Particles dispersed in water settle more or less originating from the density difference between the particles and the water. It has been pointed out that during this sedimentation process, particles exhibit the identical motion (in direction and velocity) because they are in collective motion. This may be surprising, since sedimentation is an apparently simple problem. Moreover, even when dealing with very small particles of micron or submicron size, the magnitude of their cooperative motion is surprisingly large – up to millimeters.

However, it has been very difficult to capture how particles at the submicron level (to be analyzed with microscopic instruments) form macroscopic structures at the millimeter level (to be captured in the macroscopic view). A real-time analysis could be even more difficult. The fact that the suspensions, even at low concentrations, cannot be analyzed by optical methods due to the optical turbidity of the sample is another reason why the problem has remained unresolved in this field until now.

Long-range hydrodynamic interactions, which are the factors that form large structures, are also an important issue in particle sizing measurement. This is because the velocity is also dependent on the size of the measuring cell in the real world. Thus, the cooperative motion studied in the field of fluid mechanics is a very important insight in chemistry and engineering.

Since the motion of the settling particles is also irregular, the settling velocity is, of course, expressed in terms of its average value. The method for obtaining that average velocity was already established 50 years ago. However, deviation from the mean value is an unsolved problem in fluid physics that has been pointed out as a many-body problem. This is called velocity fluctuation.

Methods for analyzing particles in liquids include dynamic light scattering (DLS), one of the optical methods, and nanoparticle particle tracking (NTA), which tracks nanoparticles with a microscope and estimates their size based on their dynamics. However, unlike the Brownian motion of nanoparticles, submicron- and micron-sized particles are subject to velocity fluctuations caused by forces other than thermal fluctuations.

The hydrodynamic interaction is more pronounced with larger particles. This velocity fluctuation is in contrast to Brownian motion, which is faster with smaller particle size. Thus, when the size of the particle is estimated from the dynamics of particles, or more technically, from the relaxation time, it shows the opposite size dependence, which shows how important the study of velocity fluctuations is. This fact has long been overlooked in the study of DLS, and in this paper we have taken these into account in our dynamic ultrasound scattering (DSS) analysis.

This paper presents results for optically turbid submicron- or micron-sized suspensions of particles. The fact that the particles are in collective motion was determined by ultrasonic phase imaging methods. We then examined the volume fraction dependence of the sedimentation velocity fluctuations of the particles at steady state, and found that the velocity fluctuations were exactly the behavior predicted by hydrodynamics. However, the velocity fluctuations were dependent on the cell height, and at certain sample depths, the concentration gradient and the collective structure of the particles broke down the collective structure caused by the velocity fluctuations. At the end of the paper, we present a summary result that suggests a collective structure, and thus a new insight into fluid physics.

This paper was published in Physics of Fluids by AIP (American Institute of Physics Publishing).

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