Rapid Electrostatic Capture of Rod-Shaped Particles on Planar Surfaces: Standing up to Shear

Abstract

We compare the electrostatically driven capture of flowing rod-shaped and spherical silica particles from dilute solutions onto a flow chamber wall that carries the opposite electrostatic charge from the particles. Particle accumulation and orientation are measured in time at a fixed region on the wall of a shear flow chamber. Rod-shaped particle aspect ratios are 2.5-3.2 and particle lengths are 1.3 and 2.67 μm for two samples, while sphere diameters were 0.72, 0.96, and 2.0 μm for three samples. At a moderate wall shear rate of 22 s^-1, the particle accumulation for both rods and spheres is well described by diffusion-limited kinetics, demonstrating the limiting effect of particle diffusion in the near-wall boundary layer for electrostatically driven capture in this particle shape and size range. The significance of this finding is demonstrated in a calculation that shows that for delivery applications, nearly the same (within 10%) particle volume or mass is delivered to a surface at the diffusion-limited rate by rods and spheres. Therefore, in the absence of other motivating factors, the expense of developing rod-shaped microscale delivery packages to enhance capture from flow in the diffusion-limited simple shear regime is unwarranted. It is also interesting that the captured orientations of the larger rods, 2.6 μm in average length, were highly varied and insensitive to flow: a substantial fraction of rods were trapped in standing and slightly leaning orientations, touching the surface by their ends. Additionally, for particles that were substantially tipped over, there was only modest orientation in the flow direction. Taken together, these findings suggest that on the time scale of near-surface particle rotations, adhesion events are fast, trapping particles in orientations that do not necessarily maximize their favored adhesive contact or reduce hydrodynamic drag.

Figure 1.

Shear flow drives particle translation and rotation away from the wall, dominating diffusion. Near the surface, shear is weaker so that both rotational and translational diffusion may be important or rate liming for particle-wall interactions, a prospect considered here. Also in this system, electrostatic attractions between cationic functionality on the wall and negative surface charge on the rods may drive rapid and strong particle capture once particles are within range of the wall. While the schematic of Figure 1 is oriented for ease of viewing, the flow chamber is oriented with the surface perpendicular to the floor and flow parallel to the floor.

Figure 2.

(A) Electron micrographs and (B) size and length distributions for Rod-1300 and Rod −2600 samples. The distributions are based on 400–600 particles of each type, far more than those in the images of (A).

Figure 3.

Accumulation of flowing particles on PLL coated channel wall. A) Example video micrographs for Rod −2600 from a bulk solution concentration of 250 ppm and a field of view of 260 μm × 177μm B) Example particle capture runs for Rod-1300 sample, from runs with different bulk solution concentrations. Field of view is 260 μm × 177μm. Two runs are included for the concentration of 125 ppm to demonstrate reproducibility. C) Example particle capture runs for Rod-2600 sample, from runs with different bulk solution concentrations. Field of view is 480 μm × 340 μm. D) Summary of particle capture rates as a function of concentration for different particle types. Accumulation rates for suspensions 2 μm sphere are not included in part D because they are off the scale. They are detailed in the supporting information.

Figure 4.

Comparison of measured rate constants to those calculated using the Leveque equation (3). Experimental error is estimated to be ~5% based on replicate data sets.

Figure 5.

Transport rate coefficient for rod shaped particles normalized by that for spheres, calculated via equation 3, for adhesion to a channel wall in laminar flow.

Figure 6.

Schematic showing rod orientations normal to the surface, and an example micrograph showing, in color, how rod orientations were assigned. Image recorded without flow.

Figure 7.

Summary of rod orientation with and without flow, as indicated. Orientation normal to the surface is summarized in pie charts. Angular rod orientation is indicated in the bar graphs.