Computation of Stokes flow due to the motion or presence of a particle in a tube

The computation of Stokes flow due to the motion or presence of a rigid particle in a fluid-filled tube with arbitrary geometry is discussed with emphasis on the induced upstream to downstream pressure change. It is proposed that expressing the pressure change as an integral over the particle surface involving ( a) the a priori unknown traction, and ( b) the velocity of the pure-fluid pressure-driven flow, simplifies the numerical implementation and ameliorates the effect of domain truncation. Numerical computations are performed based on the integral formulation in conjunction with a boundary-element method for a particle translating and rotating inside a cylindrical tube with a circular cross-section. The numerical results are consistent with previous asymptotic solutions for small particles, and complement available numerical solutions for particular types of motion.