Analytical models for laminar flow through concentric superhydrophobic and liquid-infused pipes

This article derives analytical expressions fully describing laminar flow through concentric pipe-within-pipe set-ups, focusing on scenarios where one tube is pressure driven, and the other serves as a lubricant. Both fluid zones are axially unbounded, therefore excluding recirculation, and are connected along longitudinal infinite slits situated on the inner pipe wall, representing fluid–fluid interfaces. Crucially, the viscous interaction along these interfaces is captured by means of a local slip length, for which explicit formulae are provided, allowing a straightforward evaluation. With that, these models provide a full description of the velocity field for slippery concentric pipes, taking into account the viscosity ratio of both fluids and the overall geometry, therefore extending beyond the common assumption of perfect slip applied to superhydrophobic surfaces. Thereby, they enable a precise analysis of the flow, offering important tools to decipher the intricate dynamics of the two coupled fluids within such set-ups. As a result, the insights acquired contribute to the design and optimisation of superhydrophobic and liquid-infused surfaces, with implications for numerous engineering applications such as microfluidic contactors or drag reduction. The analytical models are in excellent agreement with numerical simulations, thus confirming the selected approach. Therefore, our study further illustrates an effective methodology to derive additional analytical models through the presented mathematical techniques, which can serve as a useful template for modelling such surfaces.