Nanoscale Functionalized Particles with Rotation-Controlled Capture in Shear Flow

Abstract

Important processes in nature and technology involve the adhesive capture of flowing particles or cells on the walls of a conduit. This paper introduces engineered spherical microparticles whose capture rates are limited by their near surface motions in flow. Specifically, these microparticles are sparsely functionalized with nanoscopic regions ("patches") of adhesive functionality, without which they would be nonadhesive. Not only is particle capture on the wall of a shear-chamber limited by surface chemistry as opposed to transport, but also the capture rates depend specifically on particle rotations that result from the vorticity of the shear flow field. These particle rotations continually expose new particle surface to the opposing chamber wall, sampling the particle surface for an adhesive region and controlling the capture rate. Control studies with the same patchy functionality on the chamber wall rather than the particles reveal a related signature of particle capture but substantially faster (still surface limited) particle capture rates. Thus, when the same functionality is placed on the wall rather than the particles, the capture is faster because it depends on the particle translation past a functionalized wall rather than on the particle rotations. The dependence of particle capture on functionalization of the particles versus the wall is consistent with the faster near-wall particle translation in shearing flow compared with the velocity of the rotating particle surface near the wall. These findings, in addition to providing a new class of nanoscopically patchy engineered particles, provide insight into the capture and detection of cells presenting sparse distinguishing surface features and the design of delivery packages for highly targeted pharmaceutical delivery.

Keywords: colloid deposition; flow; flow vorticity; hydrodynamic; microparticle capture; patchy particles; shear; surface heterogeneity.

Figure 1.

(A) Schematic of engineered particles containing nanoscopic adhesive features. The zoomed square is about 600 nm on each side and emphasizes the random placement and nanoscopic (10 nm approximate diameter) of the adhesive features, at a realistic loading of 1200/μm² corresponding to 0.04 mg/m² of PLL. The circle is size of zone of influence (defined below) at a Debye length of κ⁻¹ = 2 nm and has a diameter of ~90 nm. (B) Configuration for control experiment where adhesive features are placed on the wall and the particles are bare silica.

Figure 2.

(A) Typical microscopic images of microparticles with different target loadings of Rhodamine-tagged PLL. Left panes are light microscopy. Middle panels are fluorescence. Right panels are combined. Scale bars are 5 μm. (B) Summary of particle fluorescence for different loadings of Rhodamine-PLL.

Figure 3.

Zeta potentials of silica microparticles with different amounts of PLL added. The x-axis indicates the amount of PLL present per unit of available surface area, and the dashed vertical line indicates the saturation coverage of PLL on silica from previous measurements. Below the saturation coverage, the PLL is expected to adsorb to the particles. Above the saturation coverage, any additional PLL is expected to be free in solution.

Figure 4.

Capture efficiency of particles flowing at a wall shear rate of 22 s⁻¹. (A) Capture of functionalized particles is compared to capture on a functionalized wall for a Debye length of 2 nm. (B) Showing the impact of ionic strength for variations in Debye length from 1 to 4 nm. The error bars on one datum for each data set show representative errors, applicable to all data in that set, for precision in PLL loading and in run−run reproducibility of measured particle capture rates.

Figure 5.

Ratio of capture efficiencies for functionalized walls, normalized by that for functionalized particles with the same amount of functionalization, calculated directly from the data in Figure 4B. For each PLL concentration in Figure 4B, plotted here is the capture efficiency for bare particles on a PLL-functionalized wall divided by the efficiency for capture of PLL-functionalized particles on a bare wall.

Figure 6.

Influence of wall shear rate, 22 or 110 s⁻¹, on the capture of flowing functionalized particles or with the wall bearing the adhesive functionality. (A) Capture rates for suspensions containing 250 ppm particles. Dashed lines represent the transport-limited rates for the two flow rates. (B) Data represented as capture efficiencies. (C) Ratio of capture efficiencies, with the efficiency on the functionalized wall normalized by that on the functionalized particles.

Figure 7.

State space maps for the regimes of particle capture behavior when the particles or the wall are functionalized. The boundaries between “no adhesion” and surface-limited adhesion represent the locus of adhesion thresholds for PLL-functionalized particles or wall. The boundaries between surface-limited adhesion and diffusion-limited adhesion were read from the upper features of Figure 4B.

Figure 8.

(A) Definition of the zone of influence. (B) Close-up schematic of the gap between a silica particle and a flat wall, showing equivalent positions of surface patches on the particle or the wall.