2020
DOI: 10.17512/jamcm.2020.3.05
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Slip flow of a sphere in non-concentric spherical hypothetical cell

Abstract: Slow axisymmetric flow of an incompressible viscous fluid caused by a slip sphere within a non-concentric spherical cell surface is investigated. The uniform velocity (Cunningham's model) and tangential velocity reaches minimum along a radial direction are imposed conditions at the cell surface (Kvashnin's model). The general solution of the problem is combined using superposition of the fundamental solution in the two spherical coordinate systems based on the centers of the slip sphere and spherical cell surf… Show more

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Cited by 4 publications
(2 citation statements)
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“…Despite the advantages of the numerical methods (e.g., geometrical flexibility, solvability in many kind differential equations, and boundary value problems), the analytical solutions provide qualitative results revealing or highlighting the geometrical and the physical characteristics of the flow. Indicatively, Datta and Deo [15] used the Kuwabara BCs for numerically solving the creeping flow around a sphere, while Madasu [16] studied numerically the flow of a sphere with slip boundary conditions considered in a spherical in-cell model. Furthermore, when a deformation of the RBCs is also taken into account, the corresponding flow problem is mostly numerically simulated [17][18][19][20].…”
Section: Introductionmentioning
confidence: 99%
“…Despite the advantages of the numerical methods (e.g., geometrical flexibility, solvability in many kind differential equations, and boundary value problems), the analytical solutions provide qualitative results revealing or highlighting the geometrical and the physical characteristics of the flow. Indicatively, Datta and Deo [15] used the Kuwabara BCs for numerically solving the creeping flow around a sphere, while Madasu [16] studied numerically the flow of a sphere with slip boundary conditions considered in a spherical in-cell model. Furthermore, when a deformation of the RBCs is also taken into account, the corresponding flow problem is mostly numerically simulated [17][18][19][20].…”
Section: Introductionmentioning
confidence: 99%
“…These are beyond the scope of the present research and thus are not discussed further. The analytical treatment of the flow problems is of great significance since it enables the analysis of the geometrical and physical characteristics of the flow with Kuwabara-type boundary conditions [25][26][27] and reveals features of the transport process under consideration, e.g., see for instance [28,29]. Specifically, Djedaidi and Nouri [29] provided theoretical evidence for the existence and uniqueness of flow interactions in heterogeneous porous media without using regularization techniques.…”
Section: Introductionmentioning
confidence: 99%