Axial pressure-difference between far-fields across a sphere in viscous flow bounded by a cylinder

Shahin Navardi, Sukalyan Bhattacharya

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

The presence of a particle with specified velocity inside a cylindrical channel affects the pressure-field along the length of the conduit. In this article, we quantify this effect by using a new general method, which describes hydrodynamic interactions between a cylindrical confinement and a spherical particle under creeping flow assumption. The generality of the scheme enables us to consider arbitrary values for system-defining parameters like cylinder-to-sphere ratio or separation between their centers. As a result, we can obtain accurate results for the parameter values hitherto unexplored by previous studies. Our simulations include three cases. First, we consider a fixed spherical obstacle in a pressure-driven flow through the cylinder and find the additional pressure drop due to the blockage. Then, we compute the pressure created by the pistonlike effect of a translating sphere inside a cylinder-bound quiescent fluid. Finally, we analyze the far-field pressure variation due to rotation of an asymmetrically situated sphere in confined quiescent fluid. For limiting cases, our calculations agree with existing results within 0.5% relative error. Moreover, the efficiency of the scheme is exploited in a dynamic simulation where flow dynamics due to a sedimenting sphere under gravity inside a cylinder with different inclination is explored. We determine the particle trajectory as well as the time-dependent far-field pressure-difference created due to the sedimentation process. The results agree well with approximate analytical expressions describing the underlying physics.

Original languageEnglish
Article number103305
JournalPhysics of Fluids
Volume22
Issue number10
DOIs
StatePublished - Oct 14 2010

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