Motion of a permeable shell in a spherical container filled with non-Newtonian fluid

doi:10.1007/s10483-017-2287-8

摘要/Abstract

摘要： This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.

关键词: immiscible fluids, interface movement, porous medium, instability, Darcy law, drag force, stream function, permeable sphere, spherical container, micro-polar fluid, wall correction factor

Abstract: This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.

Key words: immiscible fluids, interface movement, porous medium, instability, micro-polar fluid, spherical container, stream function, permeable sphere, wall correction factor, drag force, Darcy law

中图分类号:

76S05

V. MISHRA, B. R. GUPTA. Motion of a permeable shell in a spherical container filled with non-Newtonian fluid[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(12): 1697-1708.

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