Generalized traction integral equations and viscous erosion

Abstract eng:
Motivated by the problem of an eroding particle immersed in a viscous fluid, we present some new results on surface tractions in Stokes flows. In particular, we derive new integral equations for the surface tractions on a rigid particle immersed in a low Reynolds number fluid which may have a non-trivial background flow and/or a no-slip plane wall. The integral operator enjoys the conditioning advantages of second kind integral equations while avoiding the traditional obstacles of hypersingularity and rank deficiency. Moreover, the derivation is a simple argument using the Lorentz reciprocal theorem. This work builds on a 2011 paper of Keaveny and Shelley which considered the case of an infinite quiescent fluid. The formulation is used to explore viscous erosion of bodies in a selection of fundamental background flows, resulting in the emergence of distinct limiting body shapes involving sharp corners and ridges.

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