Bubbles in liquid-filled capillaries feature in many practical applications. In this paper, we describe the equilibrium shape of a bubble in a horizontal capillary of circular cross section, as computed numerically using energy minimization. The data is presented in terms of empirical scaling laws for bubble extension along and perpendicular to the tube axis, over a large range of the ratio of cylinder to bubble diameter and Bond numbers. We also consider the limiting case of a bubble underneath a flat plate, for which approximate analytical solutions are available. Furthermore, we deduce an equation for the mean curvature of the gas-liquid interface and the variation of contact areas, the latter being of relevance also for estimating the wall drag forces of flowing bubbles.

充满液体的毛细管中的气泡在许多实际应用中都很常见。在本文中，我们描述了圆形横截面的水平毛细管中气泡的平衡形状，这是使用能量最小化进行数值计算的。数据以气泡沿着和垂直于管轴延伸的经验比例定律的形式呈现，在圆柱体与气泡直径的比率和邦德数的大范围内。我们还考虑平板下方气泡的极限情况，对此可以使用近似解析解。此外，我们推导出气液界面的平均曲率和接触面积的变化的方程，后者也与估计流动气泡的壁阻力相关。