NANO LETTERS
Effects of Particle Size, Flow Velocity, and Cell Surface Microtopography on the Motion of Submicrometer Particles over Diatoms
2002 Vol. 2, No. 6 657-663
Michelle S. Hale* and James G. Mitchell School of Biological Sciences, Flinders UniVersity, GPO Box 2100, Adelaide SA 5001, Australia Received March 19, 2002; Revised Manuscript Received April 22, 2002
ABSTRACT In microfluidic systems, interactions between particles and surfaces dictate the mobility of particles and the effectiveness of the devices in sorting them. Here, we report that the rigid, silica, cell surface microtopographies of diatoms increased the deflection of submicrometer particles from the direction of flow and reduced uniaxial bead velocities. The extent to which particle behavior was affected depended on the particle size, the far-field flow velocity and the morphology of frustule microstructures.
Microfluidic systems are currently widely used in biology, biotechnology, and biomedicine for a variety of applications. Recently, microlithographic arrays have been incorporated into microfluidic systems, in an attempt to achieve efficient, well-controlled, and high-resolution separation techniques for analysis of macromolecules, such as DNA and proteins,1-3 and for sorting of cells.4 In these particulate systems, the interactions between particles and surfaces dictate the behavior of particles and the effectiveness of the devices. Despite recent advances in the design of microfluidic systems, little is known about the optimal designs of microlithographic arrays. Diatoms are single-celled protists that exist in an environment of continuous flow, where they are exposed to living and nonliving Brownian particles, ranging from nutrient molecules to bacteria.5,6 Previously, we examined how marine diatoms control particle distributions using their cell surface microtopographies, in order to better understand Brownian particle behavior.7,8 We have shown that the surface microtopographies of diatom frustules are able to localize Brownian particles on the ridged areas of their surfaces in stagnant water and in 135-2160 µm s-1 flow.7,8 As nonmotile phytoplankton, diatoms rely on diffusive and advective transport to supply Brownian particles (including nutrients and bacteria) to their cell surfaces. Therefore, the aim of these experiments was to investigate the behavior of particles flowing over diatom frustules, to understand how the components of fluid systems, such as the microtopography of surfaces, particle sizes, and velocity field, affect * Corresponding author. E-mail:
[email protected]. 10.1021/nl025557m CCC: $22.00 Published on Web 05/03/2002
© 2002 American Chemical Society
these transport processes. The results provide evidence that differences in frustule morphologies may be important in determining competition between diatom species and provide insight into the optimal design of microfluidic devices for sorting particles of varying sizes. To examine the effects of surface microtopographies on the advection of particles, live cells of Coscinodiscus sp. and Thalassiosira eccentrica were attached to glass coverslips and placed in small flow chambers. The chamber design was adapted from that described previously.7 Flow chambers were constructed from three metal slides, manufactured to fit on the stage of the microscope. Two of the slides had a 16 mm diameter hole cut into each of them, over which coverslips were placed and sealed to the slides by 2.5 mm thick O-rings. The third slide had a 24 mm diameter hole cut into it, to accommodate the objective lens, and was placed on top of the other two. Six small screws around the outside of the circumference of the holes were use to seal the chamber together. Live diatom cells were stuck on the underside of the coverslip with poly(lysine) (MW ) 21 000),9 and movements of beads over the frustules of diatoms and over a glass coverslip were recorded by video microscopy. Video microscopy allowed measurements of flow speeds, 20 µm above the surface and the confirmation of laminar flow in the region of the chamber being examined. Monodisperse latex beads (Sigma), with radii of 0.3 and 0.4 µm (as received from the manufacturer), were diluted in artificial seawater solutions (35‰, 20 °C, filtered through 0.24 µm) to volume fractions of 10-5. This ensured that the average separation distance between beads was approxi-
mately 16 µm, so that interactions between beads were negligible.10 NaCl, in solution, screened electrostatic interactions to approximately 4 nm, the Debye-Huckel screening length.11 We recorded the movement of beads over diatoms and glass coverslips, at flow rates of 0, 6, 13, and 25 µm s-1, measured 20 µm above the surface. As flow decreases fractionally from the surface of a sphere by 1 - (1 3/4r - 1/4r3), where r is the distance away from the surface (in units of sphere radii),12 only 37% of the total shear occurs across the first 20 µm distance from the surface of a cell with radius 50 µm. Thus, flow velocities of 6, 13, and 25 µm s-1 ((1 µm s-1), measured at 20 µm away from the surface, correspond to far-field velocities of 10, 25, and 40 µm s-1, respectively. These far-field flow velocities were more than an order of magnitude slower than those tested previously7 and enabled us to investigate bead behavior across a range of flow velocities, where transitions in the uniaxial bead velocities and the deflection of beads across frustules were observed. Chambers were viewed under Nomarski optics using a 100× oil immersion objective (numerical aperture ) 1.3), with further magnification provided by a 3.3× long distance coupling lenses to a Panasonic CCD camera (WV-BP550). Due to the depth of field of the objective, beads included in the analysis were no more than 1 µm from the surface, and only beads observed to be in focus were used. Experiments were replicated five times, each with a different diatom frustule, to account for minor shape variation that occurs among frustules. Fifty sequential frames of data were analyzed for each bead. Under flow, deviations of bead movement from the direction of flow were determined using frame-by-frame analysis of video footage of beads moving across frustule surfaces and over flat glass slides. To ensure that location and orientation data from adjacent frames were statistically independent, we plotted autocorrelograms of the trajectory angle and found there were no significant autocorrelations between frames. The sequential positions of each bead were used to determine the local velocity of the bead as it moved across the surface, calculated as total displacement per frame divided by time between frames (1/25 s). In addition, the velocity of the bead in the direction of flow was calculated and termed the “uniaxial bead velocity”. Data from the frame-by-frame analyses were also used to calculate the angle of deflection of beads from the direction of flow and the lateral deflection of beads. Lateral deflection (LD) was calculated as LD ) (x + 1)/(y + 1), where x was the displacement perpendicular to the direction of flow, and y was the displacement in the direction of flow. The equation for lateral deflection used previously,8 was altered to avoid problems encountered when y ) 0. Thus, a lateral deflection value of 1 indicates that displacement of the bead perpendicular to the direction of flow was the same as displacement in the direction of flow. Values less than 1 indicate that transport was greater in the direction of flow, and values greater than 1 indicate that transport perpendicular to the direction of flow dominated. To examine the relationship between the diffusion and advection of beads and their deflection from the direction 658
of flow, the Pe`clet number (Pe) was calculated for each combination of bead size, diatom surface, and flow velocity. Pe indicates the relative contributions of advective and diffusive transport through a fluid over a specified length scale: Pe ≡ Uro/D, where U is the characteristic velocity (flow velocity), ro is the radius of the diatom cell, and D is the diffusion coefficient of the beads. Diffusive transport dominates when Pe < 1 and, advection dominates when Pe > 1. Calculation of Pe allowed inclusion of data from previous flow experiments, which examined 0.25 µm radii beads moving over frustules of Coscinodiscus sp. at flow speeds more than an order of magnitude higher than those tested here, for comparison.8 Lateral deflection values from the previous experiments as well as those here were recalculated using the new equation (see above). For each experiment, Pe values were calculated in two ways. First, a “measured” value of Pe was calculated (Pem), using the uniaxial velocities of beads measured at the surface and the diffusion coefficients of beads determined experimentally.7 Second, a theoretical Pe value (Pet) was calculated using the far-field flow speed and the theoretical diffusion coefficient for each bead size, calculated using the StokesEinstein equation.13 Lateral deflection (LD) values were plotted against Pem to determine the relationship between lateral deflection and the relative contributions of advective and diffusive transport at the surface. LD values were also plotted against Pet to determine if far-field flow velocities could be used to predict the lateral deflection of beads across the surface, for use in designing microfluidic systems for particle sorting. To visualize the streamlines of flow over areolae, chargestabilized, spherical fluorescent polystyrene beads (Molecular Probes) with radii of 0.05 µm (2% solids) were introduced into 40 µm s-1 flow over T. eccentrica and Coscinodiscus sp. frustules and viewed using a combination of Nomarski and fluorescence video microscopy. Paths of individual beads flowing over frustule surfaces were analyzed frame-by-frame and traced onto acetate paper. This allowed us to characterize the movement of beads around individual areolae, which was difficult to do using the image analysis system, due to the high contrast required by the system to resolve the 0.05 µm radii beads against the background image of the frustule surface. Due to the regular nature of the areolation patterns of frustules, paths were transcribed onto scanning electron micrographs of frustule surfaces.7,8 All statistical analysis was conducted in SPSS 9.0. Data were transformed, where necessary, to ensure they were normally distributed, and analysis of variance tests (ANOVAs) were run to test for significant differences between the behavior of the two different bead sizes, moving over three different surfaces at three different flow velocities. Where transformation did not result in normalized data, or where variances were identified as being heterogeneous, nonparametric tests were conducted. The presence of surface microtopographies on diatom frustules had no significant effect on local bead velocity, compared to smooth glass coverslips (p > 0.09). Beads moving over all surfaces were slower than the far field flow Nano Lett., Vol. 2, No. 6, 2002
Figure 1. (A) Mean local bead velocities of 0.3 and 0.4 µm radii beads moving over diatom frustules in 10, 25, and 40 µm s-1 flow. Data for Coscinodiscus sp, T. eccentrica, and glass coverslips were pooled and presented together, as there were no significant differences in bead velocity over the three surfaces. Uniaxial bead velocities (i.e. velocity in the direction of flow) of 0.3 µm radii (B) and 0.4 µm radii (C) beads over glass coverslips, and frustules of Coscinodiscus sp. and T. eccentrica, in 10, 25, and 40 µm s-1 flow. Error bars for all figures are 95% CI (n ) 250).
Figure 2. Direction of movement of 0.3 and 0.4 µm radii beads, represented as deviations from the direction of flow (0°), over frustules of live Coscinodiscus sp. and T. eccentrica, compared to a flat glass coverslip, at flow velocities of 10 µm s-1 (A-D) and 40 µm s-1(E-H). Bead radius is indicated in the top right-hand corner of each figure. Circumference values are the angles of deviation, binned into 10° size classes. The scale in italics is the proportion of time that bead movement deviated from the direction of flow for each directional bin. Data from all replicates were pooled (n ) 250), and to allow visual comparison of beads flowing over all three surfaces, data were normalized to the most frequently observed direction of particle movement for each surface.
velocities (Figure 1A), with 0.4 µm radii beads undergoing a velocity reduction of up to 50%. Mean velocities of 0.4 µm radii beads were significantly slower than 0.3 µm radii beads, at all three flow velocities tested (p < 0.001). Although surface patterns did not affect local bead velocity, their presence did significantly affect the uniaxial bead velocities, due to beads being deflected across diatom surfaces. Beads with radii of 0.3 µm, flowing over T. eccentrica, had significantly slower uniaxial bead velocities than over the other two surfaces (p < 0.001) (Figure 1B). For example, beads in 40 µm s-1 flow moved over T. eccentrica at 3 µm s-1, compared to 22 µm s-1 over
Coscinodiscus sp. In contrast, uniaxial bead velocities for 0.3 µm radii beads were not affected by Coscinodiscus sp. frustules, compared to beads flowing over the glass coverslip controls. The uniaxial bead velocities of the larger beads (0.4 µm radii) did not differ significantly between the three surfaces, except for at the fastest far-field flow velocity tested, 40 µm s-1 (p < 0.001) (Figure 1C). At this flow velocity, mean uniaxial bead velocities were 1, 6, and 10 µm s-1 for beads flowing over T. eccentrica, Coscinodiscus sp., and glass coverslips, respectively. Mean uniaxial bead velocities of 0.4 µm radii beads were significantly slower than 0.3 µm radii beads flowing over Coscinodiscus sp. and
Nano Lett., Vol. 2, No. 6, 2002
659
Figure 3. Lateral deflection (LD) of 0.3 µm radii (A) and 0.4 µm radii (B) beads from the direction of flow, for beads flowing over glass coverslips and live frustules of Coscinodiscus sp. and T. eccentrica at three different flow velocities. The dashed line indicates where LD ) 1, and displacement of the bead perpendicular to the direction of flow was the same as displacement in the direction of flow. Values less than 1 indicate where transport was greater in the direction of flow, and values greater than 1 indicate where transport perpendicular to the direction of flow dominated. Error bars are 95% CI (n ) 250).
glass coverslips, for all flow velocities tested (p < 0.001). Uniaxial bead velocities for 0.4 µm radii beads were up to one-fifth slower than for 0.3 µm radii beads (Figures 1B,C). The surface microtopographies of diatoms affected bead behavior by deflecting beads from the direction of flow. The radar diagrams in Figure 2 show the angles that beads were deflected from the direction of bulk flow. Data for each diatom species, and each combination of bead size and flow speed, were plotted with data for beads flowing over glass coverslips, to allow a visual comparison of bead movement over surfaces with and without surface microstructures. The 0.3 µm radii beads flowing over T. eccentrica were deflected away from the direction of flow more than those flowing over Coscinodiscus sp. For 0.4 µm radii beads, deflection across all surfaces was high. Differences in deflection were quantified by comparing the mean lateral deflection and the mean proportion of time that beads were deflected more than 90° from the direction of bulk flow, for each bead size, surface, and flow velocity combination. For the 0.3 µm radii beads, the highest mean lateral deflection value was 1.4 for beads flowing over T. eccentrica 660
Figure 4. Lateral deflection of 0.3 and 0.4 µm radii beads as a function of the “measured” Pe´clet number, Pem, (A) and the theoretical Pe´clet number, Pet, (B). Note the logarithmic scale on the x-axis of each figure. Details of how Pem and Pet were calculated are given in the text. Error bars are 95% CI (n ) 5).
at the slowest flow velocity tested, 10 µm s-1. Mean lateral deflection was significantly higher over T. eccentrica than over Coscinodiscus sp. and glass coverslips (p < 0.001), and lateral deflection decreased significantly as flow velocity increased from 10 µm s-1 to 40 µm s-1, for all surfaces (p < 0.001) (Figure 3A). For the 0.4 µm radii beads, values of mean lateral deflection (LD) were greater than 1 for beads flowing over all three surfaces, indicating that displacement perpendicular to the direction of flow was always greater than displacement in the direction of flow (Figure 3B). Mean LD did not vary significantly between surfaces or with flow velocity for this bead size. Significant linear regressions were found between LD and both the “measured” Pe`clet number (Pem) and the theoretical Pe`clet number (Pet) (p < 0.002) (Figure 4). Increasing the relative contribution of advective transport compared with diffusive transport (i.e. increasing Pe) resulted in decreased lateral deflection of beads across the diatom surfaces (i.e. increased transport in the direction of flow). The trendlines for the two regression analyses were LD ) -7 × 10-5Pem + 1.4 R2 ) 0.84 Nano Lett., Vol. 2, No. 6, 2002
Figure 5. Proportion of frames where 0.3 µm radii (A) and 0.4 µm radii (B) beads were deflected more than 90° from the direction of flow for beads flowing over glass coverslips and live frustules of Coscinodiscus sp. and T. eccentrica in 10, 25, and 40 µm s-1 flow. Error bars are 95% CI (n ) 5).
and LD ) -4 × 10-5Pet + 1.3 R2 ) 0.63 As beads flowed across the surfaces of the two diatom frustules, many were deflected back against the direction of flow. For 0.3 µm radii beads, the mean proportion of frames where beads were observed travelling against the direction of flow (i.e. angle of deflection > 90°) was significantly different for the three surfaces, at each flow speed tested (p < 0.007) (Figure 5A). T. eccentrica frustules had the greatest effect on reversal of beads, with beads moving against the direction of flow in up to 35% of frames. Bead reversal did not vary significantly with flow speed over T. eccentrica (p ) 0.61). For 0.3 µm radii beads flowing over Coscinodiscus sp., the percentage of frames that beads were deflected more than 90° decreased significantly from 16% to 5%, as the flow velocity increased from 10 µm s-1 to 40 µm s-1 (p ) 0.027). For 0.4 µm radii beads, significant differences in bead reversal over different surfaces were seen only at the fastest flow velocity tested, 40 µm s-1 (p ) 0.02). Here, the mean proportions of frames where beads travelled against the direction of flow were 0.18, 0.30, 0.42 for glass coverslips, Coscinodiscus sp., and T. eccentrica respectively (Figure 5B). Nano Lett., Vol. 2, No. 6, 2002
These results are consistent with the paths observed for 0.05 µm radii beads in 40 µm s-1 flow, which were analyzed to characterize the flow around individual areolae of Coscinodiscus sp. and T. eccentrica frustules (Figure 6). Flow reversal was observed around T. eccentrica areolae but not around Coscinodiscus sp areolae. Frustule microstructures altered the behavior of particles at the surface by increasing the deflection of particles from the direction of flow and hence reducing the uniaxial bead velocity. The extent to which particle behavior was affected depended on the particle size, the far-field flow velocity, and the structure of frustule microtopographies. As discussed previously,7 at the low Reynolds number flows used in these experiments, hydrodynamic interactions between a spherical particle and a flat surface increase the viscous drag experienced by the particle as it approaches the surface.14-15 This results in a decrease in particle velocity from that of a particle in an unbounded fluid, as observed over all surfaces in this study (Figure 1A). Hydrodynamic interactions between particles and surfaces are also affected by the size of particles. As beads flow parallel over a solid surface, larger particles experience greater drag than smaller ones, due to the larger surface area in contact with the solid surface.16 This effect was evident in the differences in the velocities observed for the two bead sizes used in this study, where 0.4 µm radii beads were 2-7 µm s-1 slower than 0.3 µm radii beads. In the case of flow over diatom frustules, interactions between particles and surfaces are further complicated by the presence of areolae. Streamlines follow the rim of the pore as water moves over the surface. This effect is limited to the region at the rim of the pore, where shear stresses change rapidly. Shear stresses resume to unperturbed values at the downstream edge of the rim.17 For diatom frustules with regular arrays of areolae, shear flows remain perturbed over the entire surface and beads are directed around the edge of areolae. In our study, this resulted in beads being deflected from the direction of bulk flow and decreased the uniaxial speed of beads compared to those flowing over a flat surface (Figures 1-3). This effect was observed over both Coscinodiscus sp. and T. eccentrica frustules; however, the effect was strongest over T. eccentrica. The radius and depth of areolae are also important in determining the streamlines of flow. In laminar flow, for a shallow cylindrical pore at low Reynolds number, flow around and inside the pore depends on the ratio of the pore depth (b) and the pore radius (a).17 For T. eccentrica areolae, b/a is approximately 2, whereas areolae of Coscinodiscus sp. are covered with a fine, porous sieve plate, and b/a is close to zero.18 According to Pozrikis’17 model, as b/a increases from 0 to 2, progressively more complex features of the flow emerge, associated with multiple regions of reversed flow. Although we were not able to fully characterize flow around individual areolae of both diatom species, the movement of 0.05 µm radii beads over T. eccentrica suggests that flow reversal occurs over areolae of this species (Figure 6B). As T. eccentrica frustules are covered with regular arrays of areolae, it is likely that flow remains 661
Figure 6. Diagrammatic examples of the paths of three 0.05 µm radii beads, in 40 µm s-1 flow, over frustules of (A) Coscinodiscus sp. and (B) T. eccentrica. For each bead, sequential frames of video footage (t ) 0.02 s between frames) were viewed on a monitor and tracings were made of the frustule surface and the bead path. Due to the regular nature of the areolation patterns, we were able to transcribe bead paths onto scanning electron micrographs of acid-washed cells, with circles representing the position of the center of each bead ((0.06 µm) in sequential frames. The direction of bulk flow (measured 20 µm above the surface) is shown as the dashed line. The bead paths indicate characteristics of flow around areolae, and while flow reversal was observed over areolae of T. eccentrica, there was no evidence of flow reversal over Coscinodiscus sp. areolae.
perturbed over the entire frustule surface. In contrast, flow reversal was not observed over Coscinodiscus sp. (Figure 6A). Differences in the characteristics of flow over the two species may explain why 0.3 µm radii beads were deflected more than 90° from the direction of flow, in up to 7 times more frames over T. eccentrica than Coscinodiscus sp. (Figure 5). We have shown previously7,8 that the size and arrangement of frustule microstructures are important in determining bead behavior in a stagnant environment, and results of this study show that they are also important in conditions of flow. Although diatoms are nonmotile phytoplankton, they are able to sink or rise through the water column due to density differences between the cells and the surrounding fluid. Measured sinking velocities range from 0 to 346 µm s-1,19 therefore the flow velocities used in these experiments fall within the range of flows experienced by diatoms in the water column. The size range of particles examined here includes particulate matter that diatoms would regularly come into contact with in the water column, such as colloids and bacteria. Interactions between diatom surfaces and colloids may be important in determining the fate of colloids in the sea and the supply of nutrients to cell surface. For example, Nishioka and Takeda20 investigated changes in the concentration of iron of different size fractions during the growth of the diatom Chaetoceros sp. and found that the small colloidal particle fraction of Fe (
