### Principal investigator: Anne Mongruel

Particle collisions with walls or with other particles in a fluid play an important role in many industrial or natural multiphase flows. From a fundamental point of view, particle-particle or particle-wall hydrodynamic interactions are crucial to the understanding of the dynamics of concentrated suspensions, of wet granular media. Our work investigates how the near-wall motion of a sphere in a fluid is influenced by a controlled wall roughness. A wall texture is designed using micro-grooves or micro-pillars obtained by soft lithography. The geometrical parameter of the texture can be easily varied and controlled (Figure 1).

Figure 1 : Side-view of a sphere near a textured wall (the distance h, measured between the sphere and the top of the pillars, is very small compared to the radius of the sphere). Differents textures obtained by soft lithography.

To resolve in time and space the motion of the sphere not only before and after the collision with the wall, but also during the collision, we use a high frequency interferometer device [1], where the sphere acts as a moving mirror (Figure 2). Interference fringes are formed, that move according to the displacement of the sphere. The spatial resolution is of 0.2 micrometer, and the time resolution of 0.002 ms. The accuracy of the measurements enables us to detect, in the near-wall region, i.e. for distances to the wall smaller than 0.1 mm, the enhancement of the velocity of the sphere [2,3], compared to the case of a smooth wall (Figure 3).

Figure 2 : Interferometer device. Recorded signal when the sphere approaches a textured wall.

When the viscous forces are not sufficient to slow down the sphere, bouncing may occur. The bouncing collision is an elastohydrodynamic problem, which combines the fluid forces and the deformation of the texture. Therefore, the transition from sticking to bouncing collision is critically influenced by the geometrical parameters of the texture [4]. In the bouncing regime, the penetration of the sphere into the micro-pillars, the time duration of the collision, the height of the micro-rebounds, together with the impact and rebound velocity, can be measured (Figure 3). Different models are proposed to describe the collision dynamics [4].

Figure 3 : Velocity of a sphere of radius 14 mm as a function of the distance h. The Stokes number of the collision, based on the terminal velocity of the sphere, is St= 4.7. The sphere sticks to the wall in the case of a smooth wall, and of a wall covered with square pillars of surface fraction 0.05 and height e = 21 micrometer. For a wall covered with square pillars of surface fraction 0.05 and height e = 89 micrometer, the sphere collides the top of the pillars with a velocity of 45 mm/s, penetrates into the pillars (h<0), leaves the pillars with a rebound velocity of 15 mm/s, experiences a micro-rebound in the fluid (h>0), before landing again on top of the pillars.

### Student involved in this work :

Thibault Chastel.

### Collaborator :

Philippe Gondret (FAST, Université Paris-Sud, CNRS) .

### References :

[1] A. Mongruel, C. Lamriben, S. Yahiaoui and F. Feuillebois. The approach of a sphere to a wall at finite Reynolds number, J. Fluid Mech. 661, 229-238 (2010).

[2] A. Mongruel, T. Chastel, E.S. Asmolov and O.I. Vinogradova. Effective hydrodynamic boundary conditions for microtextured surfaces, Phys. Rev. E 87, 11002(R) (2013).

[3] T. Chastel and A. Mongruel, Squeeze flow between a sphere and a textured wall, Physics of Fluids 28, 023301 (2016).

[4] T. Chastel, P. Gondret and A. Mongruel. Texture-driven elastohydrodynamic bouncing, J. Fluid Mech. 805, 577-590 (2016).