Particle and field based methods for complex fluids and soft materials

Structural properties of a binary colloidal mixture under shear reversal

Amit e

Workshop Bartholomäberg

Particle and field based methods for complex fluids and soft materials

Amit Kumar Bhattacharjee

Courant Institute of Mathematical SciencesNew York University, New York

IISERM SeminarApril 13, 2015


Amit Bhattacharjee


Collaborators and advisors

Aleksandar Donev (New York)Andy Nonaka (Berkeley)Alejandro Garcia (San Jose)John B. Bell (Berkeley)

Juergen Horbach (Duesseldorf)Matthias Fuchs (Konstanz)Thomas Voigtmann (Koeln)

Gautam I. Menon (Chennai)Ronojoy Adhikari (Chennai)

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

“Bauschinger effect” in dense supercooled colloidal melt underinstantaneous shear reversal.

Inhomogeneous phenomena innematic liquid crystals.

USA

Germany

USA

India

1/38Amit Bhattacharjee Courant Institute (NYU)


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

2/38

Introduction Dense colloids Multispecies mixtures Liquid Crystals Conclusion

Amit Bhattacharjee Courant Institute (NYU)


Amit Bhattacharjee


Prologue

Multistage transition process in fluids composed with

anisotropic particles: mesophases (Nematic, Discotic, Cholesteric,

Smectic A – C, Columnar liquid crystals).

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).

Complex physico-chemical processes in multicomponent gases and liquids

leading to macroscale structure.

Complexity in complex fluids

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nIntroduction Dense colloids Multispecies mixtures Liquid Crystals Conclusion


Prologue

Necessity for studying

Images © [1] Vinayak Industries, Mumbai, [2] Schott AG, Mainz, [3] Wagner (Delaware)

Technological applications:

Thermometers, laptop & mobile screens,

Casting, cooling and solidification,1,2

Body armour (STF enabled Kevlar).3

Medical examples:

Sub cellular structures, blood flow,

joint lubricants, pharmaceuticals.

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Prologue

Theoretical methods Atomistic description:

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

b) approximation: 2-body interations in central forcefield (e.g. LJ,

Yukawa, WCA etc).

Mesoscopic description:

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

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

c) Temporal coarse graining.

Measurement of the equilibrium and non-equilibrium properties.

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Prologue

LLNSTDGLKMC

DPDSRDLBMLDBD

DFTMD Meso-scale

Micro-scales

Length

Time

Computational methods

Macro-scales

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Outline

Bauschinger effect in vitrifying colloidal melt Simulation methods.

Rheological properties in forward shear.

Response to instantaneous shear reversal.

Structural properties and interconnection with stresses.

Nonequilibrium thermodynamics of diffusion.

Low Mach number equations.

Numerical methods and benchmarks.

Applications: Giant nonEQ concentration fluctuations.

Compressible hydrodynamics of reactive gas.

Comparison of particle/field based methods for homogeneous systems.

Fluctuating hydrodynamics of multispecies mixtures




Workshop Gauertal

Bauschinger effect in binary supercooled colloidal glass-forming melt

=

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Amit Bhattacharjee

+ = ?

=

Courant Institute (NYU)

Zausch et al, J. Phys. Cond. Matt. (2008).

Brader et al, Phys. Rev. E (2010).

Simulation method

WCA pair potential1 (soft, purely repulsive)

Thermostat : dissipative particle dynamics[2,3] (DPD) local

conservation of momentum.

Solve N-particle Newton's equation with Lees Edwards BC.

mi˙r i= pi ; ˙pi=−∑i≠ j

∇U ij( r )−∑i≠ jζω2

( r ij)( r ij⋅v ij) r ij+√2kBT ζω( r ij)N ij r ij .

conservative dissipative stochastic

N=2N A=2NB=1300, σ AA=1.0, σBB=5 /6, σAB=(σAA+σBB)/2, ϵ=1, L=10.

[1] Chandler et al, J. Chem. Phys. (1971). [2] Espanol et al, Euro. Phys. Lett. (1996).[3] Peters, Euro. Phys. Lett. (2004).

UWCA(r )={4 ϵ[(σr)

12

−(σr)6

]+ϵ , r<21/6σ

0, r≥21/6σ

⟨N ij (t)⟩ = 0,⟨N ij(t )N kl ( , t ' )⟩ = (δik δ jl+δil δ jk )δ(t−t ' )δ(r−r ' )

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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)⟩

Δrα2 (t)=⟨∣rα(t)−rα (0)∣

2⟩

t 2

t

caging

caging

~

~

Equilibrium: structure and dynamics

Pair correlation .

Structure function .

Density autocorrelator (SISF) .

Mean squared displacement (MSD) .

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Out-of-equilibrium scenario

Shear applied through Lees-Edwards BC.

Planar Couette flow is established within a few

NEMD steps (no shear banding).

Shear rate perturbs the interplay between

intrinsic single particle time & structural

relaxation time shear thinning:

linear response breaks down.

x

y

z

gradient

vorticity

Newtonian

T=0.4

0

0−1

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T=0.4, γ=0.005τ0=0.48, τα=2.5 x103

Pe0=2.4 x10−3 , Peα=12.5 .



Properties in forward shear: dynamics

Stress tensor1:

Visco-elastic response.

Local stress:

Jump in local stress variance at 10% strain amplitude.

Overshoot in stress[2,3] : shear induced local melting

of glass (breaking of cage structure): superdiffusive

intermediate motion2.

elastic

plastic

T=0.4

EQ

⟨ r2⟩~t

tw0

xy=⟨ xy ⟩=−1/V ⟨∑i=1

N

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

kinetic virial

xy=−1/V∑ j≠ir ij , x F ij , y .

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[1] Kirkwood, J. Chem Phys. (1946). [2] Horbach et al, J. Phys. Cond. Mat. (2008). [3] Bhattacharjee, Soft Matter (accepted).



Properties in forward shear: structure

Pair correlation shows no signature of shear.

Projection onto spherical harmonics:

real and imaginary component of

is sensitive to shear.

Interconnection between stress and structure[1,3]

Maximum extension-compression exhibited

near overshoot2 seen in .

No shear banding3 found (planar Couette flow

is established for all steps).

g22αβ(r )

σ xy=K cα2∫

0

∞

dr r 3 ∂Vαβ

∂rℑ(g 22

αβ(r))

g(r)=∑l=0

∞

∑m=−l

l

glm(∣r∣)Ylm(θ ,ϕ).

N 1=K cα2∫

0

∞

dr r3 ∂Vαβ

∂ rℜ(g22

αβ (r))

σ=ρ2

2∫0

∞

d r∑α ,βcα cβ

rrr∂V αβ

∂ rgαβ(r)

g (r ,θ)

γ=0.025 γ=0.25γ=0.1

[1] Kirkwood, J Chem Phys. (1946). [2] Hess et al, Phys. Rev. A, (1987).[3] Bhattacharjee, Soft Matter (accepted)

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extension

compression

Instantaneous shear reversal: 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 banding2, STZs or

channelized stress relaxation.

No overshoot in stresses[2,3] and absence of superdiffusive motion.

−γwel −γw

max −γws

[1] Karmakar et al, Phys. Rev. E (2010).[2] Bhattacharjee et al, J. Chem. Phys. (2013).[3] Bhattacharjee, Soft Matter (accepted).

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Properties after shear reversal

γ=75−0.025 γ=75−0.25

Absence of superdiffusive motion due to cage-removal.

Osmotic pressure and local stress variance stays

unchanged.

Isotropic evolution of structure in reversal with

attainment of Couette flow in few MD steps.

Structure:


Amit Bhattacharjee 15/38Courant Institute (NYU)

Summary: rheology of dense colloidal melt

Response to forward shear: Shear and normal stress overshoot with step jump in

osmotic pressure and local stress variance at 10% strain amplitude with

super-diffusive particle motion.

Response to shear reversal : history (strain) dependent flow effect, lesser yield

strength and elastic constants, absence of overshoot and super-diffusive motion.

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

any shape distortion at equal stress at late times. No cluttering in structure found

while reversing the flow direction.

Findings in par with experiments1 and the MCT-ITT theoretical framework2.


16/38Amit Bhattacharjee

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



Workshop Gauertal

Fluctuating hydrodynamics of non-ideal multispecies mixtures

Aim: To formulate theory and accurate computation for n-component miscible liquid at finite temperature in flow.

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

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Amit Bhattacharjee

Soret effect induced giant non-equilibrium concentration fluctuations in

microgravity1.


5mm side1mm thick


Workshop Gauertal

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Amit Bhattacharjee

Theoretical prescription

Assumption of local equilibrium, balance equations

(mass, momentum, energy & entropy).

Constitutive relations, OCRR, odd and even order processes.

Relation between diffusive flux and concentration gradient in 1-component

gas/liquid: Fick's law.

In binary system, chemical potential gradient drives diffusion process

(Einstein-Teorell approach, Chapman-Enskog approach). Also, diffusion

can be induced by temperature gradient (Soret effect), heat exchange

(Dufour effect), barodiffusion and external forces.

Ideal and non-ideal systems of gas and liquid.

Straightforward generalization in multicomponent diffusion:

Maxwell-Stefan and Fickian description.

Thermal fluctuation can be added to deterministic flux (LLNS) satisfying

discrete-FDT.



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Low Mach number hydrodynamics

Sound waves are faster than momentum diffusion in liquids (Ma=0 limit).

EOS constraint .

Low Mach number equations

ensures continuity equation . EOS constraint leads to (1).

Constitutive flux-force relation obtained from non-equilibrium TD of

diffusion for nonideal liquids comparing diffusion driving force to frictional

force

Non-ideality parameter .

is SPD, zero row and column sums, so as .

where .

∂tρi =−∇⋅(ρi v)−∇⋅Fi , (i=1,2,... , N )

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

∇⋅v =−∇⋅(Σi=1N Fi /ρi) Σ = √ηkBT (W+W T )

⟨W ij (r , t )W kl(r ' , t ')⟩ = δik δ jlδ(t−t ' )δ(r−r ')

Σi=1Nρi / ρi=1

Σi=1N Fi=0 ∂t ρ=−∇⋅(ρv)

…. (1)

F=F+F (determinstic + stochastic)

F=−L(∇ Tμ

T+ξ

∇ T

T 2)=−ρW χ[Γ ∇ x+(ϕ−w)

∇ PnkBT

+ζ∇ TT

]

L , χ ξ

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ϕ i=ρi/ρi

w i=ρi /ρΓ=Ι+(X−xxT )Η

x i=wi /mi

Σi=1N wi/miχ=(Λ+TrΛ w wT

)−1−(TrΛ)−111T Λij=−xi x j/Dij


Workshop Gauertal

Low Mach number fluctuating hydrodynamics

Comparing MS and Onsager expression gives the stochastic contribution.

Complete equation for mass fraction:

Numerical scheme: staggered grid, finite-volume method implemented on

BoxLib: scalars live on centres, vectors live on faces and edges ensuring

Einstein's discrete FDT.

Benchmarks: static and dynamic correlators: &

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∂t (ρw)+∇⋅(ρw v) = ∇⋅{ρW [χ (Γ∇ x+(ϕ−w)∇ PnkBT

+ζ∇ TT )]+√2kB L1

2

Ζ}

F=√2kB L12

Ζ

S w(i , j )

(k ) Sρ(k)

⟨Ζi(r , t )Ζ j(r ' , t ' )⟩=δij δ(t−t ' )δ(r−r ' )



S ρ(kx , k y)

m1=1,m2=2,m3=3,

ρ1=0.6,ρ2=1.05,ρ3=1.35,

ρ1=2, ρ2=3, ρ3=3.857,

Lx=L y=32,Δ x=Δ y=1,

Sρeq=0.3.


Workshop Gauertal

Non-equilibrium fluctuations

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In presence of weak concentration gradient,

correlations in non-eq fluctuations occur by

coupling to velocity fluctuations : power law

spectrum[1,2] ~ .

For theoretical calculations, we create diffusion

barrier for first species and deal with ideal( ), isothermal( ),

incompressible( ) mixture with stochastic mass flux .

Barodiffusion gives ordinary equilibrium

fluctuations while thermo-diffusion (Soret

effect) gives correct enhanced spectrum as

usually done in experiments.

k−4

F=0


Amit Bhattacharjee[1] Bhattacharjee et al, Phys. of Fluids (2015). [2] Donev et al CAMCOS, 9-1, 47 (2014).

H=0 ∇ T=0

ρ1,2,3=1


Lx=128,L y=64Δx=Δ y=1


Workshop Gauertal

Compressible hydrodynamics of multispecies reactive mixture

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Elementary reaction , mass conservation

Compressible FNS with law of mass action(LMA): chemical hydrodynamics

Stochastic momentum

flux

Number density evolution for homogeneous well-mixed system,

Log mean equation (LME):

Chemical Langevin equation (CLE):

LMA:

For ideal gas,


Σs=1N s νsrΜs⇔Σs=1

N s νrsΜs

∂tρs =−∇⋅(ρs v)−∇⋅Fs+m sΩs , (s=1,2,. .. , N s)

∂t (ρ v) =−∇⋅Π−∇⋅(ρv vT+p Ι)+ρ g ,

∂t (ρE) =−∇⋅[(ρ E+p)v ]−∇⋅[ϑ+Π⋅v ]+ρ v⋅g

Π = √ηkBT (W+W T )+(√k BκT6−√k BηT3

Tr (W+W T ))

⟨W ij (r , t)W kl(r ' , t ')⟩ = δik δ jlδ(t−t ' )δ(r−r ')

Π=−η(∇+∇T)v−(κ−

23η) I (∇⋅v)+Π

Amit Bhattacharjee

∑sF s=0, ∑s

m sΩs=0.

Ω=Ω+Ω .

dns /dt=Ωs+∑rνsr √2Dr

LM/dV oW r (t)

dns /dt=Ωs+∑rν sr√2Dr

CL/dV W r (t )


+ -Σs(νsr−νrs)mr=0.N r

+ -

Ωs=Σr ν srp

τr kBT[exp(Σs νsrmsμs /kBT )−exp(Σsν srmsμs/ kBT )] ,

Ωs=Σr ν sr(k f Πs 'ns 'νs ' r−k rΠs 'ns '

νs ' r) ,- Dr

LM=logmean [k f Πsnsνsr , k rΠsns

νsr ] ,

DrCL=arthmean [k f Πsns

νsr , k rΠsnsν sr] .

+ -

+


Workshop Gauertal

Homogeneous dimerization reaction

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For ,

Production rate factors

At equilibrium , mass fraction .

Comparison with particle based methods (SSA) at EQ: LME is closest truth

to CME, while CLE has it's usual shortcoming (unphysical negative values).

At out-of-EQ states: noise covariance of CLE agrees more to SSA/CME, but

while distribution is not Gaussian, CLE is no better than LME.


Amit Bhattacharjee

[1] Bhattacharjee et al, arXiv:1503.07478 (2015).

Ω1=−2(k f n12−k r n2), Ω2=−Ω1/2, m2=2m1, n1+2n2=n02A⇔ A2

kf / kr=1/n0 Y 1=n1/n0=0.5

D LM=

k f n12−kr n2

ln (k f n12)−ln(kr n2)

, DCL=

12(k f n1

2+krn2)

100 monomer+ 4 dimer

⟨N 1⟩≈54

k f=2.78x10−4

k r=0.3

Δt=0.005

⟨N1⟩≈16

k f=0.00625k r=0.2

16 monomer+ 8 dimer


k f

kr


Workshop Gauertal

Non-equilibrium fluctuations in flow

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Effect of chemical reaction ,

is penetration depth that controls switch to spectrum

for small wave numbers ( ), long wave numbers still exhibit

spectrum[1,2]. At very small wave numbers saturates.

Linear concentration profile is only established at no-reaction limit.

Validity to couple SSA & hydrodynamics: work in progress.

k−2

S(k)=kBT (∇ Y 1)

2

ηχ k4 (1+(dk )−2)−1

k−4


Amit Bhattacharjee

[1] Bedeaux et al, J.Chem Phys (2008).[2] Bhattacharjee et al, arXiv:1503.07478 (2015)

d=√χ/3 kr


k≪1d

S(k)

RD RD + Hydro

Summary: Multispecies diffusive liquids and reactive gas

We formulated a complete theory amenable to computers for studying n-component

ideal/non-ideal liquid at finite temperature from first principles of NEQ-TD in

conjunction to low-Mach (quasi-incompressible) formulation. This is first direct solution

of the full LLNS equations, maintaining 2nd order accuracy.

We find non-equilibrium power law spectra in the presence of concentration gradient

that is put either by hand or derived via temperature gradient (Soret effect) as

incorporated in experiments.

Chemical reactions affect the spectra by truncating the low Fourier modes, giving clear

distinction between diffusion and reaction dominated regime.

Different formalism for chemical reaction hints that SSA gives correct distribution of

CME (poisson process) while SODE's (diffusion process) are not quantitatively accurate.

LME is better than CLE for close to equilibrium while in out-of-EQ, both are worse.

Hint for improving LME/CLE: Poisson noise (Tau-leaping).

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Workshop Gauertal

Thank You!


Amit Bhattacharjee

Inhomogeneous phenomena in nematic liquid crystals



Nematic “mesophase”

Consist of anisotropic molecules (e.g. rods and discs) with long-range

orientational order devoid of translational order.

Uniaxial/biaxial phase rotational symmetry about direction of order described

by one/two headless vector n (director) and l (co-director).

Liquid-nematic solid transition is weakly first order.

Motivating examples

Topological defect entanglement in NLC film of width 790mm after temperature quench, showing monopoles, boojums and various integer/half-integer defects [Turok et al, Science, '91]

Schlieren textures with two and four brushes exhibited by a uniaxial NLC film at 118deg celsius [Chandrasekhar, et al, Current Science, '98]

Nucleation of ellipsoidal NLCdroplet with aspect ratio 1.7and homogeneous director field in MC simulation. [Cuetoset al, Phys.Rev.Lett, '07]

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Workshop Gauertal

Quantified through a symmetric traceless tensor field with

five degrees of freedom.

Definition of order

Qαβ

molecular frame:principal frame:

Qαβ(x , t )=∫ d u f ( x ,u , t)uu

Qαβ(x , t )=32S (nα nβ−

13δαβ)+

T2{lα lβ−(n×l )α(n×l)β }

Principal values represent strength of uniaxial and biaxial order (S,T)

Principal axes denote director, codirector and joint normal ( ).

correspond to isotropic liquid phase.

correspond to uniaxial nematic phase.

correspond to biaxial nematic phase.

Statics:

n , l , n×l

S=T=0

S=23,T=0

T≠0

FGLdG=∫ d3 x [

12ATrQ2+

13BTrQ3+

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

+12L1(∂αQβ γ)(∂αQβγ)+

12L2(∂αQαβ)(∂γQβγ)]

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Workshop Gauertal

Statics (contd.) and kinetics

∂tQαβ(x , t)=−Γαβμ ν

δ FGLdG

δQμ ν

+ζαβ(x , t )

Landau-Ginzburg model-A kinetics for non-conserved order

is a stochastic thermal force satisfying the structure of .Qαβζαβ

Free energy diagram

Phase diagram

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Workshop Gauertal

Numerical recipe and benchmarks

Projection to orthonormal basis .

Numerical integration of a equations and back transformation to

principal frame extraction of eigenvalues/eigenvectors to get back .

Integrator benchmarks: OU process, static and dynamic correlator in

isotropic phase, angle-angle correlator in uniaxial nematic phase.

Qαβ=∑i=1

5

ai( x , t)T αβi ,ζαβ=∑

i=1

5

ai(x , t)ζαβi

Qαβ

Determinstic problems: Method of Lines (MOL).

Spectral collocation method (SCM).

High performance computing (HPC).

Stochastic Method of Lines (SMOL).

Stochastic problems:

Applications

Structure of isotropic-nematic

interface.

Spinodal coarsening kinetics.

Nucleation kinetics.

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Workshop Gauertal

Application-I

Local/nonlocal properties of isotropic-nematic interface

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Workshop Gauertal

Application-I : Local/nonlocal properties of I-N interface

Isotropic IsotropicNematicz

x

ya

L x

Free energy per unit length of having a strip:

Nature of I-N interface? de Gennes ansatz1 no

anisotropic elasticity reducing to scalar equation

in S. Later works tackled planar anchoring

problem with three variables. No results known

for oblique anchoring.

Finding the ansatz to be valid at limit.

F=−a L x(F N−F I)+L xσ

L2=0

1) P.G. de Gennes, Mol.Cryst.Liq.Cryst. (1971).

L2=0

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F distortion=∫ d3 x {12L1(∂αQβγ)(∂αQβγ)+

12L2(∂αQαβ)(∂γQβγ)}




Workshop Gauertal


L2=18L1

L2

Local biaxiality of uniaxial interface

with planar anchoring (using SCM).

In oblique anchoring, director alignment

favours sign of .

L2=−L1

L2=36L1

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ζαβ=0Fluctuating interface ζαβ≠0

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Application-II

Phase ordering spinodal kinetics

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Workshop Gauertal

Application-II : Phase ordering spinodal kinetics [2D (d=2; s=3)]

Topological classification and visualization of point defects1 –

(Uniaxial) and (Biaxial).

Defects visualized via scalar and vector order that shows all class of

defect classes partially absent in schlieren texture measured in

experiments ( ).

π1(S2/ℤ2)=Z 2 π1(S

3/D2)=ℚ8

intensity∝sin2[2θ]

S (x , t )

sin2(2θ)[ x , t ]

T (x , t )

Uniaxial defect

Biaxial defect

1) Mermin, Rev. Mod. Phys. (1979).

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Workshop Gauertal

Application-II : Intercommutation of line defects

Line defects annihilate by intercommuting (exchanging segements)

and forming loops1.

Competion between energetics and Topology no topological rigidity

found in Biaxial nematics.

Uniaxial defect

Biaxial defect

[3D (d=3; s=3)]

1) Turok et al, Science (1991)

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Workshop Gauertal

Formulation of fluctuating kinetics of uniaxial/biaxial nematic in GLdG

framework, leading to novel visualization techniques and HPC ( in 2D,

lattice in 3D).

Validated de Gennes ansatz at limit of the problem.

Isotropic-uniaxial nematic interface obtains biaxiality for .

Oblique director anchoring: scalars remain local to the interface and

anchoring follows a linear profile: planar for and homeotropic for

Classification and visualization of all defect classes.

Controversy in growth exponent been settled with clear time-scale

separation at different stages of phase ordering.

Minimal GLdG framework incapable of topological rigidity in BN.

Methods

Summary: Inhomogeneous phenomena in nematics

10242

2563

I-N InterfaceL2=0

L2≠0

L2>0 L2<0.

Coarsening kinetics




Workshop Gauertal

Thermal fluctuation inducded nucleation of NLC phase in 3D.

Uniaxial and Biaxial NLC under electric field in 3D.

Coupling incompressible flow[1,2] to Q equations and

fluctuations 3D line defects in flow.

Rheology in nematics.

Multicomponent phase flow with fluctuations2.

Field based methods

Research proposal(s)

2D uniaxial defects in electric field [Oliveira et al, Phys.Rev.E, '10]

2D slice of ellipsoidal nematic phase in isotropic phase [Bhattacharjee, PhD Thesis, '10]

Velocity field of defects pair in LB simulations [Yeomans et al, Phys.Rev.Lett., '02]

±12

[1] Berris & Edwards, Thermodynamics of flowing system, Oxford (1994).[2] Donev et al, Phys. Rev. E (2014).

Nucleation and growth of nematic phase of 5CB atcooling rate 0.001 degC/min[Sun et al, Phys.Rev.E, '09]

Amit Bhattacharjee Courant Institute (NYU) 1/2

Proposal


Workshop Gauertal

Dense colloidal rheology: role of size disparity3, flow

geometry (planar Couette[4,5], uniaxial extension, mixed),

flow history (shear cessation6, non-instantaneous flow

reversal and LAOS7), coarse graining.

Microrheology of colloid-nematic mixture8.

Glassy nematic rheology8.

Particle based methods

Research proposal(s)

A

Chemical reaction-diffusion systems: GENERIC / CLE / CME coupled

to compressible NS equations: Schlögl model1, Dimerization reaction2.

[1] Lubensky et al, Phys. Rev. E. (2012).[2] Bedeaux et al J. Chem. Phys (2011).[3] Voigtmann and Horbach, Phys. Rev. Lett. (2009). [4] Bhattacharjee et al, J. Chem. Phys. (2013).[5] Bhattacharjee, arXiv 1410.8115 (2014).[6] Zausch Horbach, Euro. Phys. Lett. (2010).[7] Brader et al, Phys. Rev. E., (2010).[8] Onuki et al, Phys. Rev. E., (2014).

Elastic map with small andlarge elastic constant at strain=0.1 [Bhattacharjee, unpublished]


Particle and field based methods for complex fluids and soft materials

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