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
Recommended
