Force–moment line element method for Stokes flow around a slender body

We present a higher-order line element method for Stokes flow around a slender body by taking into account effects of both net force and couple moment densities along its center line. The numerical technique is based on a line integral equation, which in turn is derived by reducing from a boundary integral equation of Stokes flow. The line integral equation of velocity gradient is employed along with that of velocity to close the formulation. Numerical examples of rigid slender bodies are presented to demonstrate the capability and validity of the present method, including passive motion of a slender body suspended in a simple shear flow and active motion of a slender body driven by a body moment. In the first case, it is shown that the moment density due to shear rigidity mismatch between the fluid and solid can be finite. Meanwhile, the transverse net force density is rather induced by a small velocity lag due to the impeding moment density component. Effects of slip and no-slip interfacial conditions are examined, showing their important role in determining the slender-body hydrodynamics. The present force–moment line element method provides a capable tool for solving the problems of strong and weak interactions between a slender body and a viscous fluid at low Reynolds number.