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

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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.