On the thin-film asymptotics of surface tension driven microfluidics
On the thin-film asymptotics of surface tension driven microfluidics
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DOI：
10.1017/jfm.2020.532
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发表时间：
2020-10-25
影响因子：
3.7
通讯作者：
Oliver, J. M.
中科院分区：
文献类型：
--
作者：
Calver, S. N.;Gaffney, E. A.;Oliver, J. M.
最近的技术进步已经导致了一类新型的微流体装置，其可以通过将流体印刷到固体基底上来快速制造，其中流动经由表面张力被动地产生。然而，流量和管道高度之间的非线性依赖关系，阻止直接计算所产生的动态。在本文中，我们使用匹配的渐近展开来预测如何通过这些设备的流量可以通过改变它们的几何形状来调整。我们开始与简单的“哑铃”配置，其中两个不同大小的液滴是由一个长，薄和狭窄的导管连接。我们计算的时间尺度所需的一滴排水到其他和这取决于两个几何形状的钉扎接触线和体积的流体沉积到液滴。因此，我们的模型提供了一个特定的流体流量和/或剪切应力，这往往是关键的实验约束设计管道的机械基础。我们的渐近预测被证明是在良好的协议与数值模拟，即使是中等的纵横比（导管的宽度与长度的比率）。接下来，我们将展示如何我们的简单哑铃配置的结果可以扩展到预测通过网络的管道与多个滴和节点的流量，因此可能有助于他们的设计和实施。这种新的数学框架有可能在广泛的学科中增加表面张力驱动的微流体的使用，因为它允许快速评估替代设计。
Recent technological advances have led to a novel class of microfluidic devices which can be rapidly fabricated by printing a fluid onto a solid substrate with flows generated passively via surface tension. The nonlinear dependence between flow and the heights of the conduits, however, prevent straightforward calculation of the resulting dynamics. In this paper we use matched asymptotic expansions to predict how flow through these devices can be tuned by changing their geometry. We begin with the simple 'dumbbell' configuration in which two fluid drops with different sizes are connected by a long, thin and narrow conduit. We calculate the time scale required for one drop to drain into the other and how this depends both on the geometry of the pinned contact line and volume of fluid deposited into the drops. Our model therefore provides the mechanistic basis to design conduits with a particular fluid flux and/or shear stress, which are often key experimental constraints. Our asymptotic predictions are shown to be in excellent agreement with numerical simulations even for moderate aspect ratios (the ratio of conduit width to length). Next, we show how our results for the simple dumbbell configuration can be extended to predict the flow through networks of conduits with multiple drops and nodes, and hence may assist in their design and implementation. This new mathematical framework has the potential to increase the use of surface tension driven microfluidics across a wide range of disciplines as it allows alternate designs to be rapidly assessed.