Slender body theory and finite difference computations to characterize particle-fluid interactions at moderate Reynolds numbers

细长针状粒子与流体流动相互作用的旋转和平移运动影响塑料污染物（如鱼线碎片）的命运，云中冰晶对太阳辐射的散射以及纤维复合材料的回收。大多数以前的理论，这些粒子的运动强调的作用，流体中的摩擦力或粘性力。为了预测在水或空气中大于十分之一毫米的针状颗粒的运动，该奖项将开发一种理论，该理论将解释流体惯性（运动中的流体保持运动的趋势）以及粘度。围绕自由平移和旋转粒子的精确流体运动的计算机模拟将验证和补充该理论。本科生和高中生的研究项目和推广将建立一个非球形粒子福尔斯和翻滚的方式的直觉，当它在另一个粒子的尾流草案。线性流场中颗粒平移和旋转的外区Stokes方程。通过允许惯性影响首阶单位长度的颗粒-流体力，将得到一个基于纤维长度的渐近大雷诺数有效的理论。内部有限差分模拟将验证细长体理论，并将粒子-流体相互作用的理解扩展到具有中等纵横比的长球形粒子。采用随颗粒旋转的贴体球坐标系，可以精确地求解颗粒表面附近的流动。这些方法将用于探讨：（1）流体与固定颗粒相对平移引起的与方向有关的阻力、升力和扭矩;（2）静止流体中以及水平和垂直简单剪切流中自由沉降颗粒的平移和取向动力学;（3）均匀各向同性湍流中亚Kolmogorov尺度沉降颗粒的取向;和（4）球形颗粒的稀释沉降悬浮液的均匀状态的边缘稳定性极限。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The rotational and translational motions of slender needle-like particles interacting with fluid flows influences the fate of plastic pollutants (such as fishing line fragments), the scattering of solar radiation by ice crystals in clouds, and the recycling of fiber composite materials. Most previous theories for the motion of such particles have emphasized the role of the frictional or viscous forces in the fluid. To predict the motion of needle-like particles larger than about one tenth of a millimeter in water or air, this award will develop a theory that accounts for fluid inertia (the tendency of a fluid in motion to remain in motion) as well as viscosity. Computer simulations of the exact fluid motion around a freely translating and rotating particle will validate and complement the theory. Research projects and outreach for undergraduate and high school students will build intuition for the way one non-spherical particle falls and tumbles when it drafts in the wake of another particle.A slender-body theory will be derived by matching two-dimensional solutions to the full Navier-Stokes equations in the inner region to solutions of the linearized Navier-Stokes equation in the outer region for particles translating and rotating in linear flow fields. A theory valid for asymptotically large Reynolds number based on the fiber length will be obtained by allowing inertia to influence the particle-fluid force per unit length at leading order. An in-house finite difference simulation will validate the slender-body theory and extend the understanding of particle-fluid interactions to prolate spheroidal particles with moderate aspect ratios. Adoption of a body-fitted spheroidal coordinate system that rotates with the particle will resolve the flow near the particle surface accurately. These methods will be used to explore: (1) The orientation-dependent drag, lift and torque induced by relative translation of the fluid with a fixed particle; (2) The translational and orientational dynamics of a freely settling particle in a quiescent fluid and in horizontal and vertical simple shear flows; (3) The orientation of sub-Kolmogorov scale particles settling in a homogeneous, isotropic turbulent flow; and (4) The marginal stability limits for the homogeneous state of a dilute sedimenting suspension of spheroidal particles.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.