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

Abstract This paper reports a computational and theoretical investigation of pressure-flow characteristics of a microchannel having a superhydrophobic bottom wall with embedded air-cavities and, thin deformable membrane as the top 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 microchannel with 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 (SSBT) have been investigated for the comparison of their pressure-flow characteristics. The Poiseuille Numbers (fRe) for SSBDT microchannel is found to be lowest with an average of 18.7% and 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 same dimensions. Further, critical Reynolds Number (Re critical ) (at which the air-water interface breaks and super-hydrophobicity vanishes) was found to be ∼ 20% higher for SSBDT microchannel compared to SSB microchannel. Thus, the wall compliance in SSBDT microchannel is found to increase the capability to sustain the super-hydrophobicity at higher Re numbers.