Microfabrication techniques for rectangular microchannels typically produce heterogeneous surface textures, leading to distinct roughness and slip properties at lateral and top/bottom walls. This anisotropy in surface properties modifies fluid–wall interactions and has important consequences for flow dynamics, particularly in the determination of effective slip lengths and channel permeability. In practice, slip lengths inferred from velocity measurements along a single confinement direction often fail to reconcile with observed flow rates, suggesting the presence of unresolved multidimensional effects. In this work, an exact analytical solution is derived for oscillatory Newtonian flow in a rectangular microchannel with anisotropic slip boundary conditions. Different slip lengths are prescribed at the lateral and top/bottom walls in order to quantify their coupled influence on both the velocity field and the volumetric flow rate. The solution reveals a masking effect in which the flow rate caused by the primary slip length could be effectively reduced even by an order of magnitude, or magnified twofold, by the presence of a discrepant slip at the secondary walls. Based on this analysis, explicit correlations are obtained for an effective slip length that accounts for the interaction between local wall-dependent slip lengths. These results provide a practical framework to reconcile discrepancies between local velocity measurements and global flow rates and enable indirect estimation of slip properties along the secondary confinement direction, which are typically inaccessible experimentally. The proposed formulation offers a tractable route to incorporate heterogeneous surface effects into the characterization and design of microfluidic and porous systems under oscillatory forcing.
原文链接
分享
引用
