Characterizing and predicting the partial slip subjected to variable gradients of velocity and pressure in eccentric micro-scale Taylor–Couette flows

In the context of eccentric micro-scale Taylor–Couette flow, variations in localized flow scales result in a non-uniform fluid–solid interface slip state, distinct from the typically studied uniform slip velocity distribution. This study introduces a boundary condition definition method aimed at characterizing partial slip states, complemented by a coupled iterative analysis system tailored to address this complexity. Key contributions include the development of a method for calculating the limiting shear stress, which considers local velocity gradients and pressures. Validation demonstrates that the locally derived slip state aligns more closely with Knudsen number distributions of local flow scales compared to traditional uniform slip models, and exhibits greater consistency with experimentally measured pressure distributions. Additionally, the study reveals that eccentric Taylor–Couette flow, characterized by significant variations in local flow scales and strong self-induced pressure effects, leads to complex distributions of local pressure, velocity gradients, and differences in local slip velocities. Specifically, the non-uniform distribution of local pressure gradients due to eccentricity results in partial slip occurring predominantly on the rotor in regions with positive pressure gradients, and on the stator in regions with negative pressure gradients. Furthermore, the variation in gap height exerts a greater influence on local slip compared to rotational speed and eccentricity ratio. Under certain conditions influenced by pressure gradients, the slip velocity on the rotor may exceed its tangential speed.