Colloidal particle dynamics during the steady-state bands stage

Polystyrene particles in a very dilute (volume fractions $=$ $O$(10$^{\mathrm{-5}}$--10$^{\mathrm{-3}}))$ suspension become concentrated near the wall, then assemble into streamwise structures called ``bands'' which only exist within a few $\mu $m of the wall, when subject to pressure and voltage gradients in the same direction. These bands, which attain steady-state within $O$(10$^{\mathrm{2}}$ s), have cross-sectional dimensions of a few $\mu $m, \textit{vs.} a channel depth $H \quad =$ 34 $\mu $m, and a length comparable to that of the channel of a few cm. Tracer particles were used to track the dynamics of $a \quad \approx $ 250 nm radius particles within and between the bands in this steady-state stage at different streamwise locations. The time scales of band formation appear to scale linearly with streamwise position past an ``entrance length'' region. The particles within the bands ``lag'' the flow, as do the much fewer particles between the bands, though their velocities are closer to the expected flow velocities. The time scales for achieving steady-state bands are compared with the time scales of near-wall particle concentration. Results over different wall-normal extents suggest that the particle concentration within the bands may be underestimated in these evanescent-wave visualizations because they visualize the ``edge'' of the bands.