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 surface. Numerical results for the correction factor on the inner sphere are obtained with good convergence for various values of the relative distance between the centers of the sphere and spherical cell, the slip coefficient, and the volume fraction. The obtained results are in good agreement with the published results. The effect of concentration is more in the Cunningham's model compared to the Kvashnin's model. The wall correction factor on the no-slip sphere is more compared to that of a slip sphere. The correction factor on the slip sphere is more than that of a spherical gas bubble.

Non-Convex Particle-in-Cell Model for the Mathematical Study of the Microscopic Blood Flow

“…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].…”

On the Analytical Solution of the Kuwabara-Type Particle-in-Cell Model for the Non-Axisymmetric Spheroidal Stokes Flow via the Papkovich–Neuber Representation

“…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.…”