Analytical theory for a droplet squeezing through a circular pore in creeping flows under constant pressures
Analytical theory for a droplet squeezing through a circular pore in creeping flows under constant pressures
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DOI：
10.1063/5.0156349
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发表时间：
2023-08-01
影响因子：
4.6
通讯作者：
Peng, Zhangli
中科院分区：
文献类型：
--
作者：
Tang, Zhengxin;Yaya, Francois;Peng, Zhangli
我们推导出了粘性液滴在恒定压力下挤过有限长微圆孔的渡越时间的方程和闭合解。我们的分析是由生物细胞挤压血管小孔和微流体中的正弦和液滴挤压毛孔的重要过程推动的。首先，通过结合Sampson流、Poiseuille流和Young-Laplace方程，并考虑了液滴与孔壁之间的润滑层，推导了液滴在圆孔中挤压的常微分方程组。其次，对于表面张力较小的液滴润湿壁面，我们得到了渡越时间的闭合解。对于表面张力有限的液滴，我们通过数值求解原始微分方程组来预测渡越时间。经过对比实验和有限元模拟的验证，我们研究了压力、粘度、孔/液滴尺寸和表面张力对渡越时间的影响。我们发现，与防止液滴通过的临界表面张力相比，当表面张力较低时，渡越时间与压力成反比，当液滴接近临界张力时，渡越时间变为非线性。值得注意的是，当施加固定百分比的表面张力与临界张力时，渡越时间总是与压力成反比，并且渡越时间与表面张力的关系是非单调的。我们的结果为设计液滴微流体和了解细胞通过狭窄的过程提供了一种快速定量计算渡越时间的方法。
We derived equations and closed-form solutions of transit time for a viscous droplet squeezing through a small circular pore with a finite length at microscale under constant pressures. Our analyses were motivated by the vital processes of biological cells squeezing through small pores in blood vessels and sinusoids and droplets squeezing through pores in microfluidics. First, we derived ordinary differential equations (ODEs) of a droplet squeezing through a circular pore by combining Sampson flow, Poiseuille flow, and Young-Laplace equations and took into account the lubrication layer between the droplet and the pore wall. Second, for droplets wetting the wall with small surface tension, we derived the closed-form solutions of transit time. For droplets with finite surface tension, we solved the original ODEs numerically to predict the transit time. After validations against experiments and finite element simulations, we studied the effects of pressure, viscosity, pore/droplet dimensions, and surface tension on the transit time. We found that the transit time is inversely linearly proportional to pressure when the surface tension is low compared to the critical surface tension for preventing the droplet to pass and becomes nonlinear when it approaches the critical tension. Remarkably, we showed that when a fixed percentage of surface tension to critical tension is applied, the transit time is always inversely linearly proportional to pressure, and the dependence of transit time on surface tension is nonmonotonic. Our results provided a quick way of quantitative calculations of transit time for designing droplet microfluidics and understanding cells passing through constrictions.