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(Top) Energy harvesting through VIV of flexible cables. (Bottom) Piezoelectric flag - the periodic bending of the piezoelectric flag creates an electric current.

We developed a reduced-order model for the representation of the flow around a solid body with sharp edges, when viscous effects are negligible except for the formation of the vortex wake through the detachment of the boundary layers near the solid edges. This low-order representation for the fluid flow can then be coupled to the solid body dynamics to obtain a first insight on the dynamics with a much reduced computational cost in comparison with full numerical simulations.

Below are a few examples of our research. Feel free to contact us for more information.

Current projects focus on the study of the nonlinear dynamics of such devices, their harvesting efficiency, potential couplings with the output electrical circuit and hydrodynamic interactions between multiple devices.

Fluid-solid instabilities and energy harvesting


  1. Optimal energy harvesting from Vortex-Induced Vibrations of cables, G. O. Antoine, E. de Langre & S. Michelin (2016) Proc. Roy. Soc. London A, 472, 20160583

  2. Synchronized flutter of two slender flags, J. Mougel, O. Doaré & S. Michelin (2016) J. Fluid Mech., 801, 652-669

  3. Synchronized switch harvesting applied to piezoelectric flags, M. Piñeirua, S. Michelin & O. Doaré (2016) Smart Mat. Struct., 25, 085004

  4. Resonance-induced enhancement of the energy harvesting performance of piezoelectric flags, Y. Xia, S. Michelin & O. Doaré (2016) Appl. Phys. Lett., 107, 263901

  5. Influence and optimization of the electrodes position in a piezoelectric energy harvesting flag, M. Piñeirua, O. Doaré & S. Michelin, (2015), J. Sound Vib., 346, 200-215

  6. Fluid-solid-electric lock-in of energy harvesting piezoelectric flags, Y.Xia, S. Michelin & O. Doaré (2015) Phys. Rev. Applied, 3, 014009

  7. Energy harvesting efficiency of piezoelectric flags in axial flows, S. Michelin & O. Doaré (2013) J. Fluid Mech., 714, 489-504

  8. Effect of damping on flutter in axial flow and optimal energy harvesting, K. Singh, S. Michelin & E. de Langre (2012) Proc. R. Soc. A, 468, 3620-3635

  9. Energy harvesting from fluid-elastic instabilities of a cylinder, K. Singh, S. Michelin & E. de Langre (2012) J. Fluids Struct., 30, 159-172

  10. Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency, O. Doaré & S. Michelin (2011) J. Fluids Struct., 27, 1357-1375

  11. Effect of damping on flutter in axial flow and energy-harvesting strategies, K. Singh, S. Michelin & E. de Langre (2012) Proc. R. Soc. A, 468, 3620-3635

The coupled dynamics of fluids and solid bodies can lead to self-sustained solid vibrations (e.g. Vortex-Induced Vibrations of rigid cylinders in cross-flows, flutter of flexible plates and cables in axial flows -- “flag instability”). This can be used to harvest energy from ambient flows, using either electromagnetic generators or piezoelectric materials to convert the solid motion into electricity.

Optimal swimming strokes of ciliates


  1. Efficiency optimization and symmetry-breaking in an envelope model for ciliary locomotion, S. Michelin & E. Lauga (2010) Phys. Fluids, 22 (11), 111901

  2. Optimal feeding is optimal swimming for all Péclet numbers, S. Michelin & E. Lauga (2011) Phys. Fluids, 23, 101901

  3. Unsteady feeding and optimal strokes of model ciliates, S. Michelin & E. Lauga (2013) J. Fluid Mech., 715, 1-31

Ciliates such as Paramecium swim in viscous flows using the flapping of multiple flexible cilia distributed over their surface. The flow generated by the swimmer’s deformation or stroke also stirs nutrients in its immediate vicinity. We are interested in the link between these two biological functions, swimming and feeding.

(Above) Optimal swimming and feeding stroke for a spherical squirmer. Colors correspond to material points on the surface. (Left) Optimal feeding stroke and nutrient concentration. Blue (resp. red) colors correspond to nutrient-rich (resp. nutrient-depleted) regions.

Using an envelope model for such a micro-organism, we determine the optimal strokes maximizing either the swimming velocity or the nutrient uptake. The optimal strokes are shown to be identical regardless of the diffusivity of the nutrient and are characterized by a synchronization of neighboring cilia in the form of so-called “metachronal waves”.

Stability and dynamics of flapping flags


  1. Vortex shedding model of a flapping flag, S. Michelin, S. G. Llewellyn Smith & B. J. Glover (2008), J. Fluid Mech., 617, 1-10

  2. Linear stability of coupled parallel flexible plates in an axial flow, S. Michelin & S. G. Llewellyn Smith (2009) J. Fluids Struct., 25, 1136-1157

  3. Falling cards and flapping flags: understanding fluid-solid interactions using an unsteady point vortex model, S. Michelin & S. G. Llewellyn Smith (2009), Theor. Comp. Fluid Dyn., 24, 195-200

Thin flexible plates become unstable to flutter in steady axial flows when the flow velocity exceeds a critical threshold, a phenomenon known as the flapping flag instability. Beyond this critical value, periodic or complex nonlinear flapping regimes can develop. Through linear stability analysis, reduced-order modeling and nonlinear simulations, we study the stability properties and nonlinear flapping of such structures. We are particularly interested in the characteristics of the permanent flapping regimes and transitions observed at high velocities, as well as the hydrodynamic interactions between multiple flags.

(Left) Periodic flapping of a flexible flag. (Right) In-phase flapping of two parallel flags.

Vortex shedding model for fluid-solid interactions


  1. Vortex shedding model of a flapping flag, S. Michelin, S. G. Llewellyn Smith & B. J. Glover (2008), J. Fluid Mech., 617, 1-10

  2. An unsteady point vortex method for coupled fluid-solid problems, S. Michelin & S. G. Llewellyn Smith (2009), Theor. Comp. Fluid Dyn., 23, 127-153

  3. Falling cards and flapping flags: understanding fluid-solid interactions using an unsteady point vortex model, S. Michelin & S. G. Llewellyn Smith (2009), Theor. Comp. Fluid Dyn., 24, 195-200

In this approach, point vortices are shed from each sharp edge of the solid body, and their unsteady intensity is determined through the regularity condition (Kutta) at the shedding edge (Brown-Michael model). The fluid forces can then be explicitly computed from the characteristics of these vortices. We use this method to study a large variety of problems from the dynamics of falling cards to the flapping of flexible plates in the wind.

(Left) Dynamics of a flapping flag obtained using the unsteady point vortex model. (Right) Unstable dynamics of a falling card initially released from rest horizontally.

Propulsion with flexible wings and fins

Insect wings and fish fins are not rigid, but deform under the action of the flow forces, modifying their propulsive performance. Considering a passive flexible wing actuated at its leading edge, we showed that the wing’s flexibility can induce higher thrust and efficiency than its rigid counter part. When placed in a steady flows, peaks of thrust are associated with resonances between the flapping frequency and the fundamental modes of the equivalent flag. Also, flexibility plays a major role in stabilizing the vortex wake generated by the wing.

Evolution of the thrust (solid), wing-tip flapping amplitude (circles), wake intensity (squares) and wake relative velocity (triangle) with the rigidity of the wing.


  1. Resonance and propulsion performance of a heaving flexible membrane, S. Michelin & S. G. Llewellyn Smith (2009), Phys. Fluids, 21 (7), 071902

Individual & collective swimming of active microparticles (CollectSwim)


  1. Clustering-induced self-propulsion of isotropic autophoretic particles A. Varma, T. D. Montenegro-Johnson & S. Michelin (2018) Soft Matter

  2. Geometric tuning of self-propulsion for Janus catalytic particles, S. Michelin & E. Lauga (2017) Sci. Rep., 7, 42664

  3. Stresslet induced by active swimmers, E. Lauga & S. Michelin (2016) Phys. Rev. Lett., 17, 139

  4. A regularised singularity approach to phoretic problems, T. D. Montenegro-Johnson, S. Michelin & E. Lauga (2015) Eur. Phys. J. E, 38, 139

  5. Phoretic self-propulsion at large Péclet numbers, E. Yariv & S. Michelin (2015) J. Fluid Mech., 768, R1

  6. Autophoretic locomotion from geometric asymmetry, S. Michelin & E. Lauga (2015) Eur. Phys. J. E, 38, 7

  7. Self-propulsion of pure water droplets by spontaneous Marangoni stress driven motion Z. Izri, M. N. van der Linden, S. Michelin & O. Dauchot (2014), Phys. Rev. Lett. 113, 248302

  8. Phoretic self-propulsion at finite Péclet numbers, S. Michelin & E. Lauga (2014) J. Fluid Mech., 747, 572-604

  9. Spontaneous autophoretic motion of isotropic particles, S. Michelin, E. Lauga & D. Bartolo (2013) Phys. Fluids., 25, 061701

Catalytic particles swim using self-generated physico-chemical gradients in their environment, exploiting short-range interaction of their surface with the properties and in particular chemical composition of the fluid around them, a property termed autophoresis. To achieve self-propulsion, they must break a spatial symmetry.  The most classical way to do so involves a chemical patterning of the surface that guarantees an imbalance in the solute content of the fluid around them (Janus particles). At the collective level, these particles interact hydrodynamically and chemically, leading to the formation of complex patterns in experiments.

Our work focuses on the mathematical and physical modeling of these particles, at the individual and collective level. In recent years, we have identified several possible routes to symmetry-breaking (Figure) and characterized the role of the particles’ properties such as their geometry in setting their propulsion and interaction characteristics.

This project is supported by a Starting Grant from the European Research Councing (ERC) (Project CollectSwim)

Phoretic pumping in microchannels

Multiple strategies exist to create a net flow in a microchannel: in microfluidics, a pressure gradient is imposed between the inlet and outlet channels that overcomes viscous resistance in the channel and drives a flow. In biological system, boundary actuation is used through ciliary carpet to generate a net flow outside the cilia layer.

We demonstrated that it is possible to use self-diffusiophoresis to drive a net flow within a channel with chemically-active walls. In some regard, this is the dual problem to the locomotion of autophoretic systems described above. In particular, we showed that asymmetric geometry is sufficient (without any chemical patterning).

Circular autophoretic pump. The inner wall releases solute and imposes a net slip flow in response to longitunial solute gradients. The solute concentration is shown as well as the flow’s streamlines (white: recirculating streamlines, red: traversing flow)


  1. Phoretic flows induced by asymmetric confinement, M. Lisicki, S. Michelin & E. Lauga (2016) J. Fluid Mech., 799, R5

  2. A reciprocal theorem for boundary-driven channel flows, S. Michelin & E. Lauga (2015) Phys. Fluids, 27, 111701

  3. Geometric pumping in autophoretic channels, S. Michelin, T. D. Montenegro-Johnson, G. De Canio, N. Lobato-Dauzier & E. Lauga, Soft Matter, 11, 5804-5811

Four different routes to symmetry-breaking and self-propulsion of autophoretic particles: (I) Chemical patterning of the surface ensures a broken symmetry in the concentration field, yet geometry can tune the direction of propulsion. (II) Asymmetric geometry of the particle creates local concentration gradients and self-propulsion of chemically-homogeneous particles. (III) Isotropic (chemically and geometrically) particles can self-propel if solute advection by the phoretic flows is non-negligible. (IV) Individual isotropic particles can not self-propel but can attract each other and form asymmetric clusters, whose geometric anisotropy is sufficient to enable self-propulsion.