Jens Eggers Polymer threads: formation and instability.

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Presentation transcript:

Jens Eggers Polymer threads: formation and instability

Drop breakup …creates extensional flow and produces multiple singularities water drop

Flexible polymers  characteristic time λ  extension rate  stress ~ extension  maximal extension

50 ppm PEO in water Y. Amarouchene et al. PRL 86, 3558 (2001) water 1.2mm, T = 0,1 sec Polymers Wagner + Sattler

polymer ( Ch. Clasen ) beads on a string Polymer breakup: overview blistering water jet

surface tension- inertial balance: W. Strutt (1873)fastest growing mode: Newtonian breakup: linear stability

glycerol drop center 1mm experiment by Tomasz Kowalewski Newtonian breakup: similarity solution Eggers, PRL `93

Bead formation Wagner et al., PRL ‘05 pure water PEO in water

One-dimensional approximation Entov et al. `80 Renardy `82 stretching

Thread formation Ch. Clasen and G. McKinley Bazilevskii et al, `81: thinning dominated by end effects!

Corner region threaddrop Clasen et al., JFM ‘06 similarity solution string tension:

Experiment: rescale drop thread Clasen et al. JFM ‘06 similarity form: …but experimental curvature greater x 2 Boger fluid

Blistering instability increases by 5 orders of magnitude! full strech Fontelos + Li: Rayleigh instability with effective Sattler et al., PRL ‘08 PEO in water, 2000 ppm

Rayleigh instability? time (ms) sub-pixel resolution!

Nonlinear instabilities 1)Iterated thread instability (bulk) 2) Breathing instability (end)

Weird instabilities

PEO, 4Mio M W, 2kppm, overall duration 0.016s Does it ever break? drops do not wet the fiber!

A solid fiber!

Mayonnaise, ketchup, yoghurt movies by D. Bonn

Remarks, open problems No predictive model for flow at high deformations! FENE-P: have to be treated as adjustable thinning rate of filament depends significantly on concentration (factor 10), and even on nozzle radius! no significant quantitative statement about saturation! filament thinning still open (stability, full 3D model) mechanism for demixing ???! extensional behavior of suspensions; is there extensional thinning?

Wagner, Amarouchene, Bonn, Eggers: PRL (`05) 1-D simulation Polymeric fluid (100 ppm of PEO) experiment