Pressure-flow characteristics of a microchannel combining super-hydrophobicity and wall compliance

Drag is a major concern in microfluidic devices impacting flow stability, energy efficiency, and fluid flow control. Minimizing drag enhances performance and efficiency in various applications, such as flow stabilization microdevices, microvalves, and micropumps. Often, superhydrophobicity is utilized for drag-reduction applications. However, superhydrophobic surfaces tend to fail at higher Reynolds numbers. This paper investigates the pressure-flow characteristics of a microchannel having a superhydrophobic bottom wall with embedded air-cavities, and a deformable top membrane, both numerically and theoretically. The aim is to understand fluid flows in the deformable superhydrophobic microchannel and leverage its water-repellent property and deformability both together to reduce drag while maintaining the durability of the superhydrophobic wall. Two-way fluid–structure interaction (FSI) and unsteady volume of fluid (VOF) methods are employed for fluid–solid boundary and liquid–air interface at ridge-cavity, respectively. A novel theoretical model has been developed for the pressure-flow characteristics of a microchannel with a deformable top and superhydrophobic bottom wall. The theoretical and numerical results for pressure drop across the microchannel have shown a good agreement with a maximum deviation of 6.69%. Four distinct types of microchannels viz, smooth (S) (rigid non-textured), smooth with deformable top (SDT), smooth with superhydrophobic bottom (SSB), and smooth with superhydrophobic bottom and deformable top wall (SSBDT) have been investigated for the comparison of their pressure-flow characteristics. The Poiseuille Number (fRe) for SSBDT microchannel is found to be lowest with an average of 18.7% and a maximum of 23.5% lower than S microchannel at Re = 60. Up to 48.59% of reduction in pressure drop was observed for the SSBDT microchannel as compared to smooth (S) microchannel of the same dimensions. Furthermore, critical Reynolds Number (Re_critical) (at which the air–water interface breaks and super-hydrophobicity vanishes) was found to be ~ 20% higher for the SSBDT microchannel compared to the SSB microchannel. Thus, the wall compliance in the SSBDT microchannel is found to increase the capability to sustain the super-hydrophobicity at higher Re numbers. The proposed approach for drag reduction in microchannel can be vital to enhance the efficiency and capability of numerous microdevices needing high Reynolds number flows, such as high throughput cell sorters, microvalves, and micropumps.