In this study, we focused on the effect of the degree of floc growth on the moving velocity of the interface between sediment of flocculated montmorillonite and supernatant in the semi-dilute suspension, which is characterized by the start of an extremely slow movement of interface followed by an abrupt settling and ending in consolidation. Na-montmorillonite suspension coagulated under different ionic strengths, ranging from 0.5 M to 1.5 M of NaCl, was placed in a settling cylinder. The initial height of suspension was varied from 13 cm to 50 cm. The flocculated suspension was left to settle in the cylinder after the manual mixing of end-over-end. Changes in the height of the interface between the flocculated sediment and the transparent supernatant were measured as a function of elapsed time. It was confirmed that the maximum settling velocity increased with an increase in the height of cylinder within the range of our measurement. This tendency was found to be more significantly pronounced by the growth of flocs. This result indicates the presence of a feed-forward mechanism to enhance the upward motion of fluid or downward motion of flocculated sediment, or both. That means, sedimentation is accelerated by the growth of big flocs, and the growth of big flocs is accelerated by the sedimentation. These motions will eventually induce the generation of an upward plume or channel of water. The formed plume flutters slowly with rather a large scale. We term this phenomenon the "sedimentation turbulence."

No abstract

The propagation speed, shape and stability of the rim generated by a liquid-curtain breakup are studied. In the experiment, a liquid curtain surrounded by a slot die, edge guides and the surface of a roller breaks at the contact point between the edge guide and roller in a low-Weber-number range, and the rim propagates in the horizontal direction. Except for the initial time, the rim is almost straight and has a nearly constant propagation speed. For an Ohnesorge number much smaller than 1, unevenness occurs on the rim and the droplets separate from it. When the Ohnesorge number is of the order of unity, the rim becomes convex vertically downward, and the liquid lump flows down. The shape, propagation speed and surface stability of the rim are discussed by analysing the equation proposed by Entov & Yarin (J. Fluid Mech., vol. 140, 1984, pp. 91–111). It is shown that the volume flow rate condition at the slot die exit is important to explain the propagation of the rim. Additionally, in the initial stage of the curtain breakup, the Plateau–Rayleigh instability causes unevenness on the rim surface, and after the rim reaches the slot die exit, the Rayleigh–Taylor instability generates a liquid lump on the rim, which grows into droplets when the Ohnesorge number is much less than 1.

In this study, we investigate a low-Weber-number flow of a liquid curtain bridged between two vertical edge guides and the upper surface of a moving substrate. Surface waves are observed on the liquid curtain, which are generated due to a large pressure difference between the inner and outer region of the meniscus on the substrate, and propagate upstream. They are categorized as varicose waves that propagate upstream on the curtain and become stationary because of the downstream flow. The Kistler's equation, which governs the flow in thin liquid curtains, is solved under the downstream boundary conditions, and the numerical solutions are studied carefully. The solutions are categorized into three cases depending on the boundary conditions. The stability of the varicose waves is also discussed as wavelets were observed on these waves. The two types of modes staggered and peak-valley patterns are considered in the present study, and they depend on the Reynolds number, the Weber number, and the amplitude of the surface waves. The former is observed in our experiment, while the latter is predicted by our calculation. Both the types of modes can be derived using the equations with periodic coefficients that originated from the periodic base flow due to the varicose waves. The stability analysis of the waves shows that the appearance of the peak-valley pattern requires a significantly greater amplitude of the waves, and a significantly higher Weber number and Reynolds number compared to the condition in which the staggered pattern is observed.

Upstream-advancing waves are observed in open channel flows over a fixed sinusoidal bed with large amplitude, when the Froude number is less than the resonant value, at which stream velocity is equal to the celerity of the wave with wavelength equal to that of the bottom surface. Their wavelength is about 3-6 times as long as the bottom wavelength and the celerity is close to that obtained from potential flow theory. Therefore, the wavelength of upstream-advancing waves is determined by linear stability analyses assuming that they are induced by the Benjamin-Feir-type instability of steady flow. Here, two formulas for the wavelength with different scaling are introduced and compared with experiment. In addition, the mechanisms of upstream-advancing waves are investigated qualitatively using the forced Schr6dinger equation.