在部分填充容器中约束刚性旋转液体的具有表面张力的气-液界面形状
On the shape of air-liquid interfaces with surface tension that bound rigidly-rotating liquids in partially filled containers
摘要：
流体在刚体绕轴旋转并部分充满容器时的界面形状通常是第一堂研究生流体课的家庭作业的主题。在该问题中，表面张力被忽略，界面形状为抛物线，接触角边界条件一般不满足。当考虑表面张力时，形状表现出更丰富的依赖性作为旋转速度的函数。本文分析了零重力下刚体转动条件下旋转正圆柱形容器中的稳态界面形状。我们特别注意临界附近的形状，其中界面或其一部分在某些特定的旋转速度下变得笔直并平行于旋转轴。我们研究几何形状的容器是轴向无限的，并得出其解决方案的性质。然后，我们详细研究了两种特殊情况下，在一个圆柱形容器中的气泡：一个弯月面跨越的截面;和一个弯月面形成的气泡。在每种情况下，我们都将各自轴长的精确解推导为适当旋转参数的无穷级数;并且当形状接近其临界配置时，我们发现了各自的渐进行为。最后，我们应用渐近近似的方法，在整个转速范围内产生的轴向长度的解析表达式。在这个应用中，解析解是用来检查错误的假设，接口是一个正确的圆柱，这个假设是关键的旋转气泡法用于测量表面张力。
英文摘要：
The interface shape of a fluid in rigid body rotation about its axis and partially filling the container is often the subject of a homework problem in the first graduate fluids class. In that problem, surface tension is neglected, the interface shape is parabolic and the contact angle boundary condition is not satisfied in general. When surface tension is accounted for, the shapes exhibit much richer dependencies as a function of rotation velocity. We analyze steady interface shapes in rotating right-circular cylindrical containers under rigid body rotation in zero gravity. We pay especial attention to shapes near criticality, in which the interface, or part thereof, becomes straight and parallel to the axis of rotation at certain specific rotational speeds. We examine geometries where the container is axially infinite and derive properties of their solutions. We then examine in detail two special cases of menisci in a cylindrical container: a meniscus spanning the cross section; and a meniscus forming a bubble. In each case we develop exact solutions for the respective axial lengths as infinite series in powers of appropriate rotation parameters; and we find the respective asymptotic behaviors as the shapes approach their critical configuration. Finally we apply the method of asymptotic approximants to yield analytical expressions for the axial lengths of menisci over the whole range of rotation speeds. In this application, the analytical solution is employed to examine errors introduced by the assumption that the interface is a right circular cylinder; this assumption is key to the spinning bubble method used to measure surface tension.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
