Flow rate-pressure drop relation for deformable shallow microfluidic channels
Flow rate-pressure drop relation for deformable shallow microfluidic channels
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DOI：
10.1017/jfm.2018.30
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发表时间：
2018-04-25
影响因子：
3.7
通讯作者：
Stone, Howard A.
中科院分区：
文献类型：
--
作者：
Christov, Ivan C.;Cognet, Vincent;Stone, Howard A.
由软材料制成的器件中的层流流动会引起流道几何形状的变形，从而影响流量-压降关系。对于给定的压力降，在具有狭窄矩形截面的通道中，流量随通道高度的立方而变化，因此变形可以产生显著的定量效应，包括对压降的非线性依赖(Gervais等人，Lab on a Chip，第6卷，2006，pp.500-507)。Gervais等人。通过试探性地将Hookean弹性响应与Stokes流动的润滑近似相耦合，提出了一个成功的变形引起的流量变化模型。然而，他们的模型包含一个拟合参数，必须通过执行实验为每个通道形状找到该参数。利用各向同性准静态平板弯曲理论和Stokes方程，在润滑近似下(即通道高度与宽度之比和通道高度与长度之比均为小的情况下)，给出了浅部可变形微通道中流量-压降关系的摄动方法。我们的结果不包含自由参数，证实了Gervais等人，S等人观察到的流量是压降的四次多项式，所导出的流量-压降关系与实验测量结果吻合较好。
Laminar flow in devices fabricated from soft materials causes deformation of the passage geometry, which affects the flow rate-pressure drop relation. For a given pressure drop, in channels with narrow rectangular cross-section, the flow rate varies as the cube of the channel height, so deformation can produce significant quantitative effects, including nonlinear dependence on the pressure drop (Gervais et al., Lab on a Chip, vol. 6, 2006, pp. 500-507). Gervais et al. proposed a successful model of the deformation-induced change in the flow rate by heuristically coupling a Hookean elastic response with the lubrication approximation for Stokes flow. However, their model contains a fitting parameter that must be found for each channel shape by performing an experiment. We present a perturbation approach for the flow rate-pressure drop relation in a shallow deformable microchannel using the theory of isotropic quasi-static plate bending and the Stokes equations under a lubrication approximation (specifically, the ratio of the channel's height to its width and of the channel's height to its length are both assumed small). Our result contains no free parameters and confirms Gervais et al.'s observation that the flow rate is a quartic polynomial of the pressure drop. The derived flow rate-pressure drop relation compares favourably with experimental measurements.