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The two-dimensional slow viscous fluid motion between two co-axial circular cylinders showed the inner cylinder is shear-free and the outer one is rigid. The flow is due to the presence of a line source and a line sink of equal strength on the outer cylinder. The stream function for the flow in the annular region is established. The hydrodynamic force on the inner shear-free cylinder has been evaluated. Some numerical values for the force have been presented in a table and compared with corresponding known values where both inner and outer cylinders are rigid.

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Transport of the pressure-driven perturbations with a sharp parallel velocity shear is studied in microfluidics. Studies show that when the second derivative of the parallel velocity with respect to the radial coordinate is positive, the linear mode may become unstable and turbulent momentum transport increases. On the other hand, when the second derivative of the parallel velocity is negative, the linear mode is completely stabilized and turbulent momentum transport reduces. Possible implications of this results in biomedical industry will be discussed.