Microswimmers in Flow Salima Rafaï Laboratoire Interdisciplinaire de Physique, CNRS Grenoble 1180 1181 indeed, defining feature of active systems compared to more familiar nonequilibrium systems is the fact that the energy input that drives the system out of equilibrium is local, for example, at the level of each particle, rather than at the Active Matter ns 1181 1182 1183 1184 1185 1185 er to a he meand of es from m conner, Tu, ny and known hey are Surrey et al., 2001. Motor proteins FIG. 2. Patterns organized in vitro by the action of multimeric kinesin complexes on microtubules, imaged by dark-field microscopy. The concentration of motor proteins increases from left to right. (a) A disordered array of microtubules. The other two images display motor-induced organization in (b) spiral and (c) aster patterns. The bright spots in the images correspond to the minus end of microtubules. These remarkable experiments from Surrey et al. (2001) led the way to the study of pattern formation in active systems. Adapted from Surrey et al., 2001. Bacterial biofilm Plankton bloom Fish school Bioconvection Starling flock 2 Living microswimmers E. Coli Gonyaulax Sperm cell Paramecia ❖ Full name: Chlamydomonas Reinhardtii! ❖ Microalga! ❖ Size: 10 µm! ❖ Shape : Quasi-spherical! ❖ Gender : Puller-type! ❖ Velocity ~100µm/s! ❖ favorite drinking: freshwater + nutrients 3 The complex random walk of Chlamy Power Stroke Recovery Stroke Re = 10-4 !F/2% +F%!F/2% 20 µm 800 µm 400 Hz movie slowed down 20 times 4 Y (µm) Particle tracking and classical analysis A persistent random walk X (µm) 20 ms 2s M. Garcia, S. Berti, P.Peyla & S.Rafaï Phys. Rev. E (R) (Z011) 5 Y (µm) Y (µm) Chlamy & phototaxis X (µm) VX (µm/s) VX (µm/s) X (µm) Time (s) 6 Time (s) Phototaxis & Poiseuille flow r(t) = Z t V(r)dt0 , 0 with V(r) = Vswim sin ✓(r) er + [Vswim cos ✓(r) + u(r) r z u(r) = Umax (1 ✓(r) = 8 > < dr = Vswim sin ✓(r) dt dz > : = Vswim cos ✓(r) + u(r) dt 7 dr Z t 0 r2 ) 2 R !(r)dt0 2R and 1mm Phototaxis & Poiseuille flow: Photofocusing Light Control of the Flow of Phototactic Microswimmer Suspensions X. Garcia, S.Rafaï & P.Peyla (Z013) Phys. Rev. Lett. 110 , 138106 8 Half band width (µm) Half band width (µm) Photofocusing: a reversible effect Flow rate (mL/min) Time (s) Microswimmer velocity controls the dynamics A range of flow rate where focusing occurs 9 and V(r) = Vswim sin ✓(r) er + [Vswim cos ✓(r) + u(r)] k Z A non linear model: swimming 0 !(r)dt , u(r) = Umax r2 /R speed Vswim+ flow speed u Swimming in the flow and ✓(r) = 0 u(r) = Umax (1 ✓(r) = Z t !(r)dt 0 r2 ) 2 R r z (4 2R 8 > < dr = Vswim sin ✓(r) dt dz > : = Vswim cos ✓(r) + u(r) dt t 0 8 Z t dr < steady but arbitrary> swimming angle = Vswim sin 0 dr✓(r) ✓(r) = !(r)dt dt = Vswim sin ✓(r) dz > 0 dt ✓(r) + u(r) : = Vswim cos 8 dt > < dr = Vswim sin ✓(r) dz dr dt = Vswim cos ✓(r) + u(r)= Vswim sin ✓(r) dz > : dt dt cos ✓(r) + u(r) = Vswim fluctuating arbitrary swimming angle dt dz = dr Vswim cos ✓(r) + u(r) = Vswim sin ✓(r) dt dt [1] Viscous Fluid Flow, FM White, (1991), McGraw-Hill NY dz upstream reorienting swimming angle = Vswim cos ✓(r) + u(r) [2] Introduction `a la microfluidique, P.Tabeling dt [1] Viscous Fluid Flow, FM White, (1991), McGraw-Hill NY ⇤ [2] Introduction `a la microfluidique, P.Tabeling Electronic address: [email protected] ⇤ Electronic address: [email protected] [1] Viscous Fluid Flow, FM White, (1991), McGraw-Hill NY z [2] Introduction `a la microfluidique, P.Tabeling 10 r bonded to the spherical particle. articles with an inner viscosity ⌘p much higher than the particle, we need to know both it uter fluid viscosity ⌘0 (⌘p /⌘0 = 100). The stokes equa< v >i to determine its position on is then solved on the entire domain: inside and outity < ⌦ >i to determine its orien de the particles, thus avoiding particle tracking. The firsttomodel reposition the set of forc ranslational velocity of the ith particle, < v >i is ob- Aorder i. ained by averaging the velocity v on the volume of parA single swimmer, described cle number i. The symbol < . >i means that avermoves in a fluid at rest with a v ging is done over the volume of the particle number M !F/2% the force : v0 = M f . The swimm It is also convenient to calculate the angular velocity 1 that M = (6⇣⇡⌘R) where ⇣ is < ⌦ >i = 1/2 < r ⇥ v >i . A time step t is defined +F%!F/2% eter which depends on the geome nd at each iteration, the out-of-lattice sphere number i around the swimmer. For exampl moved by the quantity ri =< v >iModel: t. Then, the field Chlamy plied on the spherical body, we w f viscosity is recalculated from the new positions of Phantom ⌘(r) flagella model = with setParticle of three forces bon he sphere centers. Time t is then simplySphere t = n t where 3Dthe Fluid Dynamics Mehandia & Nott found ⇣⇠ 1.14 in our simulations J. ofnumber Fluid Mech. Peyla et al. J. Fluid Mech. 2012 + is the of 2008 iterations. 3D Fluid particle dynamics consistent with multipole of forces is -very close to the analytical valu Despite the smallness of the Re number, we solve the Tanaka & Araki, PRL, 2000 Experimental hydrodynamic field rived with the Green’s function th - Peyla, EPL 2007,Davit & Peyla, EPL 2 Navier-Stokes equation (andDrescher not the Stokes equation) et al. Phys Rev Lett on 2010 fluid. Penalization method he whole domain with a field of viscosity ⌘(r): WeTanaka initially begin2000), the simulat 2D (PRL of swimmers as describ Peyla 3D modeled (EPL 2007)" Dv t ⇢ = rP + r.[⌘(r)(rv + rv )] + f , (1) neously distributed across a chan Dt Modeling with full hydrodynamics M M M Navier Stokes + Active forces 11 Clustering Full hydrodynamics numerical simulations (FPD method) Self-focusing and jet instability of a microswimmer suspension L. Jibuti et al. (2014) Phys. Rev. E, 90, 063019 12 Perspectives together with Philippe Peyla (Prof. UJF) Experimental evidence of clustering? Effect of hydrodynamic interactions on the dispersion of µswimmers numerics Johannes Greber PhD (Bayreuth) 13 experiments Matthieu Martin PhD Thank you People: " Philippe Peyla, Prof. " Michaël Garcia, PhD (2009-‐2013) Levan JibuC, PhD (2008 – 2011) Stefano BerC, Post-‐Doc 2008 Xabel Garcia, Master 2011 MaKhieu MarCn, PhD (2014-‐ ) " Prof. W. Zimmermmann Bayreuth Johannes Greber, PhD " " Fundings: 14

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