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Low-Reynolds-number Flows

 Hydrodynamics of slender ribbons

 Low-Re ribbon

 Credit: Lyndon Koens and Eric Lauga

Ribbons are common shapes which arise in numerous situations, for example in biology and material sciences. They are characterised by three distinct length scales — length, width and thickness — allowing them to take a variety of different configurations. We developed an asymptotic mathematical theory, similar to the classical slender-body theory framework valid for filaments, to accurately capture the hydrodynamics of ribbons at low Reynolds number. The figure depicts the three significant length scales relevant to the asymptotic slender-ribbon theory expansion. The outer region, represented in blue, scales with the length of the ribbon and accounts for variation far from the point of interest. The middle region, represented in red, scales with the width and accounts for the orientation of the ribbon surface. The inner region, represented in yellow, scales with the thickness of the ribbon and accounts for the finite size of the body. Expanding the system in each of these regions and then matching creates the asymptotic theory to describe the hydrodynamics of slender ribbons at low Reynolds number [paper].