Jens Eggers

How to make small things

Singularities!

experiment by Shi et al.

very small

scales created

here

•Singularities are nature’s way of making small things

Why singularities?

•The simple mathematical structure of singularitiespermits detailed control

Printing challenges

O. Basaran problem:satellites

satellite “engineer’sdream”

experiment byD.H. Peregine et al.,JFM `90 computed

from 1-dmodel

simulation from J. Eggers and T.F. Dupont,JFM 94

Water drop

experiment bySpudich et al.

Two-fluid breakup: Cell division

Cohen, Brenner,Eggers, Nagel, PRL’99

experiment byCh. Wagner

1-D simulation

Polymeric fluid (100 ppm of PEO)

Moseler and Landman, Science 2000

Nanojet

symmetric pinching!J. Eggers, PRL `02

sphere sphere

Coalescence

motion driven by surfacediffusion

small enclosure

A sharp cusp

Lorenceau et al, PRL ‘03

V fluid,

air,

fl

g

200 m

Ca

viscous fluid

fluid jet

cusp forms

Pouring a viscous liquid

E. Lorenceau,D. Quéré,J. Eggers, PRL ‘04

cusp

J. Eggers, PRL ‘01

E. Lorenceau,D. Quéré,PRL ‘03

Quest for microdrops: flow

Cohen et al., Science `01: selective withdrawal

but: smallest tip size 200 m

Small scales: bubble tip

Increase flow rate

tip radius(microns)

flow rate (g/s)

bubble

drain0.5mm

experiment byS. Courrech du Pont

experiment byPantano et al.

New structure: electric jetsTaylor cone

jettiny droplets

Moving contact lines

experiment by Podgorski et al., PRL `01

orientation of inclined plane

advancing contact line

receding contact line

Contact line deposits

Robert Deegan,

PRE `00

evaporationdeposit pinning-unpinning-

pinning…

0.1 particlesm surfactant

STM tips

Quaade + Oddershede EPL `02

log(tipsize)

log(tc-t)

makes nano-sized

tips!

•Singularities occur in a great variety of systems

Conclusions

•Self-similarity is the natural language to describe singularities.

•Challenge: what ways are there to fixate singularities?

( , )h z t

2 20( v ) 0zh ht mass conservation

20

0 0 0 2

( v )v v v 3

hz z

z z

hpt

inertia surf. tens. viscosity

J. Eggers, T. F. Dupont, JFM `94

2

32 2

1

1 ( ) 1 ( )

z

z z

hp

h h h

Laplace Pressure

One-dimensional approximation