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The rate of translational diffusion of particles in dispersion through brownian motion, as expressed by the diffusion coefficient, DBr [m2 s-1], depends on the particle size:
| DBr = kBT / ( 6π η a) | (1) |
where the suffix Br refers to the brownian motion, kB [J K-1] is the Boltzmann constant, T [K] is the absolute temperature of the dispersion, η [N s m-2] is the (dynamic) viscosity of the dispersion fluid, and a [m] is the particle radius. Note that this expression applies only to particles not interacting hydrodynamically with other particles (for example, Finsy R 1994).
The size-dependency of the particle diffusion coefficient is used to determine the particle size distribution (PSD) of suspensions via the dynamic light scattering (DLS) (for example, Finsy R 1994). This method, also referred to as photon correlation spectroscopy (PCS) and quasi-elastic light scattering (QELS), yields the EHD as the particle size estimate.
In DLS, temporal auto-correlation of the irradiance of monochromatic light scattered by a large number of particles is measured at constant temperature (the rate of brownian diffusion is a function of particle size and temperatue of the dispersion). Briefly, this auto-correlation, G(τ), where τ is the time delay between the measurements of light scattered by the particles, decays exponentially with the increasing τ. For non-interacting particles undergoing brownian diffusion, one has:
| GBr = a + b exp(-DBr q2τ) | (2) |
where a and b are independent of τ, and q is the magnitude of the scattering vector (for example, Lomakin A et al 2005). A key condition for successful measurements of G requires that the area of a detector of the scattered light has a size comparable to the avearge size, ls of speckles resulting from the interference of light waves scattered by the particles. This size can be expressed as follows (for example, Goodman JW 1985):
| ls = λ R / lv | (3) |
where λ is the wavelength of light in the medium surrounding the particles, R is the distance between the scattering volume and the detector, and lv is the lateral extent of that volume in respect of the direction of observation of the scattered light.
The characteristics decay time for monodisperse particles, with the size of large molecules (molecular weight ~25,000) is on the order of 1 µs. It is on the order of 1 ms for micrometer-sized particles (for example, Dzakpasu R and Axelrod 2004a). The characteristics decay time is the delay time, τ, at which the autocorrelation function, G(τ) decays to 1/e of G(0).
DLS is essentially a tool to measure particle mobility (see Scattering vector and DLS). Hence, it has been used to study particle mobility caused by factors other than brownian motion, for example those caused by turbulence. For example, Goldburg WI et al 1989 used DLS to study turbulence in fluid seeded with small particles. Leung AB et al 2006 have recently measured both the particle size and velocity in flowing dispersions with DLS, following a theory developed by Chowdhury DP et al 1984. The particle size and flow velocity have also been simultaneously determined by Zakian C et al 2005 who used self-mixing in a laser diode of light scattered by flowing particles undergoing brownian motion.
The diffusion of single particles has been also observed via optical particle tracking, see Particle mobility and size by single particle tracking. Imaging-based particle tracking has also been developed to measure diffusion coefficients of many particles simultaneously. This permits to use the tracking technique to measure the PSD.
Recently, the DLS method has been enhanced to enable mapping of the particle mobility in an object.
| CITATION: Jonasz M. 2006. Dynamic light scattering (DLS): Introduction (www.tpdsci.com/Tpc/DLS.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 17-Jan-2006 Modified: 23-Aug-2006 Peer-reviewed: PENDING |
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