Roman Mani (3)

Hans Herrmann (3)

Ciro Semprebon (1)

Stephan Herminghaus (1)

Capillary forces in assemblies of three spherical particles

B8: Capillary interactions and particle dynamics

10/9/2012 1Siegen, Piko Workshop

(1) Max Planck-Institute for Dynamics and Self-Organizatin, Göttingen, Germany

(2) Experimental Physics, Saarland University, Saarbrücken, Germany

(3) ETH Zurich

Hans Herrmann (3)

Dirk Kadau (3)

Stephan Herminghaus (1)

Martin Brinkmann (1,2)

Zuerich: collective behavior

(contact dynamic simulations)

Goettingen:

Transport phenomena in wet granular assemblies

10/9/2012 2Siegen, Piko Workshop

Stability and capillary forces in clusters:

Beyond the bridge models

Fij

Liquid transport through bridges

Qij

bridge

trimer

pentamer heptamerto

tal liq

uid

surf

ace S

[p

ixel]

tetrahedron

and trimer

liquid volume V [voxel]

tota

l liq

uid

surf

ace S

[p

ixel]

tetrahedronM Scheel et al.

Nature Materials

7: 189 (2008)

10/9/2012 3Siegen, Piko Workshop

capillary forces

• Total force acting on the center of a bead according to parallelogram rule:

• Determine relation between pressure, forces, volume and geometry

(separation distances ) using numerical energy minimization

Force between bead i and j:

Laplace pressure:

No capillary torques on beads if

contact angle hysteresis is absent

10/9/2012 4Siegen, Piko Workshop

Fij sij

Single gap trimer

TrimerDimer

Force at Force at

Trimer Dimer

Force at

contact

Force at

gap

• Force at gap for dimer negligible

• Find two different decay

mechanisms for trimer

10/9/2012 5Siegen, Piko Workshop

Trimer with two gaps, constant volume

Force at gap 02Force at contact 12

Capillary forces in trimer can be well

approximated by pair interactions

• contact betwen bead

1 and 2 ( s12 = 0 )

• bead 0 moving

10/9/2012 6

Other volumes and separations…

s12=0, Vol=0.15 s12=0, Vol=0.2

10/9/2012 7Siegen, Piko Workshop

s12=0, Vol=0.25 S12=0.05, Vol=0.25 s12=0.1, Vol=0.25

Analysis

Vol=0.25 s12=0

Trimer (diagonal)Bridge

10/9/2012 8Siegen, Piko Workshop

With first approximation…

10/9/2012 9Siegen, Piko Workshop

Trimer modeled by a superposition of

“repulsive springs”Symmetric trimers are sufficient

to calculate the coefficients.

s12=s01=s02

Model

Total energy

Modulus of force along a pair of spheres

10/9/2012 10Siegen, Piko Workshop

Coefficients are in general determined

by features of spheres and liquid volume…. Mixing rules

Pressure

Coefficients as function of volume

Offset energySpring constant

10/9/2012 11Siegen, Piko Workshop

Offset separation

Symmetric trimer stability

Checks of the model

Energy numeric

Vol=0.2

Energy model

Vol=0.2

Energy difference

Vol=0.2

10/9/2012 12Siegen, Piko Workshop

Force numeric

Vol=0.2

Force model

Vol=0.2

Force difference

Vol=0.2

Trimer with two gaps, constant pressure

Force at gap 02 Force at contact

12

In case of liquid exchange (pressure as control parameter)

Capillary forces in trimer can be well

approximated by pair interactions

• contact betwen bead

1 and 2 ( s12 = 0 )

• bead 0 moving

10/9/2012 13

Discrete liquid model (outlook)

Thanks for your attention !!!

10/9/2012 14Siegen, Piko Workshop

Linear elements(bridges)

Surface elements(trimers)

Volume elements(filled tethraedra)

Thanks for your attention !!!