Theoretical Derivation and Experimental Study of Liquid Equilibrium Shapes under Different Rotation Modes

Research shows that the surface shape of rotary liquid depends on the rotation mode. Mode A is that when the container wall rotates the liquid, the rotating liquid surface is paraboloid. Mode B is that when the rotor in the center of the container rotates the liquid, the rotating liquid surface is vortex. Based on the paraboloid formed by the mode A, the identity between the liquid level parameter and the wall slope K (K ≠ 0) is derived. When K → ∞, with the increase of the container angular spin rate, the liquid level parameter changes are infinite, the liquid level change and volume relationship are fixed. When K > 0, the container is a cylinder with a large upper part and a small lower part and the liquid level parameter changes are limited, and the limit ratio between the liquid level parameters is + 1. In addition, through the vortex experiment by the mode B, it is concluded that the vortex curve can be regarded as composed of three parabolas: the center triggering part, the rising part, and the edge attenuation part. Different from the mode A, the liquid level change and volume relationship caused by the vortex formed by the mode B are both variables. According to the experimental results, the influences of container inner diameter, initial liquid level, rotor size, and rotor speed on the vortex characteristics are discussed in detail. At the same time, based on the experiment, the liquid level change and volume relationship caused by the formation of the vortex are deduced under the ideal condition when a stable liquid surface is formed by the vortex.