Fluid Mechanics and Waves Seminar - Fall 2021

For questions about the seminar schedule, please contact Anand Oza.

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September 20

Laurel Ohm, Department of Mathematics, Princeton University

Location: CULM 611

Mathematical Foundations of Slender Body Theory

Slender body theory (SBT) facilitates computational simulations of thin filaments in a 3D viscous fluid by approximating the hydrodynamic effect of each fiber as the flow due to a line force density along a 1D curve. Despite the popularity of SBT in computational models, there had been no rigorous analysis of the error in using SBT to approximate the interaction of a thin fiber with fluid. In this talk, we develop a PDE framework for analyzing the error introduced by this approximation. In particular, given a 1D force along the fiber centerline, we define a notion of `true' solution to the full 3D slender body problem and obtain an error estimate for SBT in terms of the fiber radius. This places slender body theory on firm theoretical footing. In addition, we perform a complete spectral analysis of the slender body PDE in a simple geometric setting, which sheds light on the use of SBT in approximating the `slender body inverse problem,' where we instead specify the fiber velocity and solve for the 1D force density. Finally, we make comparisons to slender body models based on the method of regularized Stokeslets and the Rotne-Prager-Yamakawa tensor.

October 4

Nick Moore, Mathematics Department, US Naval Academy

Location: Webex

Karst Pinnacles and Rogue Waves

I will discuss two problems involving fluids in geophysical settings. The first is the formation of sharp karst pinnacles found in stone forests around the globe. Recent experiments demonstrate how the interaction between dissolution and gravitationally-induced natural convective flows can create ultra-sharp features that resemble these karst structures. Boundary-layer analysis reduces shape evolution to a single integro-PDE on the surface. While previous numerical evidence suggested the formation of geometric shocks, here we find a class of exact equilibrium solutions with large, but finite, curvature. We show the laboratory-generated profiles converge to this solution, which may offer clues about karst pinnacles. Second, I will discuss both laboratory experiments and theory to describe randomized surface waves propagating over variable bathymetry. The experiments show that an abrupt depth change can qualitatively alter wave statistics, transforming an initially Gaussian wave field into a highly skewed one. A theoretical framework, based on dynamical and statistical analysis of the truncated KdV equations, accurately captures key features of the experiments, including the skewed wave distributions that emerge downstream and the associated excitation of higher frequencies in the spectrum.

October 18

Shima Parsa, School of Physics and Astronomy, Rochester Institute of Technology

Location: Webex

Polymer Flow in Porous Media: Role of the Network in Unexpected Bulk Transport

Polymer flooding is an economically viable method in conventional enhanced oil recovery. Although it is primarily developed to increase viscosity and suppress viscous fingering at the oil-water interface, enhanced recovery is observed even for large viscosity mismatches. We investigate the physics of this anomalous recovery experimentally. Using confocal microscopy and pore level measurements, we closely examine the flow dynamics at the interfaces of oil and water and determine the changes in viscous forces responsible for the mobilization of oil in the network of pores. A counterintuitive mechanism results in oil mobilization and enhanced recovery, only measurable by accessing the flow dynamics at the microscale and of single pores. We propose a scaling for pore-level flow velocity to connect the pore-level quantities with the bulk and large-scale quantities.

November 1

Harishankar Manikantan, Department of Chemical Engineering, UC Davis

Location: Webex

Tunable Collective Dynamics of Inclusions in Viscous Membranes

The typical cell membrane is a crowded assembly of molecular motors and biomolecules embedded in a 2D fluid mosaic. Active molecular motors perform complex cellular tasks by binding, inserting, polymerizing, and changing conformations, inducing disturbance flows in the membrane and the surrounding fluid. These long-ranged hydrodynamic fields perturb neighboring inclusions, potentially leading to coordinated motion. I will build on classic theories of Newtonian fluid dynamics of viscous membranes to illustrate unique oscillations and aggregation dynamics in pairs of active membrane inclusions. The phase behavior of the pair problem reveals the underlying mechanisms and suggests strategies to tune large-scale aggregation. I will also show numerical simulations of large numbers of interacting inclusions whose collective dynamics can be tuned based on these basic insights. If time permits, I will then describe the first steps in the analysis of inclusions in membranes with a nontrivial rheology. Real membranes are often strongly non-Newtonian. I will illustrate a formulation based on the Lorentz reciprocal theorem to asymptotically capture effects of non-constant surface viscosity of phospholipids that comprise most biological membranes. I will highlight the qualitative differences that ensue, and potential implications in crowded membranes.

November 15

Brennan Sprinkle, Courant Institute of Mathematical Sciences

Location: CULM 611

Towards a Continuum Method for Fluctuating Fiber Suspensions

Microscopic dynamics in the cellular cytoskeleton must be carefully understood to predict structural and hydrodynamic behavior at the scale of the whole cell. The stochastic nature of sub-cellular processes coupled with the ever-changing topology of cytoskeletal networks make the microscopic dynamics of a cell difficult or impossible to interrogate through lab measurements or existing simulation techniques. In this talk I’ll discuss efficient methods to numerically simulate the types of flexible, fluctuating, inextensible microfilament gels that make up the cytoskeleton. I’ll introduce a method in which fibers are represented as curves on the unit sphere, so that strict inextensibility is maintained as they evolve; and go on to describe how the fluctuating hydrodynamics of a fiber suspension can be captured with a carefully designed temporal integration scheme. I'll demonstrate the unprecedented efficiency in this approach, but I'll also show why it's still not enough to interrogate cellular-scale dynamics. Motivated by this shortcoming, I'll end by discussing ongoing work to dramatically reduce the degrees of freedom in the methods that I've described.

Updated October 23, 2021