Applied Mathematics Laboratory, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA.
Applied Mathematics Laboratory, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
Phys Rev Lett. 2014 Mar 28;112(12):128304. doi: 10.1103/PhysRevLett.112.128304. Epub 2014 Mar 26.
We study theoretically the collective dynamics of immotile particles bound to a 2D surface atop a 3D fluid layer. These particles are chemically active and produce a chemical concentration field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. For a 3D diffusion-dominated concentration field and Stokesian fluid we show that the surface dynamics of active particle density can be determined using nonlocal 2D surface operators. Remarkably, we also show that for both deep or shallow fluid layers this surface dynamics reduces to the 2D Keller-Segel model for the collective chemotactic aggregation of slime mold colonies. Mathematical analysis has established that the Keller-Segel model can yield finite-time, finite-mass concentration singularities. We show that such singular behavior occurs in our finite-depth system, and study the associated 3D flow structures.
我们从理论上研究了固定在 3D 流体层之上的 2D 表面上的非运动粒子的集体动力学。这些粒子是化学活性的，并产生化学浓度场，沿表面产生表面张力梯度。由此产生的 Marangoni 应力会产生携带粒子的流动，可能会使粒子浓缩。对于 3D 扩散主导的浓度场和 Stokesian 流体，我们表明可以使用非局部 2D 表面算子来确定活性粒子密度的表面动力学。值得注意的是，我们还表明，对于深或浅的流体层，这种表面动力学都可以简化为用于粘液霉菌菌落集体趋化聚集的 2D Keller-Segel 模型。数学分析已经证明，Keller-Segel 模型可以产生有限时间、有限质量的浓度奇点。我们表明，这种奇异行为发生在我们的有限深度系统中，并研究了相关的 3D 流动结构。
