纵横比对横向扩散加宽的影响：格子Boltzmann研究
Effect of aspect ratio on transverse diffusive broadening: A lattice Boltzmann study
摘要：
采用格子玻尔兹曼方法研究了Y型层流微混合器中两种混相流体间相互扩散区的标度律。格子玻尔兹曼方法求解耦合的三维流体力学和传质方程，并结合了与此问题相关的三维流动的内在特征。我们观察到不同的幂律制度发生在中心的通道和接近顶/底壁。相互扩散区的范围与通道中心处的轴向距离的平方根成比例。在顶/底壁处，我们发现在混合的早期阶段的指数为1/3，如在Ismagilov和同事的实验中观察到的[Appl. Phys. Lett. 76，2376（2000）]。在离入口较大的距离处，靠近壁的标度指数变为1/2 [J. B. Salmon等J. Appl.Phys.101，074902（2007）]。在这里，我们专注于有限的纵横比扩散增宽的效果。有趣的是，无论通道的纵横比如何，我们都发现了相同的缩放定律。然而，表征在顶/底壁处的加宽的指数1/3恢复到下游的正常扩散行为的点强烈地取决于纵横比。我们提出了一个解释，这一观察在侧壁的剪切速率。还提供了对扩散增宽具有不可忽略影响的纵横比范围的判据。
英文摘要：
We study scaling laws characterizing the inter-diffusive zone between two miscible fluids flowing side by side in a Y-shape laminar micromixer using the lattice Boltzmann method. The lattice Boltzmann method solves the coupled 3D hydrodynamics and mass transfer equations and incorporates intrinsic features of 3D flows related to this problem. We observe the different power law regimes occurring at the center of the channel and close to the top/bottom wall. The extent of the inter-diffusive zone scales as square root of the axial distance at the center of the channel. At the top/bottom wall, we find an exponent 1/3 at early stages of mixing as observed in the experiments of Ismagilov and coworkers [Appl. Phys. Lett. 76, 2376 (2000)]. At a larger distance from the entrance, the scaling exponent close to the walls changes to 1/2 [J.-B. Salmon et al J. Appl. Phys. 101, 074902 (2007)]. Here, we focus on the effect of finite aspect ratio on diffusive broadening. Interestingly, we find the same scaling laws regardless of the channel's aspect ratio. However,the point at which the exponent 1/3 characterizing the broadening at the top/bottom wall reverts to the normal diffusive behavior downstream strongly depends on the aspect ratio. We propose an interpretation of this observation in terms of shear rate at the side walls. A criterion for the range of aspect ratios with non-negligible effect on diffusive broadening is also provided.
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