Interdisciplinary Applied Mathematics

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A three-dimensional particle-tracking technique was developed by (Kihm

FIGURE 1.19. Mass flowrate versus pressure ratio for argon microflow. The solid line denotes    slip-flow    theory,    the    dash-dot    no-slip    theory,    and    the    crosses    the

measurements. The flow is accumulated in a chamber attached to the outlet as shown in Figure 1.18. (Courtesy of K. Breuer.)

et al., 2004) to investigate nanoparticle motion near a solid surface using the Ratiometric Tot al Internal Reflection Microscopy (R-TIRFM) technique. This allowed three-dimensional reconstruction of particle trajectories by combining two-dimensional lateral tracking techniques with R-TIRFM for tracking vertical particle motions. Using R-TIRFM, they were able to measure motions of fluorescence-coated polystyrene spheres of 200 ± 20 nm diameter (specific gravity 1.05). Figure 1.21 shows Brownian motion of a single particle suspended in water at 293 K. Figure 1.21 (upper) shows the time history of three-dimensional particle locations over 67 imaging frames, recorded for a duration of 2.23 seconds. The symbols in the upper plot show particle-surface locations closest to the bottom glass surface. Figure 1.21 (lower) shows lateral displacement of particles in the x-y plane and vertical displacements in the z-direction. The results indicate horizontal and vertical resolutions of approximately 200 nm and 50 nm, respectively.

Biomimetic concepts can play an important role in designing functionalized devices at microscales; see Chapter 13. Self-assembly is a field that originated in organic chemistry, but it has had a great impact on micro- and nanofabrication of complex structures thanks to the pioneering studies of Whitesides and his collaborators (Whitesides and Grzybowski, 2002). Self-

FIGURE 1.20. MicroPIV measurements. Shown is a time-averaged velocity vector field of Stokes’ flow through a 30 x 300 ym channel. (Courtesy of C.D. Meinhart.)

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