Direct imaging of settling, non-Brownian, hard sphere, particles allows measurement of particle occupancy statistics as a function of time and sampling volume dimension. Initially random relative particle number fluctuations, ͗N 2 2 ͗N͘ 2 ͗͘͞N͘ 1, become suppressed, anisotropic, and ͗N͘ dependent. Fitting to a simple Gaussian pair correlation model suggests a minute long ranged correlation leads to strong if not complete suppression of number fluctuations. Calflisch and Luke predict a divergence in velocity fluctuations with increasing sample volume size based on random (Poisson) statistics. Our results suggest this is not a valid assumption for settling particles.

A dilute suspension of uniform, non-Brownian spheres settles slowly in a viscous solvent. The initially well-mixed system showing Poisson or random occupancy statistics evolves to a system having reduced number fluctuations, but otherwise appearing random. The reduced number fluctuations are consistent with recent measurements of velocity fluctuations in settling suspensions. These experimental results test the assumptions leading to the theoretical predictions by Calflisch and Luke that the velocity fluctuations increase without limit with increasing sample dimension. The theoretical prediction assumes Poisson occupation statistics contrary to our observations.

In this paper, a numerical simulation is performed in order to reveal the evaporation heating transfer mechanism of the falling-film of water on the outer wall of horizontal tubes, and the influence of gas-water-solid contact angles on the film distribution on the tube is mainly addressed. The simulation is performed by solving the motion equation of the fluid on fixed three-dimensional (3D) grid systems, and the so-called volume of fluid (VOF) method is employed to handle the movement of interface between the liquid and the vapor phase. The numerical results are compared with that of a simplified model and also with the experimental recordings obtained in visualization experiments conducted with tubes made of different materials, and it is shown that the numerical results are in very good agreement with the experimental observation of the falling films, indicating that the numerical methods applied in the present study is correct and accurate. Based on the numerical results, effects of the contact angle, the flow rate, the tube diameter and the liquid feeder height on the falling film behavior are discussed. Generally, the film width increases along with the increase of flow rate or the liquid feeder height, while variation of the film thickness exhibits different features at different conditions, and the contact angle is one of the major factors governing the behavior of the falling films.

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