Title: John%20Abbott
1 MTE-AMA
Elongating Bubble in an Accelerating Extensional
Flow
- John Abbott
- Mathematics in Industry Workshop 06/16/2008
2Outline
- Introduction to Corning!
- Brief Problem Statement
- Background, Introduction, and Context
- Pictures
- References Previous work
- Restatement of Problem
- Extensions, further work which might be possible
3Corning 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)
4Environmental 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..
5Display 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
6Optical 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
7Optical Fiber
8Outline
- Introduction to Corning!
- Brief Problem Statement
- Background, Introduction, and Context
- Pictures
- References Previous work
- Restatement of Problem
- Extensions, further work which might be possible
9Problem 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.
10Outline
- Introduction to Corning!
- Brief Problem Statement
- Background, Introduction, and Context
- Pictures
- References Previous work
- Restatement of Problem
- Extensions, further work which might be possible
11Blisters in volcanic magma
12Experimental measurement of bubble shapes
Rust, Manga 2002
An optical fiber airline has a large aspect ratio
l/a
13Previous 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
14Previous 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.
15Generic 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
16Velocity 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
17Input 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.
18Outline
- Introduction to Corning!
- Brief Problem Statement
- Background, Introduction, and Context
- Pictures
- References Previous work
- Restatement of Problem
- Extensions, further work which might be possible
19Problem 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?
20Outline
- Introduction to Corning!
- Brief Problem Statement
- Background, Introduction, and Context
- Pictures
- References Previous work
- Restatement of Problem
- Extensions, further work which might be possible
21 Thank you!