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Theoretical solution of the collapse motion of a bubble near a rigid or elastic wall
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DOI：10.1016/j.ijmultiphaseflow.2026.105703.png)
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Abstract
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In this work, we focus on an extended Rayleigh equation for the description of the motion of a spherical bubble collapsing near a rigid or elastic wall. When neglecting the liquid viscosity and compressibility, we show that it is possible to construct a general analytical solution of this equation by using the Sundman transformation. The corresponding general solution is expressed via the Weierstrass elliptic function. As applications, we analyze the dependence of this solution's properties on the physical parameters. The results show that the collapse process of a bubble near a rigid or elastic wall is slower than that in a free field, especially for the bubble near a rigid wall. The surface tension has a significant effect on the motion of a micro-bubble, such as a bubble with a diameter of 10 & micro;m. In addition, we also discuss the similarity between the motion of a bubble near a wall and the motion of a multi-bubble system.
Keywords:
Rayleigh-plesset equation
Weierstrass elliptic function
Bubble near a wall
Multi-bubble system
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