Sticking collision between a sphere and a textured wall in a viscous fluid

The collision of a sphere with a wettable microtextured wall in a viscous fluid is investigated experimentally, focusing on the region close to the contact with the wall. High-frequency laser interferometry is used for measuring small displacements of the sphere in that region. The wall texture consists of an a array of square micropillars, whose geometrical parameters (height, width, and spacing of the pillars) are varied. The wall texture decreases the hydrodynamic resistance, and hence the drag on the sphere, compared to the case of a smooth wall. At small Reynolds and Stokes numbers, this drag reduction is quantified in terms of an equivalent plane boundary, shifted down from the top of the pillars. The shift length depends on the geometrical parameters of the pillars array and is compared to available predictions of effective slip length for a flow over arrays of micropillars in the Wenzel state. At finite Stokes number, below the bouncing transition, the wall texture influences the relative importance of sphere inertia and drag force in the near wall region. As a result, a great diversity of sphere dynamics are obtained by varying the texture geometrical parameters. These dynamics can be captured considering a shift-length-modified drag force in the equation of motion of the sphere.