Moving contact line dynamics: from diffuse to sharp interfaces
Moving contact line dynamics: from diffuse to sharp interfaces
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DOI：
10.1017/jfm.2015.697
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发表时间：
2016-02-01
影响因子：
3.7
通讯作者：
Fielding, S. M.
中科院分区：
文献类型：
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作者：
Kusumaatmaja, H.;Hemingway, E. J.;Fielding, S. M.
我们调和了文献中提出的与扩散界面模型中移动接触线相关的滑移长度的两个标度定律，通过证明每个定律适用于微观界面宽度 l 和宏观扩散长度 l(D) = (M eta)(1/2) 的不同范围，其中 eta 是流体粘度，M 是控制分子间扩散的迁移率。对于小的 lD = l，我们发现一个扩散界面状态，其中滑移长度缩放为 xi ，类似于 (l(D)l)(1/2)。对于较大的 l(D)/l > 1，我们发现一个尖锐的界面状态，其中滑移长度仅取决于扩散长度，xi 类似于 l(D) 类似于 (Me eta)(1/2)，因此仅取决于宏观变量 eta 和 M，与微观界面宽度 l 无关。我们还提供了证据，表明修改模型自由能泛函中的微观界面项似乎仅影响扩散界面区域中的滑移长度值，这与仅取决于尖锐界面区域中的宏观变量的滑移长度一致。最后，我们证明了动态接触角对毛细管数的依赖性与 Cox 的理论预测非常一致（J. Fluid Mech., vol. 168, 1986, p. 169），前提是我们允许通过无量纲预因子重新调整滑移长度。该前因数在尖锐界面极限中似乎收敛到统一，但在扩散界面极限中较小。使用三种独立的数值方法在数十年的相关无量纲变量中获得的结果非常一致，这表明我们的发现没有数值伪影。
We reconcile two scaling laws that have been proposed in the literature for the slip length associated with a moving contact line in diffuse interface models, by demonstrating each to apply in a different regime of the ratio of the microscopic interfacial width l and the macroscopic diffusive length l(D) = (M eta)(1/2), where eta is the fluid viscosity and M the mobility governing intermolecular diffusion. For small lD = l we find a diffuse interface regime in which the slip length scales as xi similar to (l(D)l)(1/2). For larger l(D)/l > 1 we find a sharp interface regime in which the slip length depends only on the diffusive length, xi similar to l(D) similar to (M eta)(1/2), and therefore only on the macroscopic variables eta and M, independent of the microscopic interfacial width l. We also give evidence that modifying the microscopic interfacial terms in the model's free energy functional appears to affect the value of the slip length only in the diffuse interface regime, consistent with the slip length depending only on macroscopic variables in the sharp interface regime. Finally, we demonstrate the dependence of the dynamic contact angle on the capillary number to be in excellent agreement with the theoretical prediction of Cox (J. Fluid Mech., vol. 168, 1986, p. 169), provided we allow the slip length to be rescaled by a dimensionless prefactor. This prefactor appears to converge to unity in the sharp interface limit, but is smaller in the diffuse interface limit. The excellent agreement of results obtained using three independent numerical methods, across several decades of the relevant dimensionless variables, demonstrates our findings to be free of numerical artefacts.