Applied Mathematics and Mechanics

, Volume 40, Issue 1, pp 127–138 | Cite as

A new physical model on the capillary phenomenon of granular particles

  • Nan Zhang
  • Bin Cheng
  • Hexi BaoyinEmail author


Similar to the capillary phenomenon of liquid, granular particles can move up to a certain height along a vertically vibrating tube. The certain height, which is called the equilibrium height, is related to some parameters, e.g., the inner diameter of the tube, the amplitude, and the vibration frequency. In this paper, a theoretical model is proposed to explain the physical origin of the capillary phenomenon and the effects of the inner diameter of the tube, the amplitude, and the vibration frequency on the equilibrium height. In this model, the volumes of the inflowing and outflowing particles in a vibration period are calculated, which can significantly broaden our understanding in the flow of particles in the bottom of the tube. In order to prove the assumption of this physical model that the particles in the bottom of the tube move in the form of sine, several experiments are conducted. The granular climbing heights at different granular positions and different time stages are measured. The results show that granules move in the form of sine, which almost coincides with the motion of the tube. Moreover, motivated by the sampling on the asteroid regolith based on this mechanism, the sampling efficiencies for various vibration amplitudes and frequencies are discussed based on the new proposed model. It is found that there is an optimum frequency at which sampling is the most effective.

Key words

granular matter vertical vibration nonlinear dynamics theoretical analysis 

Chinese Library Classification


2010 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringTsinghua UniversityBeijingChina

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