A simplified model for unsteady pressure driven flows in circular microchannels of variable cross-section
A simplified model for unsteady pressure driven flows in circular microchannels of variable cross-section
复制标题
变截面圆形微通道中非稳态压力驱动流的简化模型
DOI：
10.1016/j.apm.2018.01.037
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发表时间：
2018
影响因子：
5
通讯作者：
Leila Issa
中科院分区：
文献类型：
--
作者：
Leila Issa
本文提出了一种快速、精确的变截面圆形微通道内压力驱动非定常流动的模型。该模型是为小直径与长度比的通道开发的，但允许通道直径沿轴沿着有较大变化。该模型的一个关键特征是，它不限制强迫的时间依赖性，在形状和频率方面。强迫的唯一条件是惯性项的平流分量很小。这是一个重大偏离许多以前的论述，假设谐波强迫。该模型是基于扩展和非稳态润滑近似的通道的纵横比。除隐式压力分布外，每个阶次的所得方程均使用有限Hankel变换解析求解，隐式压力分布采用递归时间格式进行数值求解。与经典的CFD模拟相比，降阶半分析方法快两个数量级，部分原因是这些表达式的收敛所需的模式数量不是太大。数值模拟表明，该模型是准确的一个大类通道和相当宽的雷诺数范围。这一点，再加上它不对非定常力的形状和频率施加任何条件，使模型成为快速模拟大型流体回路（如在芯片实验室、μTAS和人体中）的有价值的工具，从而允许显著减少设计参数空间。
In this paper, we present a fast and accurate model for unsteady pressure-driven flows in circular microchannels of variable cross-section. The model is developed for channels of small diameter to length ratio, but allows for large variations in the channel’s diameter along the axis. A key feature of the model is that it puts no restriction on the time dependence of the forcing, in terms of shape and frequency. The only condition on the forcing is such that the advective component of the inertia term is small. This is a major departure from many previous expositions which assume harmonic forcing. The model is based on an extended and unsteady lubrication approximation in the aspect ratio of the channel. The resulting equations for each order are solved analytically using a finite Hankel transform, except for the implicit pressure profile, which is solved numerically with a recursive time scheme. Compared to classical CFD simulations, the reduced order semi-analytic method is two orders of magnitude faster, owing in part to the fact that the number of modes required for the convergence of these expressions is not too large. The numerical simulations reveal that the model is accurate for a large class of channels and a fairly wide range of Reynolds numbers. This, combined with the fact that it imposes no conditions on the shape and frequency of the unsteady forcing, renders the model a valuable tool for rapidly simulating large fluidic circuits (as in lab-on-a-chip,μTAS and the human body), thereby allowing significant reduction in the design parameters space.
影响因子：
44.1
作者：
Marchetti, M. C.;Joanny, J. F.;Simha, R. Aditi
通讯作者：
Simha, R. Aditi