The Hygrocyst–a Stability Phenomenon in Continuum Mechanics
The Hygrocyst–a Stability Phenomenon in Continuum Mechanics
复制标题
湿囊——连续介质力学中的一种稳定性现象
作者：
R. Balmer
考虑一个长密封容器，部分装满一种液体或完全装满两种不混溶的液体，并水平方向。如果容器绕水平轴旋转，则形成层流二次流模式，其特征是分离材料的大块规则区域。这种新的流动模式的开始似乎是正常流动的自然不稳定的结果，并且发现在所有几何形状的容器中都发生。据我所知，这里讨论的流动不稳定性和相关的层流二次流型是第一次被报道和研究，并没有出现在任何已发表的科学文献中。乍一看，这似乎令人惊讶，因为这一现象看起来很简单，但当我们从数学的角度来看待它时，考虑到它困难的边界条件和不寻常的身体力方向，我们就可以理解为什么任何人都不可能仅仅从数学的角度来预测它的存在。此外，用非弹性流体的实验来证明其不稳定性是相当困难的。
CONSIDER a long sealed container partially filled with a liquid or completely filled with two immiscible liquids and oriented horizontally. If the container is rotated about a horizontal axis, a laminar secondary flow pattern develops that is characterized by large regular regions of segregated material. The onset of this new flow pattern appears to be the result of a natural instability in the normal flow, and is found to occur in containers of all geometries. The flow instability and the associated laminar secondary flow pattern discussed here are, to my knowledge, being reported and studied for the first time and do not appear anywhere in the published scientific literature. This might seem surprising at first in view of the apparent simplicity of the phenomenon, but when it is viewed in terms of its mathematics, with its difficult boundary conditions and unusual body force orientation, it becomes understandable why it would be unlikely that anyone could predict its existence from mathematical considerations alone. Further, it is rather difficult to demonstrate the instability by experiment with inelastic fluids.