# Presentation: 003355

## Jeff McFadden, NIST
Sam Coriell, NIST
Bruce Murray, SUNY Binghamton
Rich Braun, U. Delaware
Marty Glicksman, RPI
Marty Selleck, RPI

- Sam Coriell, NIST
- Bruce Murray, SUNY Binghamton
- Rich Braun, U. Delaware
- Marty Glicksman, RPI
- Marty Selleck, RPI

- Taylor-Couette Instabilities
- with a Crystal-Melt Interface

*G.I. Taylor Medalist Symposium in Honor of **Steve Davis*
*June 28, 2001*

- NASA Microgravity Research Program

## Coupled Hydrodynamic/Morphological Instabilities

- Flow in the melt modifies the thermal and solutal gradients at the crystal-melt interface that determine the  morphological stability of the interface.

- The shape of the crystal-melt interface modifies the fluid flow near the interface and affects the hydrodynamic stability of the melt.

- S.H. Davis, *Effects of Flow on Morphological Stability*,  _Handbook of Crystal Growth_, Vol. I, ed. D.T.J. Hurle (Elsevier, Amsterdam, 1993), Ch. 13.

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Benard Convection

- The interface morphology changes from rolls to hexagons as the solid thickness is varied.

- S.H. Davis, U. Muller, and C. Dietsche, JFM (1984)

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Modulated Taylor-Couette Flow

- Rigidly Co-Rotating Cylinders
- in Time-Harmonic Motion

- Radial Temperature Gradient

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Interface Instability

**Succinonitrile (SCN)**

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Taylor-Vortex Flow

- Multiple-exposure image capturing marker particle at periodic intervals of the motion

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Floquet Theory

**Floquet Theory**

- Discretize in space; solve ODEs in time over one period; or
- Fourier series in time; solve spatial eigenproblem:

- (rigid)

- (crystal-melt)

- (crystal-melt)

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Steady Rotation

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Linear Eigenmodes

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Counter-Rotating Cylinders

- Instability is localized away from the interface.

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Bouyancy-Driven Flow

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Summary

- An otherwise stable interface is destabilized by the flow
- Taylor-Couette flow is strongly destabilized for materials with moderate Prandtl numbers
- Organics and oxides have moderate-to-large Prandtl numbers; metals and semiconductors have small Prandtl numbers. (For solute diffusion, the Schmidt number is usually large.)
- Weakly-nonlinear analysis hasn’t been done for these problems
- General understanding of when strong coupling will occur is lacking

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## Material Properties of SCN

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions 

## References

- G.B. McFadden, S.R. Coriell, M.E. Glicksman, and M.E. Selleck, Instability of a Taylor-Couette flow interacting with a crystal-melt interface, *PCH Physico-Chem. Hydro.* **11** (1989) 387-409
-  G.B. McFadden, S.R. Coriell, B.T. Muarray, M.E. Glicksman, and M.E. Selleck, Effect of a crystal-melt interface on Taylor-vortex flow, *Phys. Fluids A ****2**** (1990) 700-705*.
- G.B. McFadden, B.T. Murray, S.R. Coriell, M.E. Glicksman, and M.E. Selleck, Effect of modulated Taylor-Couette flows on crystal-melt interfaces: Theory and initial experiments, in _On the Evolution of Phase Boundaries,_ ed. M.E. Gurtin and G.B. McFadden (Springer-Verlag, New York, 1992), pp. 81-100.
- R.J. Braun, G.B. McFadden, B.T. Murray, S.R. Coriell, M.E. Glicksman, and M.E. Selleck, Asymptotic behavior of modulated Taylor-Couette flows with a  crystalline inner cylinder, *Phys. Fluids A ****5**** (1993) 1891-903.*
- G.B. McFadden, B.T. Murray, S.R. Coriell, M.E. Glicksman, and M.E. Selleck, Effect of a crystal-melt interface on Taylor-vortex flow with buoyancy, in _Emerging Applications in Free Boundary Problems_, ed. J.M. Chadham and H. Rasmussen (Longman Scientific & Technical, New York, 1993), pp. 105-119.

- 28 June 2001

**Notes:**
Fern and Antii – matrix plot of sequences up to 10 proteins long – GENBANK
Fern and Tony – reconstructing a genetic sequence from an incomplete sequence with gaps and deletions