潘久强， 伍名裘

桂林电子科技大学 机电工程学院，广西制造系统与先进制造技术重点实验室，广西 桂林 541004

引用格式：

潘久强， 伍名裘. 球形颗粒间液桥形成过程实验及直接数值仿真［J］. 中国粉体技术， 2026， 32（3）： 1-15.

PAN Jiuqiang， WU Mingqiu. Experiments and direct numerical simulations on formation process of liquid bridges between spherical particles［J］. China Powder Science and Technology， 2026， 32（3）： 1-15.

DOI：10.13732/j.issn.1008-5548.2026.03.013

收稿日期： 2025-04-11， 修回日期： 2025-06-30，上线日期： 2025-11-11。

基金项目： 国家自然科学基金项目，编号：22168014；广西自然科学基金项目，编号：2023GXNSFAA026480。

第一作者： 潘久强（1998—），男，硕士生，研究方向为湿球型颗粒间液桥及液体传输理论研究。E-mail：2508778742@qq.com。

通信作者： 伍名裘（1982—），男，教授，博士，硕士生导师，研究方向为颗粒材料计算力学、多相流、颗粒流。E-mail：mingqiu_wu@126.com。

摘要： 【目的】 研究湿颗粒碰撞过程中液桥传输机制，预测工业过程中湿颗粒间液体传输过程。【方法】 结合实验与数值模拟，探究液膜厚度、颗粒初始间距及液体黏度对球形颗粒间液桥动态行为的影响规律；通过自主设计的实验装置与气-液-固三相流直接数值仿真，探讨液桥形成过程中各参数的作用机制。【结果】 实验与模拟的结果对比反映出表面特性对液体传输实际过程的影响；无量纲膜厚每增加0.01，最大无量纲液桥体积约增加0.2，当无量纲膜厚约为0.22时液桥体积趋于饱和；实验中，无量纲距离从0.067增大到0.133时，最大液桥体积平均减小率约为3.0%，无量纲距离从0.067增大到0.200时，减小率约为4.9%，仿真中液桥体积平均减小率约为2.6%，减小率约为3.9%；当动力黏度为0.92~9.74 Pa·s时，液体黏度的改变对液桥形成过程中液桥体积的变化无明显影响。【结论】 液膜厚度的增加使液桥体积显著增长，并存在使液桥体积饱和的临界厚度；颗粒初始间距的增大会抑制液桥的形成；在特定黏度范围内，液体黏度变化对液桥体积无显著作用，表明毛细力是液桥演化的主导机制。

关键词： 湿颗粒； 液桥； 液体输送； 流体体积法； 数值模拟

Abstract

Objective Liquid bridges between wet particles are commonly found in industrial processes such as chemical engineering， energy production， food processing， and pharmaceutical manufacturing. The formation mechanism of these bridges plays an important role in optimizing processes such as fluidized bed granulation and the liquefaction of mineral soil particles. It affects particle uniformity， particle migration， and alters the distribution of pore structures. Therefore， this study aims to comprehensively investigate the dynamic evolution of liquid bridges and the liquid transfer mechanism during wet particle collisions.

Methods Through a combination of experiments and numerical simulations，the study investigated the effects of three factors，i.e.，dimensionless liquid film thickness， dimensionless initial particle spacing， and liquid viscosity， on the variations in dimensionless liquid bridge volume during liquid bridge formation between spherical particles. Synchronous and counter-rotation of stepper motors were used to rotate stainless steel balls， enabling uniform coating with dimethyl silicone oil and ensuring coating stability. The contours of experimental images before and after coating were extracted and compared to ensure both the coating thickness accuracy and uniformity of the liquid film. Three-dimensional numerical simulations based on the volume of fluid （VOF） method were conducted under conditions consistent with the experiments. Trend curves of dimensionless liquid bridge volume over dimensionless time were plotted to compare and validate the experimental and numerical simulation results， confirming the reliability of the research scheme.

Results and Discussion The results indicated that increasing liquid film thickness significantly enhanced the growth of the liquid bridge volume， including both the growth rate and the maximum volume. Specifically， for every 0.1 increase in the dimensionless liquid film thickness， the dimensionless maximum liquid bridge volume increased by approximately 0.02. The liquid bridge tended to saturate once the liquid film thickness exceeded a critical limit. When the initial particle spacing was 0.067， the maximum liquid bridge volume in the concave bridge state was observed at a film thickness of 0.22. Further increases in film thickness led to a morphological transition of the bridge shape from concave to convex.Increasing the initial particle spacing inhibited liquid bridge formation， reducing both the growth rate and the maximum volume. In experiments with constant film thickness， increasing the initial particle spacing from 0.067 to 0.133 resulted in an approximate 3.0% reduction in maximum liquid bridge volume， while an increase from 0.067 to 0.200 resulted in a reduction of approximately 4.9%. In numerical simulations， the corresponding decreases were about 2.6% and 3.9%， respectively.Within a dynamic viscosity range of 0.97 Pa·s to 9.74 Pa·s， variations in viscosity had little impact on the growth of the liquid bridge volume. This limited effect was attributed to the slow liquid flow during the formation of the liquid bridge. The capillary force reached a maximum velocity of less than 1 m/s and decreased continuously over time， indicating that capillary forces， rather than the viscous forces， dominated the evolution of the liquid bridge. Overall， the results demonstrated that liquid film thickness and initial particles pacing were key parameters controlling liquid bridge formation， while the influence of viscosity was limited under specific conditions.

Conclusion and Prospects This study systematically reveals the mechanisms by which various parameters influence the variation inliquid bridge volume during bridge formation. These findings provide theoretical guidance for optimizing particle bonding and agglomeration in industrial processes and for understanding liquid transport mechanisms between mineral soil particles. Additionally， a foundational model for dynamic studies of liquid bridges under complex working conditions was established in this study.Gravity has long been recognized as an important factor influencing experimental results in liquid bridge studies. Comparison and verification of experimental and numerical simulation results in this paper confirm that gravitational effects can be neglected using this research setup， providing experimental support for further investigations.In practical industrial processes such as powder handling， coal screening， and fluidized bed granulation， particles move relative to each other， and liquid bridges continuously form and rupture. Current research primarily focuses on liquid bridges formed by localized liquid between partially wetted particles. However， in practical applications， with the increased liquid content，liquid bridges can form between fully wetted particles. Future studies may investigate the effects of factors such as relative collision velocity and temperature variation on liquid bridge formation，explore dynamics of three-particle bridge systems， and examine both the rupture distance of liquid bridges between fully coated spherical particles and the liquid distribution patterns after rupture.

Keywords： wet particle； liquid bridge； liquid transfer； liquid volume method； numerical simulation

参考文献（References）

［1］LY A， ACHOURI I E， GOSSELIN R， et al. Sequential fixed-fluidized bed foam granulation （SFFBFG） and drying： multivariate model development for water content monitoring with near-infrared spectroscopy［J］. Chemical Engineering Science， 2022， 262： 118039.

［2］CAPECE M， SILVA K R， SUNKARA D， et al. On the relationship of inter-particle cohesiveness and bulk powder behavior：flowability of pharmaceutical powders［J］. International Journal of Pharmaceutics， 2016， 511（1）： 178-189.

［3］WANG B， SUN X R， XIANG J， et al. A critical review on granulation of pharmaceuticals and excipients： principle， analysis and typical applications［J］. Powder Technology， 2022， 401： 117329.

［4］ROISMAN I， ABBOUD M， BROCKMANN P， et al. Forced flows in liquid bridges［J］. Current Opinion in Colloid & Interface Science， 2023，67：101738.

［5］宋志超， 唐天琪， 何玉荣. 基于DNS方法的湿颗粒间静态液桥形态模拟研究［J］. 工程热物理学报， 2024， 45（7）： 2040-2046.

SONG Z C， TANG T Q， HE Y R. Simulation study on the morphology of static liquid bridges between wet particles based on the DNS method［J］. Journal of Engineering Thermophysics， 2024， 45（7）： 2040-2046.

［6］邵丽丽. 喷雾流化床中湿颗粒碰撞特性研究［D］. 南京： 东南大学， 2024.

SHAO L L. Research on the collision characteristics of wetparticles in a spray fluidized bed［D］. Nanjing：Southeast University， 2024.

［7］唐天琪. 气固流化床内湿颗粒流动特性DEM模拟及实验研究［D］. 哈尔滨： 哈尔滨工业大学， 2018.

TANG T Q. DEM simulation and experimental study on the flow characteristics of wet particles in a gas-solid fluidized bed［D］. Harbin：Harbin Institute of Technology， 2018.

［8］李家园. 船载散装矿土颗粒间持液能力实验研究［D］. 哈尔滨：哈尔滨工程大学， 2023.

LI J Y. Experimental study on the liquid retention capacity between particles of ship-borne bulk mineral soil［D］. Harbin：Harbin Engineering University， 2023.

［9］YAN C Z， SU B， SHI Y S， et al. Liquid bridge induced assembly （LBIA） strategy： controllable one-dimensional patterning from small molecules to macromolecules and nanomaterials［J］. Nano Today， 2019， 25： 13-26.

［10］PU C， LIU F Y， WANG S H. Liquid force and rupture distance between two particles［J］. Advances in Materials Science and Engineering， 2021， 2021： 1-9.

［11］LI X Q， WANG D F， HUANG F L， et al. Stretching and rupture of a viscous liquid bridge between two spherical particles［J］. Asia-Pacific Journal of Chemical Engineering， 2021， 16（1）： e2579.

［12］WANG S H， LIU F Y， CUI J Y， et al. Experimental study on the rupture behavior of the liquid bridge between three rigid spheres［J］. Langmuir， 2022， 38（45）： 13857-13869.

［13］WU D L， ZHOU P， ZHAO B J， et al. Liquid redistribution upon the liquid-bridge rupture between two unequal particles with a minimal energy method［J］. Powder Technology， 2019， 354： 165-173.

［14］BOZKURT M G， FRATTA D， LIKOS W J. Capillary forces between equally sized moving glass beads： an experimental study［J］. Canadian Geotechnical Journal， 2017， 54（9）： 1300-1309.

［15］LIEVANO D， VELANKAR S， MCCARTHY J J. The rupture force of liquid bridges in two and three particle systems［J］. Powder Technology， 2017， 313： 18-26.

［16］XIAO F， JING J Q， KUANG S B， et al. Capillary forces on wet particles with a liquid bridge transition from convex to concave［J］. Powder Technology， 2020， 363： 59-73.

［17］ZHAO C F， KRUYT N P， MILLET O. Capillary bridges between spherical particles under suction control： rupture distan-ces and capillary forces［J］. Powder Technology， 2020， 360： 622-634.

［18］李云鹏. 船运固体散货液化细观机理实验研究［D］. 哈尔滨： 哈尔滨工程大学， 2022.

LI Y P. Experimental study on the mesoscopic mechanism of liquefaction of solid bulk cargoes transported by ships［D］. Harbin：Harbin Engineering University， 2022.

［19］YIN Y， LIU F Y， MIAO M， et al. Effect of surface roughness on the liquid bridge between two rigid spheres［J］. Powder Technology， 2025， 449： 120377.

［20］VALLONE A F， UÑAC R O， MAZA D， et al. On the dynamics of a liquid bridge between a sphere and a vertically vibrated solid surface［J］. Granular Matter， 2023， 25（2）： 28.

［21］NGUYEN G T， CHAN E L， TSUJI T， et al. Interface control for resolved CFD-DEM with capillary interactions［J］.Advanced Powder Technology， 2021， 32（5）： 1410-1425.

［22］MURASE K， MOCHIDA T， SAGAWA Y， et al. Estimation on the strength of a liquid bridge adhered to three spheres［J］. Advanced Powder Technology， 2008， 19（4）： 349-367.

［23］ZHANG S G， LI X K， DU Y Y. A numerical model of discrete element-liquid bridge-liquid thin film system for wet deform-ing granular medium at low saturation［J］. Powder Technology， 2022， 399： 117217.

［24］HU X L， LI H L， ZHANG H W， et al. Numerical study of head-on collisions between two glass microsphere droplets［J］. International Journal of Heat and Fluid Flow， 2024， 107： 109376.

［25］JIANG C Z， WANG Z H， YANG Q W， et al. Numerical investigations of collision modes of double droplets on a spherical surface based on the phase field method［J］. Korean Journal of Chemical Engineering， 2024， 41（6）： 1551-1566.

［26］HE Z T， WU C M， YU J J， et al. Dynamic analysis of adsorbate behavior in nanopores： liquid bridge formation， cavitation， and contact angle evaluation via molecular dynamics simulations［J］. Journal of Molecular Liquids， 2024， 414： 126146.

［27］WU M Q，RADL S，KHINAST J G.A model to predict liquid bridge formation between wet particles based on direct numerical simulations［J］. AIChE Journal， 2016， 62（6）： 1877-1897.

［28］WU M Q， KHINAST J G， RADL S. Liquid transport rates during binary collisions of unequally-sized particles［J］. Powder Technology， 2017， 309： 95-109.

［29］SOULIÉ F， CHERBLANC F， El YOUSSOUFI M S， et al. Influence of liquid bridges on the mechanical behaviour of polydisperse granular materials［J］. International Journal for Numerical and Analytical Methods in Geomechanics， 2006， 30（3）： 213-228.

［30］ROSSETTI D， SIMONS S J R. A microscale investigation of liquid bridges in the spherical agglomeration process［J］. Powder Technology， 2003， 130（1/2/3）： 49-55.