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Axial flow between sliding, non-concentric cylinders with applications to thread injection. (English) Zbl 1346.76030
Summary: An investigation is conducted into the nature of the pressure-driven axial flow between cylinders with the inner cylinder moving in the axial direction. Such a flow is often referred to in the literature as a ‘thread-annular’ flow and is relevant to the procedure of thread injection: a surgical technique that allows the injection of porous medical implants, consisting of synthetic biocompatible materials, into the body in a minimally invasive way. A perturbation solution for the fluid flow is derived under the assumption that the inner cylinder is displaced slightly from a concentric position within the outer cylinder. From the basic solution, expressions for the force on the thread and the friction factor for the flow are derived. Our results are compared with the concentric case, experimental results and also the exact solution to the problem. It is found that reported discrepancies between experimental measurements and theory based on a concentric flow model can be explained by our inclusion of thread eccentricity.

76D05 Navier-Stokes equations for incompressible viscous fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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