In-Plane Rotation of Prolate Colloids Adhered to a Planar Substrate in the Presence of Flow

Abstract

Micron-size spherical polystyrene colloidal particles are mechanically stretched to a prolate geometry with desirable aspect ratios. The particles in an aqueous medium with specific ionic concentration are then introduced into a microchannel and allowed to settle on a glass substrate. In the presence of unidirectional flow, the loosely adhered particles in the secondary minimum of surface interaction potential are easily washed off, but the remnant in the strong primary minimum preferentially aligns with the flow direction and exercises in-plane rotation. A rigorous theoretical model is constructed to account for filtration efficiency in terms of hydrodynamic drag, intersurface forces, reorientation of prolate particles, and their dependence on flowrate and ionic concentration.

Figure 1

Intrinsic distribution of particle diameter with a main peak at 2.23 μm in a sample batch of 236 particles. The inset shows a scanning electron micrograph of typical polystyrene spheres.

Figure 2

Statistical distribution of the aspect ratio η of mechanically stretched polystyrene spheres in a sample batch of 271 particles.

Figure 3

Zeta potential ζ (mV) of polystyrene particles as a function of the ionic concentration of the electrolyte. Beyond ∼20 mM, ζ reaches a plateau and becomes independent of c. A smooth curve is drawn to connect the data to show the trend.

Figure 4

Temporal filtration behavior when particles are exposed to electrolytes with different ionic concentrations. In a 3 mM KCl(aq), the initial flow reaches a steady state at t ≈ 130 s and α reduces to a constant, prior to a stepwise increase in V at A, B, and C. Experiment is repeated at other concentrations. Optical micrographs show typical particle distribution at O (quiescent) and D (V = 37 mm/s, arrow shows flow direction).

Figure 5

(a–d) Typical distribution of particle orientation at c = 3 mM. The higher the flowrate, the higher the tendency to align with flow. Flowrates are raised in a stepwise manner.

Figure 6

Tracking rotation as flow increases. In each category, images belong to the same particle at different flow velocities. Category 1 (blue) particles rotate by an acute angle as the frontal end is anchored. Category 2 (purple) particles rotate by an obtuse angle as the rear end is anchored. Category 3 (green) particles have the front end probabilistically detach from the substrate at critical V, and their axes thus move through an obtuse angle.

Figure 7

Degree of particle alignment as a function of flowrate in the presence of the electrolyte with a range of potassium chloride concentration. Every data point is obtained when the flowrate is increased to the desired value in one step. Data are slightly displaced laterally for clarity.

Figure 8

Prolate particle is subject to a flow V = 0.37 mm/s at an angle of θ to its axis. (a) Customized tetrahedral mesh around the prolate particle (top) and finite element mesh for the solution domain (bottom). (b) Hydrodynamics drag or von Mises stress on the particle surface, σ_hy with θ = 36°. (c) Hydrodynamic drag on a particle with a range of θ. It takes roughly 1.5–2 h to run a single test.

Figure 9

Computed rotation moment arm x̅/l of net torque on a particle anchored at one end monotonically increases with the angle θ inclining to the flow direction. The computed rolling moment arm is found to be z̅ ≈ 0.7d almost independent of θ. The dashed line at x̅/l=0.5 and z̅/d=0.5 denotes the axes of symmetry.

Figure 10

Hydrodynamic torque on a particle with l = 3.49 ± 0.43 μm and d = 1.36 ± 0.13 μm in c = 3 mM KCl (aq) as a function of inclination angle to the flow direction. Flowrate follows a stepwise increase to a final V = 37 mm/s. Rotation follows ABCDE (see text).

Figure 11

(a) Strain A and (b) strain H deposited on the glass substrate are exposed to 3 mM KCl (aq) and subject to V = 0.15 mm/s. Particles are observed to (i) remain stationary, (ii) detach and be removed (circled by dashed lines), or (iii) be reorientated with Δθ. Particles with frontal anchors rotate through an acute angle and those with rear anchors through an obtuse angle. Arrows show flow direction.