In this work, we aim to develop an effective hydrodynamic boundary condition over patterned surfaces for the application to microfluidics. Four different criteria to estimate the effective Navier-slip length and their performance are investigated for flows over corrugated surfaces, such as patterned surfaces or porous interfaces, which can be applied for efficient flow simulations. Four distinctive methods were discussed in the estimation of slip length, namely: mass conservation, balance of energy dissipation rate, force balance, and interfacial slip velocity averaging. Expressions of slip length were derived analytically for each criterion in a pressure-driven flat channel flow and the slip length was determined using a combination of analytic and numerical methods. We report that (i) the slip length from force balance appears to be the most accurate and exactly the same as that from interfacial slip velocity averaging, (ii) the slip length from mass conservation deviates from that of force balance, though minor, particularly for a small relative channel height to the length scale of patterns or pores, and (iii) the energy balance yields significantly different slip lengths. The slip length reduces to a single value for a sufficiently large relative channel height, which indicates that it can be considered as a surface property in general, when the pattern dimension is much smaller than the length scale of flow.

在这项工作中，我们旨在在图案化表面上开发一种有效的流体动力学边界条件，以应用于微流体。对于在波纹表面（如带图案的表面或多孔界面）上的流动，研究了四种估计有效Navier滑移长度及其性能的不同标准，这些标准可用于有效的流动模拟。在滑移长度估计中讨论了四种不同的方法，即：质量守恒，能量耗散率平衡，力平衡和界面滑移速度平均。滑移长度的表达式是在压力驱动的平坦通道流中针对每个标准进行解析得出的，并且滑移长度是使用解析和数值方法的组合确定的。我们报告（i）来自力平衡的滑移长度似乎最准确，并且与来自界面滑移速度平均的滑移长度完全相同；（ii）来自质量守恒的滑移长度偏离了力平衡的滑移长度，尽管较小，尤其是对于相对于图案或孔的长度尺度而言较小的相对通道高度而言，（iii）能量平衡会产生明显不同的滑移长度。对于足够大的相对通道高度，滑移长度减小为单个值，这表明当图案尺寸远小于流动的长度尺度时，滑移长度通常可以被认为是表面性质。尤其是对于相对于图案或孔的长度尺度较小的通道高度而言，并且（iii）能量平衡会产生明显不同的滑移长度。对于足够大的相对通道高度，滑移长度减小到单个值，这表明当图案尺寸远小于流动的长度尺度时，滑移长度通常可以被认为是表面性质。尤其是对于相对于图案或孔的长度尺度较小的通道高度而言，并且（iii）能量平衡会产生明显不同的滑移长度。对于足够大的相对通道高度，滑移长度减小为单个值，这表明当图案尺寸远小于流动的长度尺度时，滑移长度通常可以被认为是表面性质。