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Jens Eggers. How to make small things. Singularities!. very small scales created here. experiment by Shi et al. Why singularities?. Singularities are nature’s way of making small things. The simple mathematical structure of singularities permits detailed control. Printing challenges.
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Jens Eggers How to make small things
Singularities! very small scales created here experiment by Shi et al.
Why singularities? • Singularities are nature’s way of making • small things • The simple mathematical structure of singularities • permits detailed control
Printing challenges O. Basaran problem: satellites “engineer’s dream” satellite
Water drop experiment by D.H. Peregine et al., JFM `90 computed from 1-d model simulation from J. Eggers and T.F. Dupont, JFM 94
Two-fluid breakup: Cell division experiment by Spudich et al. Cohen, Brenner, Eggers, Nagel, PRL’99
Polymeric fluid (100 ppm of PEO) 1-D simulation experiment by Ch. Wagner
Nanojet symmetric pinching! J. Eggers, PRL `02 Moseler and Landman, Science 2000
Coalescence sphere sphere motiondriven by surface diffusion small enclosure
A sharp cusp air, V fluid, Ca Lorenceau et al, PRL ‘03
Pouring a viscous liquid fluid jet J. Eggers, PRL ‘01 E. Lorenceau, D. Quéré, PRL ‘03 viscous fluid E. Lorenceau, D. Quéré, J. Eggers, PRL ‘04 cusp cusp forms
Quest for microdrops: flow Cohen et al., Science `01: selective withdrawal
Small scales: bubble tip Increase flow rate bubble tip radius (microns) 0.5mm drain flow rate (g/s) experiment by S. Courrech du Pont
New structure: electric jets Taylor cone jet tiny droplets experiment by Pantano et al.
Moving contact lines receding contact line advancing contact line experiment by Podgorski et al., PRL `01 orientation of inclined plane
Contact line deposits deposit evaporation Robert Deegan, PRE `00 pinning-unpinning- pinning…
STM tips log(tipsize) log(tc-t) makes nano-sized tips! Quaade + Oddershede EPL `02
Conclusions • Singularities occur in a great variety of systems • Self-similarity is the natural language to describe • singularities. • Challenge: what ways are there to fixate singularities?
One-dimensional approximation Laplace Pressure inertia surf. tens. viscosity mass conservation J. Eggers, T. F. Dupont, JFM `94