TSU Seminar, JNCASR, March 2016

Structural properties of a binary colloidal mixture under shear reversal

Amit e

Workshop Bartholomäberg

Shear reversal simulations of a vitrifying colloidal melt: Rheology, microstructure and puzzles

Amit Kumar Bhattacharjee

Department of Physics,IISc Bangalore

March 29, 2016

Funding:

TSU Seminar, JNCASR


Amit Bhattacharjee


Prologue

Solid, liquid, gas, plasma.

F = E – TS; Hard matter (crystals) = E dominated phases (minimize E);

Soft matter (liquids) = S dominated phases (maximize S).

Changes of phase – order of transition (e.g. liquid to solid, paramagnet to

ferromagnet).

Soft to touch, easily malleable, can't withhold shear.

Examples: milk, paint (colloid), rubber, tissues (polymer), toothpaste (gels),

LCD devices (liquid crystal), ….

States of matter

Complex fluids

Amit Bhattacharjee

Introduction Methods Glassy Rheology Bauschinger effect Conclusion

2IISc Bangalore

Prologue

Theoretical methods Atomistic description:

i) Ignore electronic d.o.f. classical N-particle Newton's equation.

ii) approximation: 2-body interactions in central forcefield (e.g. LJ, Yukawa, WCA).

Mesoscopic description:

i) Identify order parameter, broken symmetry, conservation laws,

type of transition of the phase. ii) Construct a free energy functional and spatial coarse-graining.

iii) Temporal coarse graining.

Measurement of the equilibrium and nearly-equilibrium properties.

Amit Bhattacharjee


3IISc Bangalore

Prologue

CFDTDGL

LLNSDPD / SPHBDSRDLBM

DFTMDKMC

Meso-scale

Micro-scale

Length

Time

Computational methods

Macro-scale

Amit Bhattacharjee


4

μ s ms−sfs− ps

nm

μm

mm

IISc Bangalore


Workshop Gauertal

[1] Vailati et al, Nature Comm. (2011).

Amit Bhattacharjee

5mm side1mmthick

[2] GRADFLEX Experiment: https://spaceflightsystems.grc.nasa.gov/sopo/ihho/psrp/expendable/gradflex/

Work at CIMS, NYU (2013-2015)

Soret effect induced large-scale nonequilibrium concentration fluctuations in

microgravity[1,2].

We formulated complete theory to study quantitatively multicomponent liquid diffusion

with thermal fluctuations and flow from first principles of non-eq TIP.

IISc Bangalore

Post-doctoral work

∂t (ρi)+∇⋅(ρi v) = ∇⋅{ρW [χ (Γ∇ x+(ϕ−w)∇ Pnk BT

+ζ∇ TT )]+√2 k B L12 Ζ}

∂ t (ρ v)+∇ π =−∇⋅(ρ v vT )+∇⋅(η(∇+∇T)v+Σ)+ρ g

5


Workshop Gauertal

Amit Bhattacharjee

Work at IMSc (2007-2010), IISc (2015-)

Inhomogeneous phenomena in nematic liquid crystals.

We formulated first direct computation of tensorial Landau-deGennes theory of nematics

incorporating thermal fluctuations. The advantage been to settle down many controversies

ongoing in the field (e.g. “deGennes ansatz” for I-N interface).

IISc Bangalore 6

Ph.D. work

FGLdG=∫ d3 x [

12ATrQ2+

13BTrQ3+

14C (TrQ2)2+E ' (TrQ3)2+

12L1(∂αQβγ)(∂αQβγ)

+12L2(∂αQαβ)(∂γQβγ)]; ∂tQαβ(x , t)=−Γαβμ ν

δ FGLdG

δQμ ν

+ζαβ( x , t )


Workshop Gauertal

Amit Bhattacharjee

IISc (2015-)

IISc Bangalore 6

Ph.D. work

Time-lapse movies:


Amit Bhattacharjee


Amit Bhattacharjee


7

(a) Alloy of linear size 4.3nm, (b) colloidal systems, (c) a beer foam with sub-millimeter size, (d) granular materials of millimeter size grains

[Berthier & Biroli, RMP (2011)]

IISc Bangalore

Glass transition – a non thermodynamic transition:

a) no consumption/expulsion of latent heat.

b) no changes in structural properties.

c) (almost) no change in thermodynamic properties.

d) drastic change in transport properties (viscosity,

diffusion-constant etc).

Shear reversal simulation of “vitrifying” colloidal melt

Images © [1] Vinayak Industries, Mumbai, [2] Schott AG, Mainz, [3] Norm Wagner Lab (Delaware), [4] Prof.J.Mainstone, Univ. of Queensland.

Technological applications:

Casting, cooling and solidification[1,2] , Dutch tears,

Body armour (STF enabled Kevlar)[3], Pitch-drop

experiment[4] (how do glasses flow?)

Amit Bhattacharjee

Necessity for studying


8IISc Bangalore


Workshop Gauertal

=

Amit Bhattacharjee

+ = ?

=

What's the interesting question?

9IISc Bangalore

Horbach et al, 2008

Fuchs et al, 2010


Outline

Nonequilibrium MD simulation.

Steady state response in forward shear.

Transient response: dynamics and microstructure.

Shear reversal insilico experiments.

Steady state, transients and connection with microstructure.

An emergent puzzle.

Conclusion.

(If time permits) spatial coarsegraining.

Shear reversal simulation of a vitrifying colloidal melt

10Amit Bhattacharjee IISc Bangalore


Simulation method

WCA pair potential[1] (soft, purely repulsive)

Solve N-particle Newton's equation[2].

Cutoff function &

Units:

mi˙r i= pi ; ˙pi=−∑i≠ j

∇U ij ( r )−∑i≠ jζ ω

2( r ij)( r ij⋅vij) r ij+√2 k BT ζω( r ij)N ij r ij .

conservative dissipative stochastic

Amit Bhattacharjee

U ijWCA

(r )={4ϵij [(σijr)12

−(σ ij

r)6

+14]S , r<21/6σij

0, r≥21 /6σij

ω(r)={1, r<1.69x21/6σ ij

0, r≥1.69x21/6σ ij

ζ=10 .


11

N=2 N A=2 N B=1300, σAA=1.0, σBB=5/6, ϵ=1, L=10σAA .

[1] Chandler et al, J. Chem. Phys. (1971). [2] Espanol et al, Euro. Phys. Lett. (1996).

IISc Bangalore

τ=√mAσAA2/ϵ .

S (q)=1N⟨ρ(q)ρ(−q)⟩

g (r )=V

N 2⟨∑i

N

∑ j≠i

Nδ(r i−r j−r )⟩

Equilibrium: structure and dynamics

Pair correlation .

Structure function .

Amit Bhattacharjee


12IISc Bangalore

S (q)=1N⟨ρ(q)ρ(−q)⟩

g (r )=V

N 2⟨∑i

N

∑ j≠i

Nδ(r i−r j−r )⟩

F sα(q , t)=

1N α∑i

N α

⟨ρi (q , t )ρi(q ,0)⟩

Δ rα2(t )=⟨∣rα(t)−rα (0)∣

2⟩

t 2

t

caging

caging

~

~

Amit Bhattacharjee


13IISc Bangalore

Equilibrium: structure and dynamics

Pair correlation .

Structure function .

Density autocorrelator (SISF) .

Mean squared displacement (MSD) .


Workshop Gauertal

Amit Bhattacharjee

happy particle of Takeshi Egami, Univ. of Tennessee


IISc Bangalore

γ

γ

Out-of-equilibrium scenario

Shear is applied

through Lees-Edwards

boundary condition.

Planar Couette flow is established within a few NEMD steps (no shear bands formed).

Shear rate perturbs the interplay between intrinsic single particle time & structural

relaxation time

x

y

z

gradient

vorticity

0 −1

Amit Bhattacharjee


14IISc Bangalore

τ0τα

τ0=0.48, τα=2.5 x103,

γ=0.005, Pe0=2.4 x10−3 , Peα=12.5 .

T c=0.347, T=0.4, γ=0.005,

Out-of-equilibrium scenario

Shear is applied

through Lees-Edwards

boundary condition.

Planar Couette flow is established within a few NEMD steps (no shear bands formed).

Shear rate perturbs the interplay between intrinsic single particle time & structural

relaxation time shear thinning: linear response breaks down.

x

y

z

gradient

vorticity

0 −1

Amit Bhattacharjee


15IISc Bangalore

τ0τα

Newtonian

Properties in forward shear: steady-state dynamics

Stress tensor components[1]:

σ xy=⟨σ xy ⟩=−1V ⟨∑i=1

N

[mi vi , x vi , y+∑ j≠ir ij , x F ij , y ]⟩ .

kinetic virial

Amit Bhattacharjee

[1] Kirkwood, J. Chem Phys. (1946).

N 1=⟨σ xx−σ yy ⟩ , N 2=⟨σ yy−σ zz⟩ , P=−13Trσ .


16IISc Bangalore

Properties in forward shear: steady-state dynamics

Stress tensor components[1]:

Crossover from Newtonian to sub-Newtonian in

for with effective scaling

Normal stresses are in sub-Newtonian regime

with scaling laws

Osmotic pressure saturates for low Pe with

scaling law

Theoretical prediction from Generalized Maxwell

Model:

σ xy=⟨σxy ⟩=−1V ⟨∑i=1

N

[mi vi , x v i , y+∑ j≠ir ij , x F ij , y ]⟩ .

kinetic virial

Amit Bhattacharjee

[1] Kirkwood, J. Chem Phys. (1946).

N 1=⟨σ xx−σ yy ⟩ , N 2=⟨σ yy−σ zz⟩ , P=−13Trσ .

σ xy Pe>1 σ xy∼(Pe)0.36 .

N 1∼(Pe)0.51 , N 2∼(Pe)

0.58 .

P∼(Pe)0.37 .

G∞N1,2/σ xy2=2.

Flow Curve


17IISc Bangalore

Properties in forward shear: transient dynamics

Visco-elastic response.

Overshoot in stress[1,2] : shear induced local melting

of glass (breaking of cage structure): super-diffusive

intermediate motion.

elastic

plastic

T=0.4

Amit Bhattacharjee

[1] Horbach et al, J. Phys. Cond. Mat. (2008). [2] Bhattacharjee, Soft Matter (2015).


18IISc Bangalore

Properties in forward shear: transient dynamics

Visco-elastic response.

Overshoot in stress[1,2] : shear induced local melting

of glass (breaking of cage structure): super-diffusive

intermediate motion.

Local stress:

Jump in local stress variance at 10% strain amplitude.

elastic

plastic

T=0.4

EQ

⟨ r2⟩~t

tw0

σ xyi =−

1V ∑ j≠i

r ij , x F ij , y .

Amit Bhattacharjee


19IISc Bangalore

[1] Horbach et al, J. Phys. Cond. Mat. (2008). [2] Bhattacharjee, Soft Matter (2015).

⟨Δ rα2 ⟩∼tμα

Properties in forward shear: transient microstructure

Pair correlation shows no signature of shear.

Amit Bhattacharjee

t=5

t=10

t=20

t=50


20IISc Bangalore


Pair correlation shows no signature of shear.

Projection onto spherical harmonics:

real and imaginary component of sensitive to shear.

Interconnection between stress and structure[1]

Equal stress at elastic-plastic branch,

remains invariant[2].

g22αβ(r)

σ xy=K cα2∫0

∞

dr r3∂V αβ

∂ rImag (g 22

αβ(r))

g (r)=∑l=0

∞

∑m=−l

lg lm(∣r∣)Y

lm(θ ,ϕ) ,

N 1=K cα2∫0

∞

dr r3∂V αβ

∂ rReal (g 22

αβ(r))

σ=ρ2

2 ∫0

∞

d r∑α ,βcα cβ

rrr∂V αβ

∂ rgαβ(r)

[1] Kirkwood, J Chem Phys. (1946). [2] Horbach et al, JPCM (2008).

Amit Bhattacharjee

Real (g22αβ(r )) , Imag (g22

αβ(r))


21IISc Bangalore


Shear induced anisotropy in microstructure[1,2].

Maximum extension-compression exhibited

near overshoot seen in

g (r ,θ)

γ=0.025γ=0.25γ=0.05

[1] Hess et al, Phys. Rev. A, (1987).[2] Petekidis et al, Phys. Rev. Lett. (2012).

Amit Bhattacharjee

g (r ,θ).

compressionextensionγ=0.1


22

t=5

t=10

t=20

t=50

IISc Bangalore



Maximum extension-compression exhibited near overshoot

seen in

No shear banding found (linear Couette flow for all NEMD

steps).

g (r ,θ)

γ=0.025γ=0.25γ=0.05


Amit Bhattacharjee

g (r ,θ).



23IISc Bangalore



Maximum extension-compression exhibited near overshoot

seen in

No shear banding found (linear Couette flow for all NEMD

steps).

No channelized stress relaxation (STZ) seen.

g (r ,θ)

γ=0.025γ=0.25γ=0.05


Amit Bhattacharjee

g (r ,θ).



24IISc Bangalore


Workshop Gauertal

Amit Bhattacharjee


IISc Bangalore

+ = ?

Instantaneous shear reversal: transient dynamics

Strong history dependence: preparation state-dependent response.

−γwel −γw

max −γws

Amit Bhattacharjee


25IISc Bangalore

Instantaneous shear reversal: transient dynamics

Strong history dependence: preparation state-dependent response.

Bauschinger effect[1,2]: less yield strength when reversed

from plastic deformed state.

No signature of strong resistance to the back flow, shear

banding, STZs or channelized stress relaxation.

No overshoot in stresses, normal stresses remain

insensitive to shear reversal.

−γwel −γw

max −γws

[1] Bauschinger, Zivilingenieur (1881).[2] Procaccia et al, Phys. Rev. E (2010).

Amit Bhattacharjee


26IISc Bangalore

Properties after shear reversal: transient dynamics

Amit Bhattacharjee


27IISc Bangalore

Osmotic pressure and local stress variance stays

unchanged (slight downward trend at intermediate

Pe values due to re-attainment of Couette flow).

Absence of super-diffusive motion due to weakening

of cages, also evident in density autocorrelator.

Structure:

⟨δ zα2 ⟩∼tμα

q=π/σ AA

2π /σAA

3π/σ AA

4π/σ AA

Properties after shear reversal : Microstructure

γ=75−0.025 γ=75−0.05

Isotropic evolution of structure in reversal

of shear.

Amit Bhattacharjee

γ=75−0.1 γ=75−0.25


28IISc Bangalore


γ=75−0.025 γ=75−0.05


of shear.

Planar Couette flow is re-established in few

timesteps in the shear-reversed direction.

Amit Bhattacharjee

γ=75−0.1 γ=75−0.25


29IISc Bangalore


γ=75−0.025 γ=75−0.05


of shear.

Planar Couette flow is re-established in few

time steps in the shear-reversed direction.

Indifferent structure at steady flowing

states show equal anisotropy at identical

stress.

Amit Bhattacharjee

γ=75−0.1 γ=75−0.25


30IISc Bangalore

Summary: rheology of dense colloidal melt

Transient response to forward shear: State-of-the-art was shear stress overshoots

with broadening of the local stress distribution at 10% strain amplitude with

superdiffusive tagged particle motion.

Additionally we find that first normal stress overshoots and second normal stress

undershoots with equal proportion with a jump in osmotic pressure at identical strain.

Steady state flow curve shows “Newtonian” to “sub-Newtonian” behaviour for shear,

normal stresses remain sub-Newtonian while pressure saturates for lower Peclet number.

Maximal anisotropy in transient microstructure is exhibited at 10% strain amplitude.

Local structure, projected onto spherical harmonics, is sensitive to flow, without any

shape distortion at equal stress at late times.

Amit Bhattacharjee


31IISc Bangalore

Summary: rheology of dense colloidal melt











Transient response to shear reversal: history (strain) dependent response- lesser

yield strength and lowering of elastic constants, absence of overshoot(s) and

super-diffusive motion - ”Bauschinger effect”.

Local structure shows equal anisotropy at equal stress, isotropic structural evolution

without cluttering in structure when reversing the flow direction.

Findings in par with experiments[1] and the MCT-ITT theoretical framework[2].

Amit Bhattacharjee


32IISc Bangalore

[1] Egelhaaf lab, Univ. Düsseldorf.[2] Fuchs group, Univ. Konstanz.


Amit Bhattacharjee


Publications

33Amit Bhattacharjee IISc Bangalore

Local stress tensor[1]

Local stress tensor ?

Local strain tensor[1] where,

displacement field[1]

Non-affine displacement field[2]

Numerical

error

σ xy (r , t )=−12∑i∑ j≠i

r ij , x F ij , y∫0

1dsϕ[ r−r i(t )+ s r ij (t )] .

ϵxylin(r , t )=

12 (

∂u xlin

∂ y+∂u y

lin

∂ x ) u xlin(r , t)=

∑imi x i (t)ϕ[r−r i (t)]

∑ jm jϕ[ r−r j(t)]

.

δ r i(t ,0)=r i(t )−r i (0) .

δ r i(t ,0)=r i(t )−r i (0)−γ∫0

td t y i( t) x .

σ xy(r , t)=∑iσ xyi (r , t)ϕ[r−r i(t)] .

IISc BangaloreAmit Bhattacharjee

Coarse graining

[1] Goldhirch & Goldenberg, EPJE (2002).[2] Chikkadi & Schall, PRE (2012).


34

Strain (Goldhirsch) Strain (Schall) Stress Elastic-map

r i(t)−r i (0)

γ=0.001

G=σ xy /ϵxy∑iσ xyi (r ,t )ϕ[r−r i (t)]


Coarse graining


35


r i(t)−r i (0)

γ=0.001

γ=0.1



Coarse graining


36


r i(t)−r i (0)

γ=0.001

γ=0.1

γ=0.5



Coarse graining


37

Extended Summary: rheology of dense colloidal melt











Elasto-plastic zones : around stress overshoot a percolating cluster emerge.

Hard to conclude at higher strain – questioning validity of linear elasticity.

Amit Bhattacharjee


38IISc Bangalore


Amit Bhattacharjee


Collaborators and Timeline

Fluctuating hydrodynamics of multi-component non-ideal liquidsand chemically reactive gases.

Nonlinear rheology in a vitrifying colloidal melt under shear reversal.

Inhomogeneous phenomena innematic liquid crystals.

Germany (2010-2013)

USA (2013-2015)

India (2007-2010)

Amit Bhattacharjee IISc Bangalore

[1] Bhattacharjee et al, J Chem Phys, 142, 224107 (2015).[2] Bhattacharjee et al, Phys. Fluids, 27, 037103 (2015).

[3] Bhattacharjee, Soft Matter, 11, 5697 (2015).[4] Bhattacharjee et al, J. Chem Phys. (Special Topics in Glass Transitions), 138, 12A513 (2015).`

[5] Bhattacharjee el al, J Chem Phys, 133, 044112 (2010).[6] Bhattacharjee et al, J. Chem Phys., 131, 174701 (2009).[7] Bhattacharjee et al, Phys. Rev. E, 80, 041705 (2009).[8] Bhattacharjee et al, Phys. Rev. E, 78, 026707 (2008).

39


Amit Bhattacharjee


Thank you

TSU Seminar, JNCASR, March 2016

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Transcript of TSU Seminar, JNCASR, March 2016