Study on rebound behavior characteristics of droplets and dust particles at micron-scale

doi:10.11949/0438-1157.20250129

Abstract

Abstract:

This study investigates the rebound dynamics during the collision between mist droplets and particulate matter, aiming to provide theoretical guidance for particle settlement in water mist technology applications. We focused on particles ranging from 1 μm to 125 μm and used numerical simulations to analyze their rebound behavior when colliding with droplets of similar diameters. Scatter plots of collision behavior were analyzed to obtain a fitting curve for the critical rebound condition, and a physical model was constructed. The model developed in this study involves more dependent variable parameters than previous predictive equations for critical rebound conditions, comprehensively revealing the multiple factors influencing rebound behavior. The research indicates that rebound phenomena mainly occur when droplets collide with hydrophobic particles at low speeds. Smaller droplet sizes result in higher critical rebound velocities, explaining why smaller particles are more difficult to settle through water mist in dust suppression practices. Reducing the dust-mist contact angle can effectively inhibit the rebound, and the rebound phenomenon disappears when the contact angle is less than 90°. The research findings can quantitatively predict the occurrence of a rebound during a dust-mist collision, thereby guiding the optimization of water mist operating parameters in the practice of dust settlement and ultimately promoting significant improvements in dust removal efficiency. This study provides a comprehensive understanding of the rebound dynamics and offers practical guidance for enhancing the effectiveness of water mist technology in dust control applications.

Key words: dust, smoke particles, water mist dust suppression, smoke particle decontamination, solid-liquid collision, micron-scale

摘要：

细水雾除尘技术因具有环保、安全、经济等优势被广泛应用，但尘-雾碰撞时的反弹现象导致降尘效果不佳，且目前对其反弹动力学机制认识不足，缺乏理论指导。本研究针对生产性粉尘及大颗粒烟尘（直径1~125 μm），通过数值模拟分析其与相近直径雾滴碰撞时的反弹行为，并构建了考虑接触角、液滴-颗粒直径比、碰撞速度、液滴黏度、表面张力等多因素的反弹预测模型，得出了反弹临界条件。结果表明，反弹现象主要发生在液滴低速碰撞疏水颗粒时，且雾滴粒径越小，反弹临界速度越大；降低接触角可有效抑制反弹，当接触角小于90°时，反弹现象消失。本研究揭示了影响反弹行为的多重因素，可定量预测尘-雾碰撞反弹行为，为水雾降尘系统的设计优化提供理论依据。

关键词: 粉尘, 烟颗粒, 水雾降尘, 烟颗粒洗消, 固液碰撞, 微米尺度

CLC Number:

X 964

Wei ZHANG, Qiyong WU, Huazhong SUN, Shi HU, Xiaolong ZHU, Shuai KONG. Study on rebound behavior characteristics of droplets and dust particles at micron-scale[J]. CIESC Journal, 2025, 76(8): 3990-4003.

张伟, 武齐永, 孙华中, 胡适, 朱小龙, 孔帅. 微米尺度液滴与尘粒作用后反弹行为特性研究[J]. 化工学报, 2025, 76(8): 3990-4003.

Figures/Tables 20

Fig.1 Schematic diagram of traditional water mist dust removal mechanism

Table 1 Typical parameters of fog field characteristics generated by different atomization methods

雾化方法	水压/MPa	气压/ MPa	索特尔平均粒径/μm	射程/m	速度/ (m·s^-1)
单相高压雾化^[11-12]	6~10	无	30~80	< 3	12~30
两相雾化^[7,13-15]	< 0.5	< 0.6	< 30	< 1	< 10
超声雾化^[16-17]	< 0.5	< 0.5	< 30	1.5~2	4~11
超音速气流雾化^[9]	< 0.5	< 0.5	5~20	4.9~7	< 600

Table 2 Surface tension of fog droplets treated with different physicochemical properties improvement methods

液滴理化特性改善方法	表面张力/(mN·m^-1)
磁化水^[18]	69~72
多组分水雾^[19-20]	29~40
磁化+多组分水雾^[21]	26~32
荷电水雾^[18]	12~20

Table 3 Wetting characteristics of different types of liquids and solids

固体类型	液体类型	接触角	液体表面张力σ/(mN·m^-1)	液体黏度μ/(mPa·s)	来源
ST1：聚硅烷处理的二氧化硅（高度疏水）	蒸馏水	α = 168.4°，β = 91.4°	72.3	1.04	实测
ST1：聚硅烷处理的二氧化硅（高度疏水）	浓度为1 mmol·L^-1的CTAB溶液	α = 151.2°，β = 15.2°	34.2	1.04	实测
ST2：石墨（中度疏水）	蒸馏水	α = 90.0°，β = 23.0°	72.0	1.04	文献[25]
ST2：石墨（中度疏水）	浓度为1 mmol·L^-1的CTAB溶液	α = 62.0°，β = 17.0°	34.2	1.04	文献[25]
ST3：二氧化硅（亲水）	蒸馏水	α = 25.0°，β = 7.5°	72.0	1.04	文献[25]

Fig.2 Computational domain

Table 4 Computational domain sizes corresponding to different particle sizes

颗粒直径/μm	计算域尺寸/μm
3000	21000×6600
2000	14000×4400
125	875×275
25	175×55
5	35×11
1	7×2.2
0.2	1.4×0.44

Fig.3 Comparison of droplet morphology under different grid size conditions

Fig.4 Comparison between simulation results and experimental droplet morphology recorded in Ref.[29] (dp = 2 mm)

Table 5 Condition parameters set when studying the influence of viscosity

常量

变量

液滴-颗粒直径比Ω

液滴表面

张力σ/

(mN·m^-1)

接触角

液滴黏度μ/(mPa·s)

碰撞速度v₀/(m·s^-1)

颗粒直径

d_p/μm

Fig.5 The change process of the contact angle during spreading and shrinking

Table 6 Condition parameter settings when the effects of surface tension and contact angle are investigated

常量		变量
液滴-颗粒直径比Ω	液滴黏度μ/(mPa·s)	碰撞速度v₀/(m·s^-1)	颗粒直径d_p/μm	液滴表面张力σ/(mN·m^-1)	接触角
1.31	1.04	1~500	1, 5, 25, 125 (ST1)	72 (纯水)	α = 168.4°，β =91.4°
1.31	1.04	1~500	1, 5, 25, 125 (ST1)	34.2 (CTAB)	α =151.2°，β =15.2°

Table 7 The condition parameter setting is studied when the contact angle affects the rebound critical condition

常量			变量
液滴- 颗粒直径比Ω	液滴表面张力σ/(mN·m^-1)	液滴黏度μ/(mPa·s)	颗粒直径d_p/μm	碰撞速度 v₀/(m·s^-1)	接触角
1.31	72	1.04	1, 5, 25, 125	1~500	α = β = 168.4°
					α = β = 151.2°
					α = β = 120°
					α = β = 100°
					α = β = 90°
					α = β = 80°

Fig.6 Scatter plot of collision behavior distribution under different contact angle conditions

Table 8 Dimensionless parameter interpretation

液滴无量纲参数	参数解释
$R e = ρ l d l v l μ l$	ρ_l 为液滴密度，d_l 为液滴直径，v_l 为尘雾相对速度，μ_l 为液滴动力黏度
$O h = μ l ρ l d l σ$	μ_l 为液滴动力黏度，ρ_l 为液滴密度，d_l 为液滴直径，σ为液滴表面张力
$W e = ρ l v l 2 l σ$	ρ_l 为液滴密度，v_l 为尘雾相对速度，l为液滴特征长度（在本文中为液滴直径d_l ），σ为液滴表面张力

Table 8 Dimensionless parameter interpretation

液滴无量纲参数	参数解释
$R e = ρ l d l v l μ l$	ρ_l 为液滴密度，d_l 为液滴直径，v_l 为尘雾相对速度，μ_l 为液滴动力黏度
$O h = μ l ρ l d l σ$	μ_l 为液滴动力黏度，ρ_l 为液滴密度，d_l 为液滴直径，σ为液滴表面张力
$W e = ρ l v l 2 l σ$	ρ_l 为液滴密度，v_l 为尘雾相对速度，l为液滴特征长度（在本文中为液滴直径d_l ），σ为液滴表面张力

Table 9 Bounce-back boundary condition equations for different contact angles

条件编号	接触角	液滴表面张力σ/(mN·m^-1)	反弹边界条件方程
1	𝛼α = 168.4° β = 91.4°	72	5.807 = $R e c r 1.080$ Oh，R²=0.9998 0.00965 ≤ Oh ≤ 0.0483
2	𝛼α = 168.4° β = 168.4°	72	7.301 = $R e c r 1.119$ Oh，R² = 0.9987 0.00965 ≤ Oh ≤ 0.0483
3	𝛼α = 151.2° β = 151.2°	72	10.034 = $R e c r 1.189$ Oh，R² = 0.9989 0.00965 ≤ Oh ≤ 0.0483
4	𝛼α = 120.0° β = 120.0°	72	12.491 = $R e c r 1.274$ Oh，R² = 0.9962 0.00965 ≤ Oh ≤ 0.0483
5	𝛼α = 100.0° β = 100.0°	72	9.077 = $R e c r 1.238$ Oh，R² = 0.9967 0.00965 ≤ Oh ≤ 0.0483
6	𝛼α = 90.0° β = 90.0°	72	6.663= $R e c r 1.186$ Oh，R² = 0.9965 0.00965 ≤ Oh ≤ 0.0311
7	𝛼α = 80.0° β = 80.0°	72	当Oh=0.00965，Re = 219.99 当Oh ≥ 0.0193，无反弹现象

Table 9 Bounce-back boundary condition equations for different contact angles

条件编号	接触角	液滴表面张力σ/(mN·m^-1)	反弹边界条件方程
1	𝛼α = 168.4° β = 91.4°	72	5.807 = $R e c r 1.080$ Oh，R²=0.9998 0.00965 ≤ Oh ≤ 0.0483
2	𝛼α = 168.4° β = 168.4°	72	7.301 = $R e c r 1.119$ Oh，R² = 0.9987 0.00965 ≤ Oh ≤ 0.0483
3	𝛼α = 151.2° β = 151.2°	72	10.034 = $R e c r 1.189$ Oh，R² = 0.9989 0.00965 ≤ Oh ≤ 0.0483
4	𝛼α = 120.0° β = 120.0°	72	12.491 = $R e c r 1.274$ Oh，R² = 0.9962 0.00965 ≤ Oh ≤ 0.0483
5	𝛼α = 100.0° β = 100.0°	72	9.077 = $R e c r 1.238$ Oh，R² = 0.9967 0.00965 ≤ Oh ≤ 0.0483
6	𝛼α = 90.0° β = 90.0°	72	6.663= $R e c r 1.186$ Oh，R² = 0.9965 0.00965 ≤ Oh ≤ 0.0311
7	𝛼α = 80.0° β = 80.0°	72	当Oh=0.00965，Re = 219.99 当Oh ≥ 0.0193，无反弹现象

Fig.7 Influence of contact angle on rebound critical condition

Fig.8 Constant value change of equation (3) under different advance angles

Fig.9 Schematic of the definition of different angles in the equation

Table 10 Comparison of Wecr in previous studies with the results of this study

α/(°)	β/(°)	Oh	Ω	式（30）得出的We_cr	式（31）得出的We_cr	式（36）得出的We_cr	前人文献中的We_cr	来源
90	23	0.00211	0.31	128.59	115.43	62.43	63.21	文献^[23]的实验结果
90	23	0.00211	0.62	27.86	29.01	15.61	15.80
90	23	0.00211	1.24	5.65	7.37	3.90	3.95
90	23	0.00211	1.31	5.03	6.62	3.50	3.54
160	23	0.00262	2.00	5.65	2.79	2.53	< 3.96	文献^[28]的模拟结果
160	23	0.00262	1.00	24.90	11.09	10.14	9.87~30.23
160	23	0.00262	0.67	51.66	50.66	12.27	70~90
160	23	0.00262	0.50	95.29	89.83	21.82	130~150
160	23	0.00262	0.33	222.17	201.68	49.09	130~150
125	23	0.00262	2.00	7.30	4.51	1.49	< 3.96
125	23	0.00262	1.00	16.82	17.96	5.95	9.87~30.23
125	23	0.00262	0.67	40.73	40.73	4.65	70~90
125	23	0.00262	0.50	75.90	72.20	8.27	130~150
125	23	0.00262	0.33	178.60	162.06	18.60	130~150
90	23	0.00262	2.00	2.46	2.78	1.40	< 3.96
90	23	0.00262	1.00	9.17	11.07	5.60	3.96~9.87
90	23	0.00262	0.67	23.61	25.16	6.78	70~90
90	23	0.00262	0.50	45.50	44.57	12.05	130~150
90	23	0.00262	0.33	110.29	99.96	27.11	130~150

Fig.10 Predicted values of the critical velocity of rebound for different droplet diameters and viscosities

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