Yield stress fluid flows in superhydrophobic channels: From creeping to inertial regime

In this work, inertial flows of a yield stress fluid in a channel equipped with a superhydrophobic groovy wall are studied through numerical computations. Assuming an ideal Cassie state, the superhydrophobic wall is modeled via arrays of slip, quantified using the Navier slip law, and arrays of stick, corresponding to the no-slip boundary condition. The viscoplastic rheology is modeled using the Bingham constitutive model, implemented via the Papanastasiou regularization technique. The focus is on inertial flows in the thin channel limit, where the groove period is much larger than the half-channel height. The effects of the flow parameters are quantified on the flow variables of interest, including the slip and axial velocity profiles, unyielded plug zones, regime classifications, flow asymmetry indices, effective slip lengths, and friction factors. In particular, an increase in the flow inertia quantified via the Reynolds number affects the flow in several ways, such as reducing the dimensionless slip velocity and effective slip length, increasing the friction factor, inducing an asymmetry in the velocity profile, and showing a non-monotonic effect on the yielding of the center plug. The present work addresses the complex interplay between the yield stress fluid rheology, the wall superhydrophobicity, and the flow inertia, and it can find applications in macro-/micro-transports of non-Newtonian fluids, from oil and gas to health-related industries.