### Study of the equilibrium free surface of a capillary liquid in a toroidal vessel

**Published:**24.03.2021

**Authors:** Zhaokai Y., Temnov A.N.

**Published in issue: **#3(111)/2021

**DOI: **10.18698/2308-6033-2021-3-2060

**Category:** Mechanics | **Chapter:** Mechanics of Liquid, Gas, and Plasma

The paper considers an axisymmetric problem of determining the forms of equilibrium of liquid in spacecraft toroidal tanks under conditions close to weightlessness. In the absence of significant mass gravitational forces, the behavior of liquid fuel in tanks begins to be determined by surface tension forces, which are intermolecular forces at the interface of two phases. Relying on the principle of stationary potential, we obtained the conditions of equilibrium of the closed system "liquid - gas - solid wall" under microgravity conditions. The study introduces a system of differential equations that determines the form of equilibrium of a liquid in toroidal tanks, the Young — Dupre equation, the condition for the contact of a free surface with a solid wall, and the condition for the conservation of the volume of the liquid. Furthermore, we quantified the influence of various parameters, such as the contact angle α_0, the Bond number B_0, the ratio of the radii of the circles δ=R_0⁄r_0 and the relative filling volume of liquids V_0, on the form of the equilibrium of the capillary liquid. The study of the forms of equilibrium of liquid fuel makes it possible to develop recommendations for the design of intake devices for fuel tanks in rocket and space technology. Findings of research show that the obtained equilibrium surface is also the unperturbed boundary of the region occupied by liquid fuel, which gives necessary information for further investigation of the spacecraft dynamics.

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