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 𝑣Ԧ + ∇ ⋅ 𝜌 𝑣Ԧ ⊗ 𝑣Ԧ = −∇𝑝 + ∇ ⋅ 𝜎 𝑣𝑖𝑠𝑐𝑜𝑢𝑠 + 𝜎 𝑐𝑜𝑚𝑝𝑙𝑒𝑥
General Framework
Model & Methods of numerical fluid dynamics: coarse grained approach
Generalized Navier-Stokes equation
Binary mixtures scalar field 𝜑
𝜕𝑡 𝜌 𝑣Ԧ + ∇ ⋅ 𝜌 𝑣Ԧ ⊗ 𝑣Ԧ = −∇𝑝 + ∇ ⋅ 𝜎 𝑣𝑖𝑠𝑐𝑜𝑢𝑠 + 𝜎 𝑐𝑜𝑚𝑝𝑙𝑒𝑥
Concentration 2
𝜕𝑡 𝜑 + ∇ ⋅ 𝜑 𝑣Ԧ = 𝑀 ∇ 𝜇 ,
𝜇=
𝛿𝐹 𝑏𝑚 𝛿𝜑
General Framework
Model & Methods of numerical fluid dynamics: coarse grained approach
Generalized Navier-Stokes equation
Binary mixtures
Concentration
scalar field 𝜑
𝜕𝑡 𝜌 𝑣Ԧ + ∇ ⋅ 𝜌 𝑣Ԧ ⊗ 𝑣Ԧ = −∇𝑝 + ∇ ⋅ 𝜎 𝑣𝑖𝑠𝑐𝑜𝑢𝑠 + 𝜎 𝑐𝑜𝑚𝑝𝑙𝑒𝑥
2
𝜕𝑡 𝜑 + ∇ ⋅ 𝜑 𝑣Ԧ = 𝑀 ∇ 𝜇 ,
𝜇=
Anisotropic contributions: vector/tensor order parameters Ψ
𝜕𝑡 Ψ + 𝑣Ԧ ⋅ ∇Ψ + S = Γ
𝛿𝐹 𝛿Ψ
𝛿𝐹 𝑏𝑚 𝛿𝜑
3d Lattice Boltzmann Method
Boltzmann Equation
Distribution functions 𝑓𝑖 (𝑥Ԧ𝛼 , 𝑡)
Physical observables 𝜌 𝑥Ԧ𝛼 , 𝑡 = σ𝑖 𝑓𝑖 𝑥Ԧ𝛼 , 𝑡
DF dynamics
Discretized time, space and velocity 𝜌𝑣Ԧ = σ𝑖 𝑒Ԧ𝑖 𝑓𝑖 (𝑥Ԧ𝛼 , 𝑡)
Collision (BGK approximation) 1 𝑒𝑞 𝑓𝑖𝑐𝑜𝑙𝑙 𝑥Ԧ𝛼 , 𝑡 = 𝑓𝑖 𝑥Ԧ𝛼 , 𝑡 − 𝑓𝑖 𝑥Ԧ𝛼 , 𝑡 − 𝑓𝑖 (𝑥Ԧ𝛼 , 𝑡) 𝜏
Streaming 𝑓𝑖 𝑥Ԧ𝛼 + 𝑒Ԧ𝑖 Δ𝑡, 𝑡 + Δ𝑡 = 𝑓𝑖𝑐𝑜𝑙𝑙 𝑥Ԧ𝛼 , 𝑡
Equilibrium DF Expansion at II order in 𝑣Ԧ continuum equations
Recover
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 Massage Passing Interface ~ 40Gb of Memory ~ 3y of CPU
Summer school on Parallel Computing – Cineca (BO)
Advanced School on Parallel Computing – Cineca (BO)
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 𝑎 𝐹 = න 𝑑𝑉 𝜑 2 𝜑 − 𝜑0 4 𝜑𝑐𝑟 2 𝑘𝜑
2
𝑘𝜑 + ∇𝜑 2
𝛽2 𝑘𝑃
2
Lamellar phase if 𝑎 <
Active stress tensor 𝜎 𝑎𝑐𝑡𝑣𝑒 = −𝜁𝜑𝑃 ⊗ 𝑃
4𝑐
+
𝑐 2 + ∇ 𝜑 2
𝑘𝜑 < 0 , 𝑐 > 0
2
𝛼 𝛼 4 𝑘𝑃 2 + 𝜑𝑃 + 𝑃 + ∇𝑃 2 4 2
2
+ 𝛽𝑃 ⋅ ∇𝜑
Results Activity favours ordering Transition towards mesoscale turbulence Wealth of different morphologies
G.Negro,L.N.Carenza,P.Digregorio,G.Gonnella,A.Lam ura 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.Orl andini,A.Tiribocchi Lamellar ordering, droplet formation and phase inversion in exotic active emulsions, Accepted with minor revisions Scientific Reports (Nature)
L.N.Carenza,G.Gonnella,A.Lamura,G.Negro,A.Tiriboc chi Lattice Boltzmann Methods and Active Fluids, Submitted to EPJ
Active Turbulence
Energy injection on small scales
What is new?
Mesoscale turbulence
Active Turbulence
Energy injection on small scales
What is new?
KOLMOGOROV TURBULENCE :
High Reynolds number
Hydrodynamics non-linearities
-5/3 spectrum (universal behavior)
Mesoscale turbulence
Active Turbulence
Energy injection on small scales
What is new?
Mesoscale turbulence
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
PhD SCHOOLS
How to prepare a technical speech in Summer school on Parallel Computing – English Cineca (Bologna) Management and knowledge of European research model and promotion Advanced School on Parallel of research results Computing – Cineca (Bologna) Introduction to parallel Computing and GPU Programming using CUDA XXX National Seminar of Nuclear and Subnuclear Physics "Francesco C++ Romano" OTRANTO Atom-photon interactions Standard model and beyond Linear stability analysis* Computational fluid dynamic*
Courses labelled with * are being erogated.
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