Fig 1.
Schematic representations of typic DLVO interaction energy profiles.
The DLVO interaction energy profiles in (a), (b), (c), and (d) were denoted as type I, II, III, and IV respectively.
Fig 2.
Illustration of a spherical colloid interacting with a planar surface covered with a hemispheroidal asperity.
dS is a differential area element on the colloid surface, k is the unit vector directed towards the positive z axis, n is the outward unit normal to the colloid surface, dA is the projected area of dS on the collector surface, h is local distance between dS and dA, H is separation distance between the particle and collector surface. Modified from Shen et al. [30].
Table 1.
Zeta potentials of 1156 nm colloid, sand, and alumina.
Fig 3.
DLVO energy profiles for the 1156 nm colloid interacting with the planar surface carrying a hemisphere with different radii (a, 100 nm; b, 5 nm; c, 20 nm; d, 15 nm) at different ionic strengths (black, 0.2 M; pink, 0.01 M; red, 0.001 M; blue, 0.0001 M).
The calculated primary minimum depth (Upri), maximum energy barrier (Umax), and secondary minimum depth (Usec) are also shown.
Fig 4.
Calculated primary minimum depths Upri for the 1156 nm colloid interacting with the planar surface carrying a hemisphere with different radii at different ionic strengths (a, 0.0001 M; b, 0.001 M; c, 0.01 M; d, 0.2 M).
Note the change in scale of the y axes among the various graphs.
Fig 5.
Calculated primary minimum depth Upri for the negatively charged 1156 nm colloid interacting with the negatively charged planar surface carrying a (1) negatively or (2) positively charged hemispheroid as a function of equatorial radius for various hemispheroid heights at ionic strength of 0.0001 M.
(b) are replotted figures in a different scale of the y axis for (a) to highlight the shallow primary energy wells.
Fig 6.
Calculated adhesive torque for the 1156 nm colloid attached atop the hemispherical asperity in Fig 2 as a function of the asperity’s radius at different ionic strengths (□, 0.0001 M; Δ, 0.001 M; ○, 0.01 M; *, 0.2 M).
The maximum hydrodynamic torques for approach velocity of 1.2 × 10−5 m/s (solid line) was also shown for comparison.
Fig 7.
Effluent concentrations for the 1156 nm latex particles from the columns.
Phase 1, attachment of colloids at (a) 0.2 M or (b) 0.01 M; Phase 2, elution with colloid-free electrolyte solution; Phase 3, elution with DI water; Phase 4, flow interruption for 3 days; Phase 5, elution with DI water. (2) is re-plotted figure for (1) on a semi-log scale.
Fig 8.
Effluent concentrations for the 133 nm fullerene C60 nanoparticles from the columns.
Phase 1, attachment of nanoparticles at 0.01 M; Phase 2, elution with colloid-free electrolyte solution; Phase 3, elution with DI water; Phase 4, flow interruption for 1 days; Phase 5, elution with DI water; Phase 6, flow interruption for 2 days; Phase 7, elution with DI water; Phase 8, flow interruption for 3 days; Phase 9, elution with DI water; Phase 10, flow interruption for 4 days; Phase 11, elution with DI water.
Fig 9.
Calculated primary minimum depths (Upri) and secondary minimum depths (Usec) between a planar surface and nanoparticles of different radii (□, 10 nm; ◊, 20 nm; Δ, 30 nm; ○, 50 nm; *, 100 nm) at different ionic strengths.
The zeta potentials of the nanoparticles and the planar surface were assumed to be the same as those of 1156 nm colloid and sand in Table 1, respectively.
Fig 10.
Calculated primary minimum depths (Upri) and secondary minimum depths (Usec) between two identical nanoparticles of different radii (□, 10 nm; ◊, 20 nm; Δ, 30 nm; ○, 50 nm; *, 100 nm) at different ionic strengths.
The zeta potentials of the nanoparticles were assumed to be the same as those of 1156 nm colloid in Table 1.