# Presentation: 003352

## Analysis of Hydrodynamic and Interfacial Instabilities During Cooperative Monotectic Growth

- Cooperative monotectic growth
- Sources of flow with a fluid-fluid interface
- Regular solution model of the Al-In miscibility gap
- Modes of instability for a growing fluid-fluid interface
- Compute the morphological stability of a fluid-fluid interface during directional growth

- G.B. McFadden, NIST
- S.R. Coriell, NIST
- K.F. Gurski, NIST
- B.T. Murray, SUNY Binghamton
- J.B. Andrews, U. Alabama, Birmingham

- NASA Physical Sciences Research Division

## Slide 2

**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 

## Modeling Flow Effects During Monotectic Growth:

- Difficulty: Cooperative growth is a complex process with three phases in a complicated geometry. Typical theoretical approaches involve rough order-of-magnitude estimates or full-scale numerical calculations in 2-D or 3-D.

- Idea: Idealize to two phases (fluid-fluid) in a simplified geometry (planar interface) where flow effects can be assessed quantitatively by their effects on linear stability.

- Related Work: Directional solidification of liquid crystals; convective stability of liquid bi-layers.

**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 

## Sources of convection with a liquid-liquid interface:

- Thermosolutal convection (Coriell et al.)
- Density-change convection
- Thermocapillary convection (Ratke et al.)
- Pressure-driven convection (Hunt et al.)

**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 

## Al-In Phase Diagram

- C.A. Coughanowr, U. Florida (1988)

**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 

## Equilibrium Thermodynamics

**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 

## Sub-regular solution model of Al-In miscibility gap

- U. Kattner, NIST; C.A. Coughanowr, U. Florida (1988)

**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 

## Do directional transformation of L1 () phase into L2 () phase

- Do directional transformation of L1 () phase into L2 () phase

- 

- 

- V

**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 

## Modes of instability with a fluid-fluid interface:

- Double-Diffusive instability [Coriell et al. (1980)]
- Rayleigh-Taylor instability [Sharp (1984)]
- Marangoni instability [Davis (1987)]
- Morphological Instability [Mullins & Sekerka (1964)]

- Consider the flows driven by inhomogeneities generated by morphological instability at micron-sized length scales.

**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 

## V = 2 m/s

- V = 2 m/s

**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 

## Morphological Stability Analysis with No Flow

**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 

## [Pole in dispersion relation for k < 0]

**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 

## Slide 13

**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 

## Morphological Stability Analysis with Flow

**BVSUP** – Orr-Sommerfeld equations + transport
-                  H. Keller’s  approach for eigenproblem

- Re-introduce flow terms one at a time:

**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 

## Slide 15

**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 

## Slide 16

**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 

## Slide 17

**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 

## Slide 18

**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 

## Orders of Magnitude of Flow Effects

**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

- Flow interactions with the morphological mode may be computed numerically.
- Buoyancy, density-driven, and thermocapillary flows interact weakly at micron scales (thermocapillary has bimodal behavior at 100 micron scale).
- Pressure-driven flow shows large stabilizing effect at micron scales.

- In progress: Interpretation of eigenfunctions; additional modes

**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