Pressure and forces in active matter

Transcription

1 1 Pressure and forces in active matter Alex Solon (MIT) University of Houston, February 8th 2018

2 Active matter 2 Stored energy Mechanical energy Self-propelled particles Found at all scales in living systems sub-cellular cellular macroscopic Active matter = Assemblies of active particles?

3 Collective behaviours Bird flocks Cell migration StarFlag collaboration Yamaguchi et al, Sci. Rep Actin density waves Microtubule gels Schaller et al Nature 2010 Dogic lab, Nature

4 Challenges 4 In biology: Mechanics of living matter In engineering Painting with bacteria W. Poon lab Mixing, targeted delivery, crystal annealing Smart materials?

5 The Stat. Mech. approach 5 Nonequilibrium systems with a reversed energy cascade Simple models Universality Controlled experiments v Artificial self-propelled particles Janus colloids Precisely controlled interactions Bacterial patterns J. Huang lab

6 My researches in active matter 6 Transition to collective motion Motility-induced phase separation Expansion of cell colonies Pressure and forces

7 7 Active particle Self-propelled at speed v Different reorientation mechanisms v v dx dt Run and Tumble Particles (Bacteria) = v e(θ)+(interactions), dθ dt Active Brownian Particles (Janus colloids) = 2D r ξ+(interactions) (in 2d) Dry active matter: no hydrodynamic interactions

8 8 Scales v v Relevant scales: Persistence time τ r Persistence length l r = vτ r E.Coli: Pt-coated Janus colloids: Colloidal rollers: τ r 1s, l r 30µm τ r 5s, l r 10µm τ r 0.3s, l r 150µm At large scale: SPP Hot colloid with T eff vl r

9 Harmonic potential 9 RTP in a circular harmonic potential U(r) = λ r 2 2 Slowly varying potentials Effective equilibrium Solon, Cates and Tailleur, EPJST (2015)

10 Outline 10 Mechanical pressure Curved objects and flexible filaments Forces mediated by an active medium

11 From passive to active pressure 11 In an equilibrium fluid: P = F wall S = Tr σ d In an active fluid: No free energy Forces in biological systems = F V P = F wall S =? = f (ρ, T ) N Equation of state Actin cortex Wound healing

12 Mechanical pressure 12 Particles confined by a potential V w ρ(x) V w 0 x w x Mechanical pressure: P = 0 dxρ(x)v w(x) Ideal gas: ρ(x) = ρ 0 e Vw (x)/k BT P = ρ 0 k B T P independent of V w Equation of state P(ρ 0, T )

13 Wall 13 Two effects of the wall Γ w Force V w + Torque Γ w V w

14 Active ideal gas pressure 14 Equation of motion dx dt = ve(θ) γv w(x)e x, dθ dt = Γ w (x, θ) + 2D r ξ Exact expression for the pressure P = ρ 0 k B T eff v dx D r T eff = v 2 2γD r 0 2π 0 dθ Γ w (x, θ) sin(θ)p(x, θ) Spherical particles (Γ W = 0) = Ideal gas law Torques = P depends on the wall potential: No equation of state

15 Self-propelled ellipses 15 (x xw )2 Ellipses in a harmonic wall potential V w (x) = λ 2 ] P = ρ 0v 2 2λκ [1 e λκ Dr When Γ w increases, P decreases

16 Interacting spherical ABPs Effect of interactions? 20 P P 10 λ = 2 λ = 4 λ = 6 λ = 0.1 λ = 1 λ = 10 ρ non-interacting Pairwise forces Equation of state P 6 4 λ = 0.1 λ = 1 λ = 10 non-interacting ρ Quorum sensing v( ρ) No Equation of state λ = 0.1 λ = 1 λ = 10 non-interacting 2 Confusing Need a simple test 0 ρ Alignment 16

17 A simple test 17 Place an asymmetric piston in the middle of a cavity Equation of state wall always static.

18 A simple test - All cases 18 No equation of state Spontaneous compression Solon, Fily, Baskaran, Cates, Kafri, Kardar and Tailleur Nat. Phys. 2015

19 Outline 19 Mechanical pressure Curved objects and flexible filaments Forces mediated by an active medium

20 Curved walls 20 Active particles accumulate in curved regions Aranson lab. DiLeonardo lab. Wall P Equation of state Nikola, Solon, Kafri, Kardar, Voituriez, Tailleur Phys. Rev. Lett. 2016

21 Flexible filament 21 Semi-flexible filament in a bath of ABPs Instability for q < q i (T, κ b ) 200 y y y t = 10 2 t = 10 3 t = Coarsening x x x Nikola, Solon, Kafri, Kardar, Voituriez, Tailleur Phys. Rev. Lett. 2016

22 22 Free filament 200 D κ b = 250 κ b = L f Spontaneous symmetry breaking Polymer in active medium

23 23 Experiments Absence of equation of state and Instability Juno et al, Phys. Rev. Lett. (2017) Flexible filament Junang Li, Shreyas Gokhale, Nikta Fakhri, Jeff Gore (MIT)

24 Outline 24 Mechanical pressure Curved objects and flexible filaments Forces mediated by an active medium

25 Flow generated by an object F F Force exerted by the object on the bath Generates flows Similar to an electric dipole Steady-state density given by D eff 2 ρ = µ (ρ V + G) ρ(r) = electrostatic potential r 1 J(r) = electric field r 2 p F 6 3 y/l r x/l r Baek, Solon, Xu, Nikola, Kafri, Phys. Rev. Lett ρl 2 r

26 Two-body interactions 26 p 1 p 2 p= 2 0 Long-range interaction µ r p 1 F 2 (r) = 2πD eff ρ b r 2 p 2 + R 2 J 1 (r) + O(r 3 ) µ r p 1 τ 2 (r) = 2πD eff ρ b r 2 T 2 + γ 2 J 1 (r) + O(r 3 ) p i, T i, R i, γ i : one-body properties Can be tuned (in principle) by designing the object Different dynamical phenomena

27 Synchronized rotations 27 Two semi-circles pinned at different points J A C J C A CA C C AC A A Changing the mobilities: transition between phase-locking and synchronized rotations

28 Alignment of moving semi-circles 28 Two semi-circles with different center of mass C I A I II II J A III II III IV III IV A C I Snake-like motion

29 29 Conclusion Unusual forces in active matter Absence of equation of state Instability of filaments Long-range interactions Long-lived Casimir forces following a quench Rohwer, Solon, Kardar, Krüger, arxiv: Importance in biological systems? Toward self-assembly mediated by active forces?

30 Acknowlegments 30 Mehran Kardar (MIT) Julien Tailleur (Paris Diderot) Mike Cates (Cambridge) Yariv Kafri (Technion Haifa) Matthias Krüger (MPI Göttingen) Christian Rohwer (MPI Stuttgart) Nikta Fakhri (MIT) Joakim Stenhammar (Lund) Aparna Baskaran (Brandeis) Yaouen Fily (Florida Atlantic) Yongjoo Baek (Cambridge) PLS fellowship Solon, Cates and Tailleur, EPJST 2015 Solon, Fily, Baskaran, Cates, Kafri, Kardar and Tailleur, Nature Physics 2015 Solon, Stenhammar, Wittkowski, Kardar, Kafri, Cates, Tailleur, Phys. Rev. Lett Nikola, Solon, Kafri, Kardar, Voituriez, Tailleur, Phys. Rev. Lett Baek, Solon, Xu, Nikola, Kafri, Phys. Rev. Lett Rohwer, Solon, Kardar, Krüger, arxiv 2017