The slip boundary is usually realized by microstructured surfaces, where primary fluid flows over the microstructures being filled with a secondary immiscible fluid. The characteristics of the microstructures and the properties of the secondary fluid have a specific effect on the primary flow, which eventually affects the properties of the slip boundary. The coupled flow of two fluids needs to be considered, although it is challenging to theoretically solve the coupled flow problem. In the current work, we establish a theoretical framework for interfacial coupled flow on a slip boundary over a microstructured surface. Taking shear flow over a periodic microstructured boundary as an example, by finding integral relation between the slip velocity and the slip velocity gradient, we decouple the binary fluid system on the slip boundary and solve the slip problem under the low-Reynolds-number limit. It is found that a small viscosity ratio, large fluid interfacial fraction, or large depth-to-width ratio of a groove will result in a large vorticity flux in the groove, leading to a large slip length. Thus, we propose a method to enhance the slippage by introducing a jet flow in the grooves, which is verified by our theory. The current work provides a new method for theoretically solving the coupled flow problem, which can be extended to cases of high-speed flow.

• Received 4 October 2022
• Accepted 4 April 2023

DOI:https://doi.org/10.1103/PhysRevFluids.8.054003