Synchronization of polymer Synchronization of polymer moleculesmolecules

Andriy Hlod

dr. R. Koopmansdr. ir. J. den Doelderdr. J. ClaracqThe Dow Chemical Company, Terneuzen

prof. dr. J. Molenaardr. ir. A.A.F. van de VenEindhoven University of Technology

OutlineOutline

• SynchronizationSynchronization

• Flow instabilitiesFlow instabilities

• Problem descriptionProblem description

• Model of polymer moleculesModel of polymer molecules

• Model of moving moleculesModel of moving molecules

• Conclusions Conclusions

• RecommendationsRecommendations

Sync. (discovering)Sync. (discovering)

• Christiaan HuygensChristiaan Huygens(1665)(1665)

• Mutual Mutual synchronization of two synchronization of two pendulum clockspendulum clocks

• Coupling through Coupling through beam or wallbeam or wall

Sync. (examples)Sync. (examples)

1. Applause in theater

2. Male fireflies flashes

3. Circadian rhythm

Sync. (definition)Sync. (definition)

Synchronization:Synchronization: Adjustment of rhythms of oscillating objects due to their weak interaction

Sync. (polymer molecules)Sync. (polymer molecules)

•Polymer molecules are oscillators

•Polymer molecules are coupled, they can influence oscillations of each other

Can polymer molecules be synchronized?

Flow instabilities (extruder)Flow instabilities (extruder)

Flow instabilitiesFlow instabilities

Flow instabilities (videos)Flow instabilities (videos)

flow stress birefringence images from Christelle Combeaud,from CEMEF, Francefor the 3PI project

Problem descriptionProblem description

Is it possible that the dynamics of the polymer molecules show synchronization?

If the answer is positive, is there a relation with flow instabilities in polymers?

Model of a polymer moleculeModel of a polymer molecule

•Elastic dumbbellElastic dumbbell (two beads and(two beads and Maxwell element) Maxwell element)

•Kicks to compensateKicks to compensate energy dissipationenergy dissipation

Model of a polymer molecule (kicks)Model of a polymer molecule (kicks)

Model of two molecules

- Maxwell elementM

Result (model of two molecules)

Is it possible that the dynamics of the polymer molecules show synchronization?

Synchronization is possible for this Synchronization is possible for this specific configuration of polymer molecules.specific configuration of polymer molecules.

Still to answer: Still to answer: Is there a relation with flow instabilities in polymers?

Moving molecules (flow)

• Shear flow

• Small region with two parallel layers of molecules

Moving molecules

Moving molecules (model)

cFE – finitely

extensible spring

20

( )1 ( / )

FEc RF R

R R

Moving molecules (model)

D - dash-pot

2

0( ) ijad

C ijd e

Results (synchronization for small V)

Results (oscillations increase for large V)

Results (energy)

small V

Edissipation + Eoscillations = Einput

larger V

Edissipation + Eoscillations = Einput

Results (energy for large V)

Results (influence of V)

V

Synch Chaos E oscillations

0 Vcritical

Is there a relation with flow instabilities in polymers?

Vcritical indicates the onset of instabilities in the model of moving molecules.

Conclusions

• Polymer molecules show synchronous behaviour

• Model of moving molecules shows instabilities for V> Vcritical

Recommendations

• Continue research

• Use real parameters for the model of moving molecules