Title: Mobility tensor of a sphere moving on a super-hydrophobic wall: application to particle separation,
Abstract: The paper addresses the hydrodynamic behavior of a sphere close to a
micro-patterned superhydrophobic surface described in terms of alternated
no-slip and perfect-slip stripes. Physically, the perfect-slip stripes model
the parallel grooves where a large gas cushion forms between fluid and solid
wall, giving rise to slippage at the gas-liquid interface. The potential of the
boundary element method (BEM) in dealing with mixed no-slip/perfect-slip
boundary conditions is exploited to systematically calculate the mobility
tensor for different particle-to-wall relative positions and for different
particle radii. The particle hydrodynamics is characterized by a non trivial
mobility field which presents a distinct near wall behavior where the wall
patterning directly affects the particle motion. In the far field, the effects
of the wall pattern can be accurately represented via an effective description
in terms of a homogeneous wall with a suitably defined apparent slippage. The
trajectory of the sphere under the action of an external force is also
described in some detail. A resonant regime is found when the frequency of the
transversal component of the force matches a characteristic crossing frequency
imposed by the wall pattern. It is found that, under resonance, the particle
undergoes a mean transversal drift. Since the resonance condition depends on
the particle radius the effect can in principle be used to conceive devices for
particle sorting based on superhydrophobic surfaces.