Dropping slender-body theory into the mud

Abstract

The equations describing classical viscous fluid flow are notoriously challenging to solve, even approximately, when the flow is host to one or many immersed bodies. When an immersed body is slender, the smallness of its aspect ratio can sometimes be used as a basis for a 'slender-body theory' describing its interaction with the surrounding environment. If the fluid is complex, however, such theories are generally invalid and efforts to understand the dynamics of immersed bodies are almost entirely numerical in nature. In a valiant effort, Hewitt & Balmforth (J. Fluid Mech., vol. 856, 2018, pp.870-897) have unearthed a theory to describe the motion of slender bodies in a viscoplastic fluid, 'fluids' such as mud or toothpaste which can be coaxed to flow, but only with a sufficiently large amount of forcing. Mathematical theories for some tremendously complicated physical systems may now be within reach.