Rolling Spheres on Bioinspired Microstructured Surfaces.

Microstructured surfaces, such as those inspired by nature, mediate surface interactions and are actively sought after to control wetting, adhesion, and friction. In particular, the rolling motion of spheres on microstructured surfaces in fluid environments is important for the transport of particles in microfluidic devices or in tribology. Here, we characterize the motion of smooth silicon nitride spheres (diameters 3-5 mm) as they roll down inclined planes decorated with hexagonal arrays of microwells and micropillars. For both types of patterned surfaces, we vary the area fraction of the micropatterned features from 0.04 to 0.96. We measure directly and independently the rotational and translational velocities of the spheres as they roll down planes with inclination angles that vary between 5 and 30°. For a given area fraction, we find that spheres have a higher translational and rotational velocity on surfaces with microwells than on micropillars. We rely on the model of Smart and Leighton [Phys. Fluids A 5, 13 (1993)] to obtain an effective gap width and coefficient of friction for all microstructured surfaces investigated. We find that the coefficient of friction is significantly higher for a surface with micropillars than that for one with microwells, likely due to the presence of interconnected drainage channels that provide additional paths for the fluid flow and favor solid-solid contact on the surface with micropillars. We find that while the effective gap width at a very low solid fraction is equal to the height of the patterned features, the effective separation decreases exponentially as the surface coverage of microstructures increases, with little measured differences between the two geometries. Superposition of resistance functions is used to relate the rapid decrease in the effective gap height with increase in the surface coverage observed in experiments.