Oscillations of coaxial hydrophobic spherical colloidal particles in a micropolar fluid

Abstract

The microstructured flow field of a micropolar model around a straight chain of multiple hydrophobic spherical particles oscillating rectilinearly along their line of centers is studied under the conditions of low Reynolds numbers. In general, the particles can exhibit variations in both radius and amplitude of oscillations, and they are allowed to be unevenly spaced. The amplitudes are required to be small in comparison with a characteristic length, which can be considered as the radius of the larger particle. The concepts of slip length and spin slip length are introduced to characterize the partial slip and spin slip boundary conditions at the hydrophobic surfaces of the colloidal particles. The differential equations that govern the system are solved through a semi-analytical approach in combination with boundary collocation techniques. The interaction effects between the particles are assessed through the in-phase and out-of-phase drag force coefficients acting on each particle for various values of geometrical and physical parameters. The numerical schemes are carried for the case of two oscillating spherical particles. The results of this investigation indicate that the drag coefficients are notably influenced by the presence of the second particle, micropolarity, frequency, and slip parameters. The current study reveals that the impact of the micropolarity parameter is not significant on the in-phase force coefficient for slippage parameter values less than one. However, it becomes significant for slippage parameter values exceeding one. Typically, when particles oscillate in opposing modes, in-phase coefficient values surpass 1, whereas they fall below 1 when oscillating in the same mode. The present study is driven by the necessity to gain a deeper comprehension of the fluid tapping mode employed in atomic force microscope devices, especially when this mode pertains to microstructures in the vicinity of a curved surface.