Flow of a micropolar drop in an impermeable micropolar circular pipe

In light of the blood cells motion inside the vein or artery, there is no knowledge available about the importance of the flow of a non-deformable micropolar drop inside a circular cylindrical pipe filled with a micropolar fluid. This paper provides a two-fluid phase motion problem of an axially symmetrical quasisteady movement of a micro-structure fluid drop embedded in another micro-structure fluid of micropolar kind on the axis of an impermeable cylindrical pipe that is discussed under the low Reynolds number conditions. The interfacial tension between the immiscible fluid phases at the drop’s interface is assumed to be very large to ensure that the droplet remains spherical in shape. Also, the microrotation and couple stress relations at the droplet’s interface are used. The general solutions for the differential equations are fulfilled by the stream functions of the micropolar fluids, which are constructed by combining fundamental solutions in cylindrical and spherical coordinates, and then the conditions on the boundaries are fulfilled at the inner surface of the pipe by the Fourier-transform and also at the interface of the drop using collocation methods. The paper’s significance is to discuss and see the effectiveness of the pipe’s inner surface on the hydrodynamic normalised force influencing the drop sphere because of its filling with and existence in a micropolar fluid. Findings indicate that the hydrodynamic normalised force is increasing monotonically with the increase of the droplet-to-pipe radius ratio, and tends to infinity when the droplet’s interface touches the pipe’s inner surface. Additionally, the findings show that when the micropolarity parameters increase, so does the normalised drag force. Our findings for the normalised force agree well with the solutions that are provided in publications. The current study is also significant in the domains of industrial and biomedical operations like coagulation, sedimentation, and rheology of suspension, to name a few.