Motion of several slender rigid filaments in a Stokes flow

In this talk I would present a joint work with Richard H\"ofer and Christophe Prange regarding the dynamics of several slender rigid bodies moving in a flow driven by the three-dimensional steady Stokes system in presence of a smooth background flow. More precisely we consider the limit where the radii of these slender rigid bodies tend to zero with a common rate $\epsilon$, while their volumetric mass density is held fixed, so that the positions occupied by the bodies shrink into separated massless curves. While for each positive $\epsilon$, the bodies’ dynamics are given by the Newton equations and correspond to some coupled second order ODEs for the positions of the bodies, we prove that the limit equations are decoupled first order ODE whose coefficients only depend on the limit curves and on the background flow. These coefficients appear through appropriate renormalized Stokes' resistance tensors associated with each limit curve, and through renormalized Fax\’en-type force and torque associated with the limit curves and the background flow.

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