TY - JOUR

T1 - Axial pressure-difference between far-fields across a sphere in viscous flow bounded by a cylinder

AU - Navardi, Shahin

AU - Bhattacharya, Sukalyan

N1 - Funding Information:
This work has been supported by ACS Petroleum Research Foundation under Grant No. PRF#49053-DN19.

PY - 2010/10/14

Y1 - 2010/10/14

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79251592585&partnerID=8YFLogxK

U2 - 10.1063/1.3489350

DO - 10.1063/1.3489350

M3 - Article

AN - SCOPUS:79251592585

VL - 22

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 10

M1 - 103305

ER -