Cholesteric Liquid Crystals

&

Active Emulsions

DOTTORANDO: LIVIO NICOLA CARENZA

SUPERVISOR: PROF. GONNELLA

Summary

General Framework

Lattice Boltzmann Method for Liquid Crystals in three-dimensional

geometries

Cholesteric Liquid Crystals

Active Emulsions

Active Turbulence

General Framework

Model & Methods of numerical fluid

dynamics: coarse grained approach

General Framework

Model & Methods of numerical fluid

dynamics: coarse grained approach

Generalized Navier-Stokes equation

𝜕𝑡 𝜌 Ԧ𝑣 + ∇ ⋅ 𝜌 Ԧ𝑣 ⊗ Ԧ𝑣

= −∇𝑝 + ∇ ⋅ 𝜎𝑣𝑖𝑠𝑐𝑜𝑢𝑠 + 𝜎𝑐𝑜𝑚𝑝𝑙𝑒𝑥

General Framework

Model & Methods of numerical fluid

dynamics: coarse grained approach

Generalized Navier-Stokes equation

Binary mixtures Concentration

scalar field 𝜑

𝜕𝑡 𝜌 Ԧ𝑣 + ∇ ⋅ 𝜌 Ԧ𝑣 ⊗ Ԧ𝑣

= −∇𝑝 + ∇ ⋅ 𝜎𝑣𝑖𝑠𝑐𝑜𝑢𝑠 + 𝜎𝑐𝑜𝑚𝑝𝑙𝑒𝑥

𝜕𝑡𝜑 + ∇ ⋅ 𝜑 Ԧ𝑣 = 𝑀 ∇2𝜇 , 𝜇 =𝛿𝐹𝑏𝑚

𝛿𝜑

General Framework

Model & Methods of numerical fluid

dynamics: coarse grained approach

Generalized Navier-Stokes equation

Binary mixtures Concentration

scalar field 𝜑

Anisotropic contributions:

vector/tensor order parameters Ψ

𝜕𝑡 𝜌 Ԧ𝑣 + ∇ ⋅ 𝜌 Ԧ𝑣 ⊗ Ԧ𝑣

= −∇𝑝 + ∇ ⋅ 𝜎𝑣𝑖𝑠𝑐𝑜𝑢𝑠 + 𝜎𝑐𝑜𝑚𝑝𝑙𝑒𝑥

𝜕𝑡𝜑 + ∇ ⋅ 𝜑 Ԧ𝑣 = 𝑀 ∇2𝜇 , 𝜇 =𝛿𝐹𝑏𝑚

𝛿𝜑

𝜕𝑡Ψ+ Ԧ𝑣 ⋅ ∇Ψ + S = Γ𝛿𝐹

𝛿Ψ

3d Lattice Boltzmann Method

Boltzmann Equation Discretized time, space and velocity

Distribution functions 𝑓𝑖( Ԧ𝑥𝛼 , 𝑡)

Physical observables 𝜌 Ԧ𝑥𝛼 , 𝑡 = σ𝑖 𝑓𝑖 Ԧ𝑥𝛼 , 𝑡 𝜌 Ԧ𝑣 = σ𝑖 Ԧ𝑒𝑖𝑓𝑖( Ԧ𝑥𝛼 , 𝑡)

DF dynamics

Collision (BGK approximation)

𝑓𝑖𝑐𝑜𝑙𝑙 Ԧ𝑥𝛼, 𝑡 = 𝑓𝑖 Ԧ𝑥𝛼, 𝑡 −

1

𝜏𝑓𝑖 Ԧ𝑥𝛼, 𝑡 − 𝑓𝑖

𝑒𝑞( Ԧ𝑥𝛼, 𝑡)

Streaming 𝑓𝑖 Ԧ𝑥𝛼 + Ԧ𝑒𝑖Δ𝑡, 𝑡 + Δ𝑡 = 𝑓𝑖𝑐𝑜𝑙𝑙 Ԧ𝑥𝛼, 𝑡

Equilibrium DF Expansion at II order in Ԧ𝑣 Recover

continuum equations

Parallelization

Long simulation times

Huge amount of memory

Parallelization

Long simulation times

Huge amount of memory

Summer school on Parallel Computing – Cineca (BO)

Advanced School on Parallel Computing – Cineca (BO)

Parallelization

Long simulation times

Huge amount of memory

Summer school on Parallel Computing – Cineca (BO)

Advanced School on Parallel Computing – Cineca (BO)

Massage Passing Interface

~ 40Gb of Memory

~ 3y of CPU

Cholesteric

Liquid Crystals

Long chained

molecules in solution

Lost traslational order,

preserved directional

order

Cholesteric

Liquid Crystals

Long chained

molecules in solution

Lost traslational order,

preserved directional

order

Chirality

Cholesteric LC

Optical properties

Defects in CLC

droplets

Fundamental for optical properties

Strong dependence on geometry and boundary condition

Relaxing dynamics*

Merging droplets*

Droplets under shear

Switching dynamics under electric field

Active Emulsions

Active matter: energy injection on small scales

Bacteria Suspensions

Cytoskeleton extracts

Polar order

Confinment of active behavior

𝐹 = න𝑑𝑉𝑎

4 𝜑𝑐𝑟𝜑2 𝜑 − 𝜑0

2 +𝑘𝜑

2∇𝜑 2 +

𝑐

2∇2𝜑 2 +

𝛼

2𝜑𝑃2 +

𝛼

4𝑃4 +

𝑘𝑃2

∇𝑃2+ 𝛽𝑃 ⋅ ∇𝜑

Lamellar phase if 𝑎 <𝑘𝜑2

4𝑐+

𝛽2

𝑘𝑃𝑘𝜑 < 0 , 𝑐 > 0

Active stress tensor 𝜎𝑎𝑐𝑡𝑣𝑒= −𝜁𝜑𝑃⊗ 𝑃

Results

Activity favours ordering

Transition towardsmesoscale turbulence

Wealth of differentmorphologies

G.Negro,L.N.Carenza,P.Digregorio,G.Gonnella,A.Lamura Morphology and flow patterns in highly asymmetric active emulsion, Physica A, Vol. 503, 2018, 464-475

F.Bonelli,L.N.Carenza,G.Gonnella,D.Marenduzzo,E.Orlandini,A.Tiribocchi Lamellar ordering, dropletformation and phase inversion in exotic activeemulsions, Accepted with minor revisions ScientificReports (Nature)

L.N.Carenza,G.Gonnella,A.Lamura,G.Negro,A.Tiribocchi Lattice Boltzmann Methods and Active Fluids, Submitted to EPJ

Active Turbulence Energy injection on small scales Mesoscale turbulence

What is new?

Active Turbulence Energy injection on small scales Mesoscale turbulence

What is new?

KOLMOGOROV TURBULENCE :

High Reynolds number

Hydrodynamics non-linearities

-5/3 spectrum (universal behavior)

Active Turbulence Energy injection on small scales Mesoscale turbulence

What is new?

KOLMOGOROV TURBULENCE :

High Reynolds number

Hydrodynamics non-linearities

-5/3 spectrum (universal behavior)

ACTIVE TURBULENCE

Low Reynolds number

Complex coupling source/sink power terms

No universal behavior

Exams and Schools

PhD COURSES How to prepare a technical speech in

English

Management and knowledge of European research model and promotion of research results

Introduction to parallel Computing and GPU Programming using CUDA

C++

Atom-photon interactions

Standard model and beyond

Linear stability analysis*

Computational fluid dynamic*

Courses labelled with * are being erogated.

PhD SCHOOLS

Summer school on Parallel Computing –

Cineca (Bologna)

Advanced School on Parallel

Computing – Cineca (Bologna)

XXX National Seminar of Nuclear and

Subnuclear Physics "Francesco

Romano" OTRANTO

Thank you for

your attention

Thank you for

your attention

questions?