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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
Structural properties of a binary colloidal mixture under shear reversal
Amit Bhattacharjee
Workshop Bartholomäberg
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
3IISc Bangalore
Prologue
CFDTDGL
LLNSDPD / SPHBDSRDLBM
DFTMDKMC
Meso-scale
Micro-scale
Length
Time
Computational methods
Macro-scale
Amit Bhattacharjee
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
4
μ s ms−sfs− ps
nm
μm
mm
IISc Bangalore
Amit Kumar Bhattacharjee
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
Amit Kumar Bhattacharjee
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 )
Amit Kumar Bhattacharjee
Workshop Gauertal
Amit Bhattacharjee
IISc (2015-)
IISc Bangalore 6
Ph.D. work
Time-lapse movies:
Structural properties of a binary colloidal mixture under shear reversal
Amit Bhattacharjee
Workshop Bartholomäberg
Amit Bhattacharjee
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
8IISc Bangalore
Amit Kumar Bhattacharjee
Workshop Gauertal
=
Amit Bhattacharjee
+ = ?
=
What's the interesting question?
9IISc Bangalore
Horbach et al, 2008
Fuchs et al, 2010
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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 .
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
13IISc Bangalore
Equilibrium: structure and dynamics
Pair correlation .
Structure function .
Density autocorrelator (SISF) .
Mean squared displacement (MSD) .
Amit Kumar Bhattacharjee
Workshop Gauertal
Amit Bhattacharjee
happy particle of Takeshi Egami, Univ. of Tennessee
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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 .
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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).
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
20IISc Bangalore
Properties in forward shear: transient microstructure
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))
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
21IISc Bangalore
Properties in forward shear: transient microstructure
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
22
t=5
t=10
t=20
t=50
IISc Bangalore
Properties in forward shear: transient microstructure
Shear induced anisotropy in microstructure[1,2].
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
[1] Hess et al, Phys. Rev. A, (1987).[2] Petekidis et al, Phys. Rev. Lett. (2012).
Amit Bhattacharjee
g (r ,θ).
compressionextensionγ=0.1
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
23IISc Bangalore
Properties in forward shear: transient microstructure
Shear induced anisotropy in microstructure[1,2].
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
[1] Hess et al, Phys. Rev. A, (1987).[2] Petekidis et al, Phys. Rev. Lett. (2012).
Amit Bhattacharjee
g (r ,θ).
compressionextensionγ=0.1
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
24IISc Bangalore
Amit Kumar Bhattacharjee
Workshop Gauertal
Amit Bhattacharjee
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
IISc Bangalore
+ = ?
Instantaneous shear reversal: transient dynamics
Strong history dependence: preparation state-dependent response.
−γwel −γw
max −γws
Amit Bhattacharjee
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
26IISc Bangalore
Properties after shear reversal: transient dynamics
Amit Bhattacharjee
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
28IISc Bangalore
Properties after shear reversal : Microstructure
γ=75−0.025 γ=75−0.05
Isotropic evolution of structure in reversal
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
29IISc Bangalore
Properties after shear reversal : Microstructure
γ=75−0.025 γ=75−0.05
Isotropic evolution of structure in reversal
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
31IISc 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.
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
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
32IISc Bangalore
[1] Egelhaaf lab, Univ. Düsseldorf.[2] Fuchs group, Univ. Konstanz.
Structural properties of a binary colloidal mixture under shear reversal
Amit Bhattacharjee
Workshop Bartholomäberg
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).
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
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)]
IISc BangaloreAmit Bhattacharjee
Coarse graining
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
35
Strain (Goldhirsch) Strain (Schall) Stress Elastic-map
r i(t)−r i (0)
γ=0.001
γ=0.1
G=σ xy /ϵxy∑iσ xyi (r ,t )ϕ[r−r i (t)]
IISc BangaloreAmit Bhattacharjee
Coarse graining
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
36
Strain (Goldhirsch) Strain (Schall) Stress Elastic-map
r i(t)−r i (0)
γ=0.001
γ=0.1
γ=0.5
G=σ xy /ϵxy∑iσ xyi (r ,t )ϕ[r−r i (t)]
IISc BangaloreAmit Bhattacharjee
Coarse graining
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
37
Extended 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.
Elasto-plastic zones : around stress overshoot a percolating cluster emerge.
Hard to conclude at higher strain – questioning validity of linear elasticity.
Amit Bhattacharjee
Introduction Methods Glassy Rheology Bauschinger effect Conclusion
38IISc Bangalore
Structural properties of a binary colloidal mixture under shear reversal
Amit Bhattacharjee
Workshop Bartholomäberg
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
Structural properties of a binary colloidal mixture under shear reversal
Amit Bhattacharjee
Workshop Bartholomäberg
Thank you