Creeping flows through confined arrays of cylinders

Hair-covered appendages serve a variety of purposes in Nature, from
chemical sensing and particle capture on the antennae of a crustacean to
drag generation on bristled wings. Despite their large porosity, these
finite porous structures experience very little flow through at low
Reynolds numbers. This flow regime, characterized by large viscous
boundary layers around the hairs, is known as the paddle or rake regime.
As the Reynolds number of the flow increases, so does the relative flow
rate through the array, which corresponds to the deflection and sieve
regimes. Confining structures, such as the animal body or larger hairs,
have been hypothesized to focus the flow on the hair-covered region. We
investigate the influence of confinement on the flow through and around an
array of cylinders, using a combination of experiments and numerical
simulations. Experimentally, we vary the hair spacing, channel dimension,
and flow rate and measure the velocity field using Particle Image
Velocimetry. After comparing the results of finite element analysis with
the experimental data, we numerically investigate a broader range of
system geometries and flow parameters. Our results show that the
confinement focuses the flow in the array and shifts the domains of
existence of the three regimes. We present an analytical model that relies
on the permeability of rectangular slits to predict the relative flow rate
through and around the array. The model is in quantitative agreement with
the numerical results, demonstrating that the flow through the array
increases with increasing confinement, while the flow angle decreases.
These results should provide insight into the morphology of hairy surfaces
and have implications in the design of bio-inspired flow sensors and
filters.