Observations of the near‐wall accumulation of suspended particles due to shear and electroosmotic flow in opposite directions

Abstract

On the basis of previous studies, the particles in a dilute (volume fractions φ ∞ < 4 × 10 -3 ) suspension in combined Poiseuille and electroosmotic "counterflow" at flow Reynolds numbers Re ≤ 1 accumulate, then assemble into structures called "bands," within ∼6 μm of the channel wall. The experimental studies presented here use a small fraction of tracer particles labeled with a different fluorophore from the majority "bulk" particles to visualize the dynamics of individual particles in a φ ∞ = 1.7 × 10 -3 suspension. The results at two different near-wall shear rates and three electric field magnitudes E show that the near-wall particles are concentrated about 150-fold when the bands start to form, and are then concentrated about 200-fold to a maximum near-wall volume fraction of ∼0.34. The growth in the near-wall particles during this accumulation stage appears to be exponential. This near-wall particle accumulation is presumably driven by a wallnormal "lift" force. The observations of how the particles accumulate near the wall are compared with recent analyses that predict that suspended particles subject to shear flow and a dc electric field at small particle Reynolds numbers experience such a lift force. A simple model that assumes that the particles are subject to this lift force and Stokes drag suggests that the force driving particles toward the wall, of O(10 -17 N), is consistent with the time scales for particle accumulation observed in the experiments.

Near‐wall velocities of particles suspended in shear flow and a streamwise electric field

“…First, interparticle effects could be significant, as the particle concentration is much greater than the bulk value during the late accumulation and steady‐state stages. Specifically, near the beginning of the accumulation stage, evanescent‐wave visualizations indicate that there are about 1–15 tracer particles near the wall, where the tracer particles are 1% of all the particles, over a 203 µm square field of view; the number of particles rapidly increases to about 200 at the end of accumulation [7]. Assuming that only a single layer of particles is visualized by the illumination, the average interparticle spacing can be estimated to be twice the radius of a circle with the average area occupied by a single particle: $$\begin{equation}{\delta _{\rm{w}}} = 2\sqrt {\frac{A}{{\pi N}}} \end{equation}$$where A is the area of the field of view.…”

“…The tracer particles, which comprised 1% of all the suspended particles, were illuminated with evanescent‐waves in the combined Poiseuille and EO “counterflows” of a dilute (total volume fraction 1.7 × 10 −3 ) particle suspension at Re p $$ \ll $$ 1 through silica microchannels. Under these conditions, the particles are attracted to, and accumulate near the wall, with at least a 100‐fold increase in the particle concentration then assemble into highly elongated streamwise structures, or “bands” [7].…”

“…The bottom wall of the channel is illuminated with evanescent waves of wavelength λ = 514 nm and intensity‐based penetration depth z p ≈ 110 nm; and an x – y plane of the flow over a field of view 203 µm square is imaged from below by a magnification M = 40, numerical aperture NA = 0.55 objective (Leica 506059) through a band‐pass filter that transmits light of wavelengths λ = 530 ± 10 nm, that is, the green emissions from the tracer particles. In contrast to our previous work [7], the channel was continuously illuminated, and the images used to estimate particle velocities were recorded as sequence of 640 × 640 pixels images (exposure 0.2 ms) at 500 Hz by a complementary metal oxide semiconductor (CMOS) camera (Photron FASTCAM SA4) after the electric field is applied at t = 0. The thickness ( z ‐extent) of the region interrogated by the evanescent‐wave illumination, if scattering by the particles is negligible, is 3 z p ≈ 330 nm, so the particles imaged in these experiments are estimated to have centers at z ≤ 3 z p + a ≈ 570 nm.…”

“…Given that the scattering of the particle fluorescence is likely to be significant, especially in the latter stages of accumulation and beyond when near‐wall particle volume fractions exceed 0.1, however, it is unlikely that the brightness of the particle image will decay exponentially with z , although the particle (image) brightness should still decrease monotonically as z increases. No attempt was therefore made to estimate the z ‐position of the particle velocities, in contrast to our previous evanescent‐wave particle velocimetry studies [7].…”

“…This study uses the approach detailed in Ref. [7] but focuses instead on the velocities along the channel axis (vs. number) of the tracer particles. The remainder of this paper gives a brief description of the flow visualizations and the data processing used to obtain tracer particle velocities, followed by results and discussion.…”