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

细针状颗粒与流体相互作用的旋转和平移运动影响塑料污染物(如钓鱼线碎片)的去向，影响云中冰晶对太阳辐射的散射，以及纤维复合材料的回收。以前大多数关于这类粒子运动的理论都强调了流体中摩擦力或粘性力的作用。为了预测大于约十分之一毫米的针状颗粒在水或空气中的运动，该奖项将开发一种解释流体惯性(运动中的流体保持运动的趋势)和粘度的理论。对自由平移和旋转粒子周围的精确流体运动的计算机模拟将验证和补充这一理论。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在跟随另一个粒子运动时坠落和翻滚的直观方式。细长体理论将通过匹配内部区域完整的Navier-Stokes方程的二维解和外部区域粒子在线性流场中平移和旋转的线性化Navier-Stokes方程的解来推导。通过允许惯性在先导阶处影响单位长度上的颗粒流体力，可以得到一个适用于基于纤维长度的渐近大雷诺数的理论。室内有限差分模拟将验证细长体理论，并将对颗粒-流体相互作用的理解扩展到具有中等长宽比的长球形颗粒。采用与颗粒一起旋转的贴体球面坐标系，可以准确地求解颗粒表面附近的流动。这些方法将被用来探索：(1)由固定颗粒的流体相对平移引起的与方位有关的阻力、升力和扭矩；(2)在静止流体以及水平和垂直简单剪切流中自由沉降颗粒的平移和定向动力学；(3)均匀、各向同性湍流中沉淀的亚科尔莫戈罗夫尺度颗粒的取向；以及(4)球形颗粒稀释沉积悬浮的均匀状态的边缘稳定极限。这一裁决反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，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.