流动聚焦微通道内牛顿微液滴在幂律剪切致稀流体中的生成研究

doi:10.11949/0438-1157.20191331

摘要/Abstract

摘要：

采用开源CFD软件OpenFOAM中的interFoam求解器对流动聚焦微通道内微液滴的形成过程进行了数值模拟。通过与文献中的实验数据进行对比，验证了VOF模型和幂律非牛顿流体模型的准确性。并以此为基础模拟了幂律剪切致稀流体中牛顿微液滴的形成过程，研究了幂律流体的幂律指数n和稠度系数K对微液滴生成的影响。研究表明，在滴状和挤压状流型中，离散线颈部宽度与周期内剩余时间呈幂律关系；离散线长度在坍塌阶段呈现线性缓慢增长，在夹断阶段呈现近似指数迅速增长的趋势。随着n和K的增大，液滴的尺寸逐渐减小，而生成频率则逐渐增大，且n的变化比K的变化对其产生的影响更明显。

关键词: 多相流, 流动聚焦微通道, 微流体学, 非牛顿流体

Abstract:

The interFoam solver in the open source CFD software OpenFOAM was used to numerically simulate the formation of micro-droplets in a flow-focused microchannel. Predictions using the volume-of-fluid(VOF) model and the power-law non-Newtonian model were first validated against measurements in the literature. Then, the formation of Newtonian droplets in power-law shear-thinning fluids was modeled in three different flow regimes. The results illustrate the effects of the power-law index（n） and the consistency coefficient（K） of the power-law fluid on the droplet generation. The results show that the minimum width of the stretching thread has a power-law relationship with using the remaining time in the droplet release cycles in the squeezing and dripping regimes. The thread length increases slowly during the collapse stage and then grows rapidly during the pinch-off stage. The final droplet length decreases with increasing n or K. However, the generation frequency increases as n or K increase. The results also show that n has a greater effect than K on the droplet formation.

Key words: multiphase flow, flow-focusing microchannel, microfluidics, non-Newtonian fluids

中图分类号:

O 359⁺.2

陈琦, 李京坤, 宋昱, 何倩, 李雪芳. 流动聚焦微通道内牛顿微液滴在幂律剪切致稀流体中的生成研究[J]. 化工学报, 2020, 71(4): 1510-1519.

Qi CHEN, Jingkun LI, Yu SONG, Qian HE, Christopher David M, Xuefang LI. Newtonian droplet generation in shear-thinning fluids in flow-focusing microchannel[J]. CIESC Journal, 2020, 71(4): 1510-1519.

图/表 15

表 1 方程各项离散格式

Table 1 Discretization schemes for different terms of governing equations

项	表达式	离散格式
ddt	$? (ρ u) ? t$ , $? α ? t$	CrankNicolson 1
div	$? ? (ρ u u)$ , $? ? (α u)$	Gauss linear Upwind grad(U)
div	$? ? (α (1 - α) u c)$	Gauss Interface Compression
grad	$? u$ , $? α$	Gauss linear
snGrad	$? p$	corrected
Laplacian	$? ? (μ (? u + ? u T))$	Gauss linear corrected
interpolation	$(X) f$	linear

表 1 方程各项离散格式

Table 1 Discretization schemes for different terms of governing equations

项	表达式	离散格式
ddt	$? (ρ u) ? t$ , $? α ? t$	CrankNicolson 1
div	$? ? (ρ u u)$ , $? ? (α u)$	Gauss linear Upwind grad(U)
div	$? ? (α (1 - α) u c)$	Gauss Interface Compression
grad	$? u$ , $? α$	Gauss linear
snGrad	$? p$	corrected
Laplacian	$? ? (μ (? u + ? u T))$	Gauss linear corrected
interpolation	$(X) f$	linear

图1 流动聚焦型微通道几何模型

Fig.1 Geometry of flow-focusing microchannel

图2 网格独立性验证

Fig.2 Mesh independence validation

表2 两相流体属性设置

Table 2 Physical properties of two phases

流体	密度/(kg/m³)	K/(Pa·sⁿ)	n	界面张力/(mN/m)
离散相	920	0.011	1	29.1
连续相	1000	0.2~0.7	0.3~1	29.1

图3 液滴脱离过程中形态变化对比

Fig.3 Comparison between calculated results and experimental data

图4 液滴生成过程中主要形态参数的瞬态变化

Fig.4 Temporal evolutions of thread tip and minimum width of thread neck during droplet formation process

图5 微通道内速度及黏度分布状况

Fig.5 Velocity and viscosity distribution in microchannel

图6 液滴形成过程中速度分布（Qd = 60 μl/min，Qc = 480 μl/min，K = 0.35 Pa?sn，n = 0.47）

Fig.6 Velocity distribution during droplet formation process

图7 不同n下不混溶线形态的变化过程（Qd = 60 μl/min，Qc = 480 μl/min，K = 0.35 Pa?sn）

Fig.7 Break-up dynamics of dispersed thread for various n

图8 不同n幂律流体中牛顿液滴的形成机制（Qd = 60 μl/min，Qc = 480 μl/min，K = 0.35 Pa?sn）

Fig.8 Newtonian droplet formation mechanism in power-law fluids with different n

图9 液滴尺寸及生成频率随n的变化（Qd = 60 μl/min，Qc = 480 μl/min，K = 0.35 Pa?sn）

Fig.9 Variations of droplet size and formation frequency with n

图10 不同K下不混溶线形态的变化过程（Qd = 60 μl/min，Qc = 480 μl/min，n = 0.47）

Fig.10 Break-up dynamics of dispersed thread for various K

图11 不同K幂律流体中牛顿液滴的形成机制（Qd = 60 μl/min，Qc = 480 μl/min，n = 0.47）

Fig.11 Newtonian droplet formation mechanism in power-law fluids with different K

图12 液滴长度及生成频率随K的变化（Qd = 60 μl/min，Qc = 480 μl/min，n = 0.47）

Fig.12 Variations of droplet size and formation frequency with K

图13 液滴长度与连续相毛细数的关系

Fig.13 Relationship between droplet length and capillary number of continuous phase

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