Particle tracking methods

A substantial recent theme has been comparison of the dependences of one-particle and two-particle displacement correlation functions Sxi(t)) ) and Sxi(t)8xj t)) (for i 7 j). Crocker, et al. used videomicroscopy to capture the positions of pairs of particles at an extended series of times(82). Cross-correlations 

Goodman, et al. studied 1 p,m fluorescent-labeled carboxylate-modified polystyrene spheres in solutions of circular-supercoiled and linearized (single cut at controlled location) DNAs, size 2.96, 5.4, and 10.3 ldlobasepairs(87). The depends on DNA molecular weight, concentration, and circularization. Goodman, 

et al used video tracking to measure the one-particle diffusion and two-particle cross-diffusion coefficients of naturally-occurring particles in the intracellular medium(88). The observed behaviors are more complex than in simple viscoelastic media for example, in these cells the relative displacement Ar of two particles follows (Ar (r))  

Particle tracking can also be used to monitor particle orientation. Cheng and Mason studied rotational motion of micron-size a-eicosane microdiscs in 900 kDa polyethylene oxide(92). Hill and Soane examined the rotation of collagen molecules in aqueous 4 MDa polyethylene oxide using the electro-optic Kerr effect(93). 

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Motion analysis and particle tracking methods enable users to follow the movement over time of tagged particles, such as fluorescently labeled cell surface molecules, microtubules, nucleic acids, lipids, and other objects with subpixel resolution.287 These methods allow scientists to measure jc and y coordinates, velocity, mean displacement, mean vector length, and more. 

For the motion of particles submitted to an electric field we have described in the last section a single particle tracking method that allows one to determine the zeta potential. Nevertheless, if we want to have some statistics on this measurement, the selection and data recording for one particle can take typically between one and two minutes, which makes a determination on one... 

FIGURE 3.7. Photograph of a typical diffusion flame for heptane burning in air with streamlines revealed by a particle-track method [165]. 

Eulerian grid box or Lagrangian particle tracking methods using turbulence models (not suitable for real time emergency response computation), above canopy. Input from obstacle or continuum scale data (for local sources). Upwind data for distant sources. 

Dullien (1992) and Ferrand (1992) have applied numerical particle tracking methods to compute dispersion coefficients for such networks. In the study by Ferrand (1992) the conductivity of each bond was calculated using an expression that included entrance and exit effects as fluid moves between larger sites and narrower bonds, as well as the resistance of the bond itself. The lattice dispersivity was shown to increase linearly as the geometric standard deviation of the bond-size distribution was increased. Although not widely used at present, this modeling approach offers much promise for future research on the interplay between pore shape and size distribution in determining the relationship between K and Pn. 

Cross boundary calculation by particle tracking method. 

Kang, T. G., Kwon, T. H. Colored particle tracking method for mixing analysis of chaotic micromixers, J. Micromech. Microeng. 14, (2004) 891-899. 

In order to obtain a correlation, the outflow of the effervescent spray was simulated by a numerical model based on the Navier-Stokes equations and the particle tracking method. The external gas flow was considered turbulent. In droplet phase modeling, Lagrangian approach was followed. Droplet primary and secondary breakup were considered in their model. Secondary breakup consisted of cascade atomization, droplet collision, and coalescence. The droplet mean diameter under different operating conditions and liquid properties were calculated for the spray SMD using the curve fitting technique [43] ... 

Future developments will improve singlecamera techniques for 3D imaging. Since particle tracking methods do not suffer from depth-of-correlation errors nor spatial averaging over interrogation windows, they will be applied more often in the future [3]. 

Particle size is an important consideration in any particle tracking method. Particles should be small compared to the dimensions of the microfluidic channels, and should be much smaller in size (less than 1% of the hydraulic diame-... 

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