A model for calculating the force profile and the moment profile of a floating body in two dimensions with an arbitrary cross-section is proposed. Three types of cross-sections with different contact angles and densities are calculated by using the model to determine the vertical and rotational equilibria and their stabilities. Results show that the model can be applied to convex floating bodies with finitely many sharp edges. The study is then extended to investigate the surface tension effects on the vertical and rotational stabilities by varying the following parameters: the radii of curvature of the solid surface at the contact lines and the size of floating body. In general, the smaller the radii of curvature the better the vertical and rotational stabilities. However, for the contact angle $\unicode[STIX]{x1D703}=0$ (or $\unicode[STIX]{x1D703}=\unicode[STIX]{x03C0}$) the radii of curvature have no effect on the vertical stability of the floating body. By varying the size of the floating body, it is found that the vertical and rotational stabilities of mesoscale floating bodies vary continuously between the stabilities of the macroscale and microscale floating bodies with other parameters remaining unchanged.
This paper theoretically studies the effect of eccentricity on the conditions of capillary emptying (determined by critical Bond number) in a horizontal annular tube in a downward gravity field. Experiments are conducted to compare with theoretical results. We find that non-horizontal eccentricity can lead to the occurrence of a re-entrant liquid-state transition (from liquid non-occlusion to liquid plug to liquid non-occlusion) with increasing Bond number, when the eccentricity (e) or inner-to-outer radius ratio (χ) is large enough, and the two liquid non-occlusion states correspond to different emptying mechanisms dominated by the gravity effect and the ‘wedge’ effect, respectively. Existence of the re-entrant transition is accompanied by occurrence of unconditional liquid non-occlusion at large enough or small enough contact angles regardless of Bond numbers. The critical Bond numbers at a contact angle γ for vertical upward eccentricity are equal to those at a contact angle 180° − γ for vertical downward eccentricity. In a parameter space (γ, e/(1 − χ)), the region with the re-entrant transition becomes larger with the eccentric angle varying from 0° (horizontal) to 90° (vertical). Optimization of geometrical parameters and inner and outer contact angles can lead to better effect of capillary emptying. This paper provides a very effective scheme for removing a liquid blockage from a capillary in optofluidics/microfluidics.
In recent years, circulating fluidized beds (CFBs) have been extensively employed in a variety of industrial applications related to coal combustion and gasification, solid waste incineration, catalytic cracking of oil, and so on. To accomplish successful and reliable operation of CFBs, a number of in- Detailed researches in this direction will considerably help in the optimum and economic designs of CFB boilers. To aid in this direction, we have measured the three-dimensional particle velocities in a square-section CFB cold model under certain operating conditions at ambient temperature and pressure. Particle turbulent intensities and bed cross-sectional averaged voidage along its height are also measured. A majority of the investigations have been conducted in circular cross-section CFBs, but industrial preference is for a square cross-section boiler, and hence we have adopted this configuration in our present work. Our measurements, while confirming the coreannulus flow structure for CFBs, also provide a more comprehensive microscopic detail of particle velocities in the two regions, in addition to providing a basis for particle aggregation. Experimental Apparatus and ResultsThe schematic of the CFB employed in the present work is shown in Figure 1. The riser section is 3 m long and has a square cross-section, 222 mm by 222 mm. Seventeen pressure taps (13) are installed along the metal bed wall starting from a height of 250 mm' above the air distributor plate (3) and up
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