On the translation of a cylinder in a long tube

We study the motion of a cylindrical particle translating slowly in a long tube as a function of the particle’s dimensions and placement both in the presence and the absence of external pressure gradients. The cylinder acts as a “leaky” piston, generating both fluid recirculation and through flow. When the particle is long, analytic expressions are obtained for both the velocity field and the force needed to sustain the particle’s motion as functions of the particle’s position and dimensions. When the particle is short, a superposition-based algorithm is outlined to facilitate economical numerical calculations. When the particle is placed off center in the tube, torque will act on the particle. When the particle is unguided, this torque will preclude coaxial motion and cause the particle to follow an oscillatory trajectory.