Hydrodynamic force on a spherical particle oscillating in a micropolar fluid near a plan wall

Considering the importance of the microstructure fluid model of micropolar type, a semi analytical model has been developed to analyse the rectilinear oscillations of a spherical particle immersed in an incompressible micropolar fluid bounded by a rigid plane wall. The particle oscillates rectilinearly along a diameter perpendicular to the plane wall. The differential equations describing the micropolar fluid flow are constructed under the assumptions of low Reynolds numbers and when the amplitude of the oscillations is small compared to the characteristic length of the particle. The concept of slip and spin slip boundary conditions at the surface of the particle are introduced in the analysis of motion. The general solution of the fluid flow is obtained from the superposition of fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions at the plane wall are satisfied first by the Fourier-Bessel transforms and then at the surface of the particle by a boundary collocation scheme. The in phase and out-phase drag force coefficients acting on the particle are highlighted through graphs and tables for different values of geometrical and physical parameters. The findings of the present study demonstrate that the presence of the bounding wall and micropolarity and slip parameters have significant effects on the drag coefficients. This investigation is motivated by the need to better understand the fluid tapping mode of atomic force microscope devices, in particular when the fluid tapping mode is of microstructure nature (micropolar fluid).

Automated summary

A semi-analytical model has been developed to analyze the rectilinear oscillations of a spherical particle immersed in an incompressible micropolar fluid bounded by a rigid plane wall. The study shows that the presence of the bounding wall and micropolarity and slip parameters have significant effects on the drag coefficients.