Controlling the position of desiccation cracks

using memory effect of paste

Physics of Glassy and Granular Materials YITP, Kyoto, 17 July 2013

Y. Matsuo, H. Nakayama Ooshida Takeshi M. Otsuki S. Kitsunezaki

Nihon Univ. Tottori Univ.

Shimane Univ.

Nara Women’s Univ.

A. Nakahara (Nihon Univ.)

H. Nakayama

Y. Matsuo

A. N.

A. N.

S. Kitsunezaki

Ooshida Takeshi

M. Otsuki

Nihon Univ. Tottori Univ.

Shimane Univ.

Nara Women’s Univ.

Contraction due to drying ＋

Adhesion at the bottom

Formation of cracks spacing ~ depth of paste

To release stress horizontally

crack

Desiccation cracks of colloidal suspension

Usually cellular isotropic cracks

Crack patterns produced by memory effect

water

Colloidal particles

（~μm)

= + Random Structure?

(memory)

? Memory is induced by plasticity

vibration

Desiccation crack patterns produced by memory effect

Lamellar Radial lattice Diameter 500mm

Spiral Spiral Ring

Depth ~ 10mm

Protocol of our drying experiments CaCO3 powder

Mix

Water

Pour

t

Shake horizontally

Paste

0

Leave still and dry

cracks 1 minute

2 days (1 month)

Top view

Paste remembers the direction

of initial vibration

Cracks run perpendicular to initial vibration

Paste

Top view

Pour

Paste

Cracks

perpendicular

to vibration

t

Shake horizontally

0

Leave still and dry

cracks 1 minute 2 days Memory

of

vibration

Cracks

perpendicular

to vibration

Memory of vibration

Stop vibration & dry

Water-poor CaCO3 paste

Lamellar cracks

(perpendicular to vibration)

Memory of vibration

Initial vibration

(horizontally)

Crack formation (top view)

Paste is

vibrated

Water-rich CaCO3 paste

Cellular cracks

(isotropic and homogeneous)

No memory

Paste is

vibrated

and fluidized

+ charged

A. Nakahara and Y. Matsuo J. Phys. Soc. Jpn. 74 (2005) 1362.

Water-rich

Uncharged Pastes remember vibration and flow !

Memory of flow

Initial vibration

paste

vibration

paste

flow

Stop & dry

Water-poor

Memory of vibration

Crack formation

Magnesium Carbonate Hydroxide, Carbon, Kaolin, etc.

Water-too-much

No memory

paste

Turbulence

Uncharged A. Nakahara and Y. Matsuo

PRE. 74 (2006) 045102.

Morphological Phase Diagram of uncharged paste Yield stress

vibration flow

lamellar cracks (perpendicular)

lamellar cracks

(parallel)

Liquid limit

Plastic limit

cellular cracks no movement

cellular cracks

turbulence

B C

cellular cracks (no movement) no movement no experience A

C

B vibration

flow

remember

forget

Lamellar cracks (perpendicular)

Cellular cracks (no memory) D turbulence

remember Lamellar cracks (parallel)

magnesium carbonate hydroxide

Movies of

Uncharged paste has memories of vibration and flow.

cellular cracks (no movement)

Morphological phase diagram of charged CaCO3 paste

Yield stress

vibration

Lamellar cracks

(perpendicular)

no movement no experience A

Liquid limit Plastic limit

Cellular cracks

turbulence

no movement

Cellular cracks

B

A

C

flow

C

CaCO3 paste has a memory of vibration, but it has no memory of flow.

Solid volume fraction ρ[%]

B vibration

flow

turbulence

remember

forget

forget

Lamellar cracks (perpendicular)

Cellular cracks (no memory)

Cellular cracks (no memory)

Memory effect and jamming transition

Plastic limit Liquid limit

Density ρ

Shear stress γ

Yield stress σY

jammed

unjammed

t

Shake horizontally

0 1 minute

Pour

Shake

0

Stress σ

Stre

ss σ

・

jammed － σY σY

Imprint memory here!

unjammed

unjammed

σY

Shake 0

Memory effect and jamming transition

Plastic limit Liquid limit

Density ρ

Shear stress γ

Yield stress σY

jammed

unjammed

t

Shake horizontally

0

Leave still and dry

cracks 1 minute 2 days Pour

Shake

0 Leave still and dry

cracks

Stress σ

Stre

ss σ

・

jammed － σY σY

Imprint memory here!

unjammed

unjammed

σY

Shake 0

Memory effect

Horizontal stretching compression Model A (Otsuki)

Residual tension models for memory of vibration M. Otsuki, PRE 72 (2005) 046114.

Ooshida T., JPSJ 78 (2009) 104801.

g

Model B (Ooshida) Shear deformation vibration

Ooshida Model shear

deformation

Otsuki Model horizontal stretching

Crack here

Cracks anywhere

g

g

Where will cracks appear by Residual tension models? M. Otsuki, PRE 72 (2005) 046114.

Ooshida T., JPSJ 78 (2009) 104801.

Model B (Ooshida) Shear deformation

Horizontal stretching compression Model A (Otsuki)

vibration

g

stretching compression

Model A (Otsuki) Horizontal stretching

g

vibration Model B (Ooshida) Shear deformation

stre

tch

ing

Model A (Otsuki) : Rewriting experiment Model B(Ooshida) : Only shear

① ① ②

①Only vibration ① Vibration＋② Go and Stop

shear

Go and Stop

Verification of two residual tension models

Both models are needed!

Memory of vibration Memory of vibration Memory of vibration

Conclusion 1

● Memory of vibration = residual tension

● Memory of flow = elongation of dilute network under flow

flow

shear

compression stretching

vibration

Water-poor

Water-rich Uncharged

flow

vib

rati

on

Attractive interaction is needed.

Can we control position of cracks?

paste

position ・・・stochastic

dry cut

Horizontal vibration

ρ=6.7%

Direction: imprinted by memory effect Position : stochastically formed

Memory of flow (memory of vibration)

direction・・・by same memory

Memories are formed not by macroscopic hydrodynamic structure like convection.

stop

By horizontal vibration… Control only Direction of crack propagation!

Experimental setup for vertical vibration

Circular container diameter d = 200 cm

Paste: Water-poor CaCO3 paste (only memory of vibration)

Position control of cracks using Faraday waves

Square container 150mm side

vertical vibration

Position control by vertical vibration

Vertical vibration (Faraday waves)

↓ Stop and dry!

Square lattice

Turbulence

stripe

diameter d = 200 cm

Water-poor CaCO3 paste

which has only

memory of vibration

Stop vibration & dry

stripe

Ring

Stripe and ring cracks produced by vertical vibration Vertical vibration→ Faraday waves desiccation crack patterns

overlap

Faraday waves Desiccation crack pattern

Spatial correlation between Faraday waves and cracks

Where do cracks appear?

At overlapping process, give attention to subharmonic oscillation!

Structure of Faraday waves of CaCO3 paste

Period of Faraday waves TF

= 2 × Period of vertical vibration TV

Side view : Square waves

Tim

e

t +TV

t

t +2TV

TF

Subharmonic oscillation

One shake

One more shake

Same phase

Same phase

Horizontal oscillation in node regions

Analytic

Schematic

A

N : Node regions A : Anti-node regions

A A A

N N N

A

A A

A

A

A A

A N

N

N

N N

N

Localized horizontal vibration

at node regions (Memory of vibration)

One shake One more shake

Superposition of successive Faraday waves and desiccation cracks

t +TV

t desiccation cracks Superposition of

successive Faraday waves

Superposition of successive Faraday waves and desiccation cracks

Faraday waves at each snapshot

Node regions

Anti-node regions

Ratio of observing cracks at node regions to that of anti-node regions

Statistical analysis

Check this crack

Ln : length of cracks at node region

La : length of cracks at anti-node region

Node regions

Anti-node regions

Statistical analysis

Check this crack

Ratio of observing cracks at node regions to that of anti-node regions

La

Ln

Ln La

aa

nnlog

SL

SLP e

node regions

anti- node regions

Sn : Area of node region Sa : Area of anti-node region

At node regions, cracks are formed

1.276.0 eeP times

more frequently than in anti-node regions.

40.076.0 P

From 10 experiments

Cracks emerge at node regions.

Square lattice cracks produced by vertical vibration Vertical vibration → Faraday waves

Lattice structure desiccation crack patterns

Stop & dry

Square lattice

Stop & dry

Why tilt by 45o ?

Square lattice

Why tilt by 45o ?

Reason for tilt by 45o

excited

anti-node

Cracks at nodes

Localized

horizontal

vibrations

across

node-lines

Descended

anti-node

node

Tilt by 45o

● Using vertical vibration, we can control

not only the direction but also the position of cracks.

Conclusion 2

● Cracks with lattice structure can be created !

Square lattice

H. Nakayama, Y. Matsuo, Ooshida Takeshi and A. Nakahara European Physical Journal E 36 (2013) 1.

Further applications 1. What will happen in future (Technology)

Control microstructure of materials,

anisotropy in conductivity and elastic moduli,

and macroscopic crack patterns

2. What happened before (Geoscience)

Know past by memories and cracks in rocks

Future plans Flow ・・・ large deformation

● Definition and quantification of Memories in pastes

including Memory of flow

● Theoretical model which explains Memory of flow

● Transition from Memory of vibration to Memory of flow

Future plans 2

Mechanical method (vibration, flow) A. Nakahara & Y. Matsuo JPSJ (2005), PRE (2006)

Physics Today, September (2007) 116

Electrical method D. Mal et. al., Physica A (2007)

Magnetic method L. Pauchard et. al., PRE, (2008) A. T. Ngo et. el., Nano Letters (2008)

Combine various external fields to control crack patterns

Desiccation cracks