Coalescence dynamics of sessile and pendant droplets on fibers and mechanisms of secondary droplet formation

Abstract

As a cost-effective oil-water separation technology, fiber coalescers rely on a thorough understanding of the droplet coalescence mechanism. However, current research has primarily focused on the single process of sessile-sessile droplet coalescence. Using high-speed imaging and the mask region-based convolutional neural network, this study provided the first quantitative characterization of the complete dynamics of asymmetric pendant-sessile droplet coalescence, a phenomenon more prevalent in industrial settings. It was discovered that this process comprises three stages. In the liquid bridge formation stage (Stage I), the lateral expansion of the liquid bridge was dominated by the capillary pressure difference, and the influence of sessile-to-pendant droplet radius ratios on this process was negligible. The oscillation decay stage (Stage II) exhibited the uniqueness of the asymmetric system, where fiber adhesion accelerated energy dissipation, leading to rapid oscillation decay, while the amplitude of the capillary wave on the pendant droplet side was significantly enhanced with an increasing the size ratio. Ultimately, in the stable morphology formation stage (Stage III), increasing the size ratio to 1.5 could significantly reduce the size of the secondary droplets. These findings provided direct strategies for reducing polydisperse secondary droplets in industrial coalescers and enhancing separation efficiency.

Graphical abstract

Keywords

asymmetric droplet coalescence / sessile-pendant droplets / coalescence dynamics / secondary droplet / Mask R-CNN

References

[1] Deng Y , Peng C , Dai M , Lin D , Ali I , Alhewairini S S , Zheng X , Chen G , Li J , Naz I . Recent development of super-wettable materials and their applications in oil-water separation. Journal of Cleaner Production, 2020, 266: 121624

[2] Bhagwat S B , Jaspal D . Application of biodegradable materials in oil-spill cleanup: recent advances and future perspectives. Advanced Engineering Materials, 2023, 25(20): 2300315

[3] Jernelöv A . How to defend against future oil spills. Nature, 2010, 466(7303): 182–183

[4] Schrope M. Deepwater Horizon: a Scientist at the Centre of the Spill. London: Nature, 2010

[5] Kaur S , Gopal R , Ng W J , Ramakrishna S , Matsuura T . Next-generation fibrous media for water treatment. MRS Bulletin, 2008, 33(1): 21–26

[6] Lu H , Pan Z , Wang H , Liu Y , Dai P , Yang Q . Fiber coalescence treatment of oily wastewater: a new theory and application. Journal of Hazardous Materials, 2021, 412: 125188

[7] Šećerov Sokolović R , Sokolović S , Šević S . Oily water treatment using a new steady-state fiber-bed coalescer. Journal of Hazardous Materials, 2009, 162(1): 410–415

[8] Manica R , Connor J N , Carnie S L , Horn R G , Chan D Y C . Dynamics of interactions involving deformable drops: hydrodynamic dimpling under attractive and repulsive electrical double layer interactions. Langmuir, 2007, 23(2): 626–637

[9] Eggers J , Lister J R , Stone H A . Coalescence of liquid drops. Journal of Fluid Mechanics, 1999, 401: 293–310

[10] Wu M , Cubaud T , Ho C M . Scaling law in liquid drop coalescence driven by surface tension. Physics of Fluids, 2004, 16(7): L51–L54

[11] Zhang Y , Yan S , Yang X , Bai Z . Hydrodynamics and morphologies of droplets coalescence on fiber. AIChE Journal, 2022, 68(7): e17673

[12] Rayleigh L . On the instability of jets. Proceedings of the London Mathematical Society, 1878, 1(1): 4–13

[13] Brik M , Harmand S , Zaaroura I , Saboni A . Experimental and numerical study for the coalescence dynamics of vertically aligned water drops in oil. Langmuir, 2021, 37(10): 3139–3147

[14] Chireux V , Tordjeman P , Risso F . Bridge expansion after coalescence of two droplets in air: inertial regime. Physics of Fluids, 2021, 33(6): 062112

[15] Luo X , Xu K , Li W , Huang X , He L . Mixing characteristics and energy conversion in the coalescence process of the two droplets. Chemical Engineering Science, 2022, 248: 117153

[16] Zhang Y , Yang C , Yuan S , Yao X , Chao Y , Cao Y , Song Q , Sauret A , Binks B P , Shum H C . Effects of particle size on the electrocoalescence dynamics and arrested morphology of liquid marbles. Journal of Colloid and Interface Science, 2022, 608: 1094–1104

[17] Coons J E , Halley P J , McGlashan S A , Tran-Cong T . Scaling laws for the critical rupture thickness or common thin films. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2005, 263(1): 258–266

[18] Manev E D , Nguyen A V . Critical thickness of microscopic thin liquid films. Advances in Colloid and Interface Science, 2005, 114: 133–146

[19] Bai H , Tian X , Zheng Y , Ju J , Zhao Y , Jiang L . Direction controlled driving of tiny water drops on bioinspired artificial spider silks. Advanced Materials, 2010, 22(48): 5521–5525

[20] Bai H , Sun R , Ju J , Yao X , Zheng Y , Jiang L . Large-scale fabrication of bioinspired fibers for directional water collection. Small, 2011, 7(24): 3429–3433

[21] Chen Y , Wang L , Xue Y , Zheng Y , Jiang L . Bioinspired spindle-knotted fibers with a strong water-collecting ability from a humid environment. Soft Matter, 2012, 8(45): 11450–11454

[22] Lee C L , Chan T S , Carlson A , Dalnoki-Veress K . Multiple droplets on a conical fiber: formation, motion, and droplet mergers. Soft Matter, 2022, 18(7): 1364–1370

[23] Xue Y , Chen Y , Wang T , Jiang L , Zheng Y . Directional size-triggered microdroplet target transport on gradient-step fibers. Journal of Materials Chemistry A: Materials for Energy and Sustainability, 2014, 2(20): 7156–7160

[24] Zhang Y , Yan S , Bai Z . Effect of salt addition on the coalescence process of droplets on fiber. Chemical Engineering Science, 2023, 274: 118628

[25] Narsimhan G . Model for drop coalescence in a locally isotropic turbulent flow field. Journal of Colloid and Interface Science, 2004, 272(1): 197–209

[26] Balachandar S , Eaton J K . Turbulent dispersed multiphase flow. Annual Review of Fluid Mechanics, 2010, 42(1): 111–133

[27] Maggioris D , Goulas A , Alexopoulos A H , Chatzi E G , Kiparissides C . Prediction of particle size distribution in suspension polymerization reactors: effect of turbulence nonhomogeneity. Chemical Engineering Science, 2000, 55(20): 4611–4627

[28] Kalluri R R , Cahela D R , Tatarchuk B J . Comparative heterogeneous contacting efficiency in fixed bed reactors: opportunities for new microstructured systems. Applied Catalysis B: Environmental, 2009, 90(3): 507–515

[29] Singh C J , Mukhopadhyay S , Rengasamy R S . Fibrous coalescence filtration in treating oily wastewater: a review. Journal of Industrial Textiles, 2022, 51(3): 3648S–3682S

[30] Chaudhuri J , Boettcher K , Ehrhard P . Numerical investigation of coalescence filtration: multiphase flow through fibrous structures. Separation and Purification Technology, 2021, 257: 117853

[31] Ajogbeje O J , Stammitti-Scarpone A , Cao S , Akanni T , Ng S , Acosta E J . Separation of emulsions with fibrous filter-coalescers. Langmuir, 2021, 37(25): 7630–7642

[32] Singh C J , Mukhopadhyay S , Rengasamy R S . Oil separation from oil in water emulsion by coalescence filtration using kapok fibre. Environmental Technology, 2023, 44(3): 381–393

[33] Ren H , Xu S , Wu S . Effects of gravity on the shape of liquid droplets. Optics Communications, 2010, 283(17): 3255–3258

[34] Zhang X , Wang H , Davis R H . Collective effects of temperature gradients and gravity on droplet coalescence. Physics of Fluids A: Fluid Dynamics, 1993, 5(7): 1602–1613

[35] Moradi M . Droplet dynamics on a vibrating fiber: a numerical study. Langmuir, 2025, 41(21): 13092–13106

[36] Ray B , Biswas G , Sharma A . Generation of secondary droplets in coalescence of a drop at a liquid-liquid interface. Journal of Fluid Mechanics, 2010, 655: 72–104

[37] Lu Z , Zhang L , Yang X , Ding Z , Bai Z . Retention amount and flow behavior of droplets on cross-fiber intersections during coalescence separation. AIChE Journal, 2024, 70(5): e18317

[38] Archana R , Jeevaraj P S E . Deep learning models for digital image processing: a review. Artificial Intelligence Review, 2024, 57(1): 11

[39] Dargan S , Kumar M , Ayyagari M R , Kumar G . A survey of deep learning and its applications: a new paradigm to machine learning. Archives of Computational Methods in Engineering, 2020, 27(4): 1071–1092

[40] He K , Gkioxari G , Dollár P , Girshick R . Mask R-CNN. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020, 42(2): 386–397

[41] Gharehchobogh B K , Kuzekanani Z D , Sobhi J , Khiavi A M . Flotation froth image segmentation using Mask R-CNN. Minerals Engineering, 2023, 192: 107959

[42] Wen D , Chen W , Yin J , Song Y , Ren M , Wang D . Overlapping bubble detection and tracking method based on convolutional neural network and Kalman filter. Chemical Engineering Science, 2022, 263: 118059

[43] He KZhang XRen SSun J. Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Seattle: IEEE, 2016, 770–778

[44] Lin TDollár PGirshick RHe KHariharan BBelongie S. Feature pyramid networks for object detection. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. Honolulu: IEEE, 2017, 2117–2125

[45] Alzubaidi L , Zhang J , Humaidi A J , Al-Dujaili A , Duan Y , Al-Shamma O , Santamaría J , Fadhel M A , Al-Amidie M , Farhan L . Review of deep learning: concepts, CNN architectures, challenges, applications, and future directions. Journal of Big Data, 2021, 8(1): 53

[46] Wang J , Qian J , Wang H , Sun M , Wu L , Zhong M , Mao Y , Chen Y . Dual-directional small-sampling deep-learning modelling on co-flowing microfluidic droplet generation. Chemical Engineering Journal, 2024, 485: 149467

[47] Omocea I L , Patrascu C , Mihailescu M , Balan C . Coalescence phenomenon at the interface between immiscible fluids. UPB Scientific Bulletin: Series D, 2016, 78: 153–160

[48] Narayan S. Complex droplet interfaces at the microscale: surfactant and hydrodynamic effects in the separation of water-in-oil emulsions. Dissertation for the Doctoral Degree. Saint Paul: University of Minnesota, 2020

[49] Eggers J , Sprittles J E , Snoeijer J H . Coalescence dynamics. Annual Review of Fluid Mechanics, 2024, 57: 61–87

[50] Aarts D G , Lekkerkerker H N , Guo H , Wegdam G H , Bonn D . Hydrodynamics of droplet coalescence. Physical Review Letters, 2005, 95(16): 164503

[51] Paulsen J D , Burton J C , Nagel S R , Appathurai S , Harris M T , Basaran O A . The inexorable resistance of inertia determines the initial regime of drop coalescence. Proceedings of the National Academy of Sciences of the United States of America, 2012, 109(18): 6857–6861

[52] Eddi A , Winkels K G , Snoeijer J H . Influence of droplet geometry on the coalescence of low viscosity drops. Physical Review Letters, 2013, 111(14): 144502

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