning Corporate Blue PowerPoint Template allowing

MTE-AMA
Elongating Bubble in an Accelerating
Extensional Flow
John Abbott
Mathematics in Industry Workshop 06/16/2008
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
• R&D 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 Corning’s 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 R&D 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
Mathematical Problems in Industry June 2008
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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
Mathematical Problems in Industry June 2008
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“Blisters” in volcanic magma
Rust, Manga, Cashman 2003
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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/DopantFinal.pdf
Because of cylindrical
geometry 2D plot does not
show cross-sectional area.
log R
dT/dz=0
determines
‘inflection’
Where log R vs. z is convex,
heat is going into blank.
Where log R vs. z is concave,
heat is coming out.
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Velocity U(z) and extension rate dU/dz
We can approximate u(z) by
something convenient: exponential
heating, exponential cooling.
log u(z)
z
(du/dz)
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
Mathematical Problems in Industry June 2008
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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!
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