Suspension particle nonlinear dynamics

First, and most important, nonlinear dynamics provides an intellectual framework to pursue the consequences of nonlinear behavior of transport systems, which is simply not possible in an intellectual environment that is based upon a linear mentality, characterized by well-behaved, regular solutions of idealized problems. One example that illustrates the point is the phenomenon of hydrodynamic dispersion in creeping flows of nondilute suspensions. It is well known that Stokes flows are exactly reversible in the sense that the particle trajectories are precisely retraced when the direction of the mean flow is reversed. Nevertheless, the lack of reversibility that characterizes hydrodynamic dispersion in such suspensions has been recently measured experimentally [17] and simulated numerically [18], Although this was initially attributed to the influence of nonhydrodynamic interactions among the particles [17], the numerical simulation [18] specifically excludes such effects. A more general view is that the dispersion observed is a consequence of (1) deterministic chaos that causes infinitesimal uncertainties in particle position (due to arbitrarily weak disturbances of any kind—... 

Static and dynamic scattering techniques are spectroscopic characterisation methods in the sense of Sect. 2.2. These techniques evaluate the functional dependency of measurement signals on a spectral parameter, i.e. on time, space, or classically on wavelength or frequency. The major advantage of spectroscopic methods is the reduced sample preparation (no fractionation), but they involve the inversion problem. That is, the spectrum is a—most frequently incomplete and discrete— nonlinear projection of the size distribution. Beside the scattering techniques, there are further spectroscopic methods which are based on the extinction of radiation or on any other response of the particle system to an external field. This section describes optical, acoustic, and electroacoustic methods that have gained relevance for the characterisation of colloidal suspensions. 

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