肥皂膜中的流场：表面粘度与膜厚度的关系
Flow fields in soap films: relating surface viscosity and film thickness
摘要：
我们遵循不同的$h/d$，其中$h$是膜的厚度和$d$颗粒的直径的肥皂膜中的胶体颗粒的扩散运动。这些膜的流体动力学通过观察作为分离$R$的函数的粒子对的相关运动来确定。Trapeznikov近似[A. A. Trapeznikov，\emph{PICSA}（1957）]用于将肥皂膜建模为与大量空气相接触的有效界面，其表现为2D流体。从相关粒子运动确定的流场表现出良好的协议与预期的二维流体理论为我们所有的电影，其中$0.6 \leq h/d \leq 14.3$，与表面粘度匹配，预测Trapeznikov。然而，对于具有$h/d > 7 \pm 3$的较厚的膜，单个粒子运动比预期的快。此外，虽然流场仍然匹配那些预期的2D流体，这些流场的参数变化显着厚膜。我们的研究结果表明，从2D到3D流体的行为发生在这个值的$h/d$。
英文摘要：
We follow the diffusive motion of colloidal particles in soap films with varying $h/d$, where $h$ is the thickness of the film and $d$ the diameter of the particles. The hydrodynamics of these films are determined by looking at the correlated motion of pairs of particles as a function of separation $R$. The Trapeznikov approximation [A. A. Trapeznikov, \emph{PICSA} (1957)] is used to model soap films as an effective interface in contact with bulk air phases, that behaves as a 2D fluid. The flow fields determined from correlated particle motions show excellent agreement with what is expected for the theory of 2D fluids for all our films where $0.6 \leq h/d \leq 14.3$, with the surface viscosity matching that predicted by Trapeznikov. However, for thicker films with $h/d > 7 \pm 3$, single particle motion is faster than expected. Additionally, while the flow fields still match those expected for 2D fluids, the parameters of these flow fields change markedly for thick films. Our results indicate a transition from 2D to 3D fluid-like behavior occurs at this value of $h/d$.
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