Standard predictions induced by the balance of surface tension and pressure dictate that static soap bubbles must be spherical. However, definite non-spherical shapes appear in large bubbles, where noticeable oblate or prolate deformations occur. Gravity is the principal cause of such deformations, and multiple approaches for including its influence appear in recent literature. This paper derives a general surface-theoretic model by applying asymptotic and variational methods to a fully three-dimensional set-up where the soap bubble is a finite-thickness film. The procedure illuminates implicit assumptions, clarifying the discrepancies seen in previous models. Then the model is studied in four physical situations. In three of these situations, results show that there is a maximum stable span and volume of the soap bubbles, implying that their behaviour is qualitatively more similar to liquid drops than standard soap bubbles. Also, the model presented is directly analogous to the two-dimensional version of a hanging chain, and the derived predictions give practical insights into the construction of heavy containment vessels.

由表面张力和压力平衡引起的标准预测表明，静态肥皂泡必须为球形。但是，在较大的气泡中会出现一定的非球形形状，在该处会出现明显的扁圆形或长形变形。重力是造成这种变形的主要原因，在最近的文献中出现了多种包括其影响的方法。本文通过将渐近和变分方法应用于肥皂泡为有限厚度薄膜的全三维结构，得出了一般的表面理论模型。该过程阐明了隐含的假设，从而澄清了先前模型中出现的差异。然后在四种物理情况下研究该模型。在这三种情况下，结果表明，肥皂泡的最大跨度和体积最大，这意味着它们的行为在质量上与液滴相比，更像是标准的肥皂泡。此外，提出的模型直接类似于吊链的二维版本，并且得出的预测为重载安全壳的建造提供了实用的见识。