Abstract
The computational analysis of the importance of dynamic contact angle on the dynamic of air entrapped and spreading factor of hollow droplet impact is presented in this paper. The transient fluid flow of the impacting droplet is considered in this numerical work. The Semi-Implicit Method for Pressure Linked Equations (SIMPLE) method has been used for solving the governing equations numerically. Through the continuum surface force model, the surface tension force of the droplet is represented. The computational model for droplet simulation is well in line with the experimental findings available in the literature. The parameters of dynamic contact angle for the liquid droplet have been found by comparing with experimental data available in the literature. The findings from this paper suggest that modelling the dynamic contact angle accurately is critical in simulating droplet impact behaviour. The numerical simulation quantitatively captures the experimentally observed spreading behaviour when we use a dynamic contact angle model based on experimental findings. It has been numerical found that the splat size of the hollow droplet impact is independent of cavity size at Eu ˂˂ 1. With the systemic simulation of hollow droplets, an empirical relation has been developed for hollow droplet impact splat size.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability Statement
The authors confirm that this article has no associated data.
References
Arjmandi-Tash, O., Kovalchuk, N.M., Trybala, A., Kuchin, I.V., Starov, V.: Kinetics of Wetting and Spreading of Droplets over Various Substrates. Langmuir 33, 4367–4385 (2017). https://doi.org/10.1021/acs.langmuir.6b04094
Balla, M., Tripathi, M.K., Sahu, K.C.: A numerical study of a hollow water droplet falling in air. Theor. Comput. Fluid Dyn. 34, 133–144 (2020). https://doi.org/10.1007/s00162-020-00517-z
Bennon, W.D., Incropera, F.P.: A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems—II. Application to solidification in a rectangular cavity. Int. J. Heat Mass Transf. 30, 2171–2187 (1987). https://doi.org/10.1016/0017-9310(87)90095-0
Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354 (1992). https://doi.org/10.1016/0021-9991(92)90240-y
Cherepanov, A.N., Solonenko, O.P., Bublik, V.: V: Numerical and analytic investigation of the dynamics of hollow droplet impact onto substrate. Thermophys. Aeromechanics. 15, 631–641 (2008). https://doi.org/10.1007/s11510-008-0012-4
Diana, A., Castillo, M., Brutin, D., Steinberg, T.: Sessile Drop Wettability in Normal and Reduced Gravity. Microgravity Sci. Technol. 24, 195–202 (2012). https://doi.org/10.1007/s12217-011-9295-0
Göhl, J., Mark, A., Sasic, S., Edelvik, F.: An immersed boundary based dynamic contact angle framework for handling complex surfaces of mixed wettabilities. Int. J. Multiph. Flow. 109, 164–177 (2018). https://doi.org/10.1016/j.ijmultiphaseflow.2018.08.001
Gulyaev, I.P., Solonenko, O.P.: Hollow droplets impacting onto a solid surface. Exp. Fluids. 54, (2012). https://doi.org/10.1007/s00348-012-1432-z
Gulyaev, I.P., Solonenko, O.P.: Modelling of the behavior of hollow ZrO2 particles in plasma jet with regard to their thermal expansion. Thermophys. Aeromechanics. 20, 769–782 (2013). https://doi.org/10.1134/s0869864313060140
Ingebrigtsen, T., Toxvaerd, S.: Contact Angles of Lennard-Jones Liquids and Droplets on Planar Surfaces. J. Phys. Chem. C. 111, 8518–8523 (2007). https://doi.org/10.1021/jp0676235
Kamnis, S., Gu, S.: Numerical modelling of droplet impingement. J. Phys. D. Appl. Phys. 38, 3664–3673 (2005). https://doi.org/10.1088/0022-3727/38/19/015
Lee, J.B., Derome, D., Guyer, R., Carmeliet, J.: Modeling the Maximum Spreading of Liquid Droplets Impacting Wetting and Nonwetting Surfaces. Langmuir 32, 1299–1308 (2016). https://doi.org/10.1021/acs.langmuir.5b04557
Li, D., Duan, X., Zheng, Z., Liu, Y.: Dynamics and heat transfer of a hollow droplet impact on a wetted solid surface. Int. J. Heat Mass Transf. 122, 1014–1023 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.017
Li, D., Zhang, D., Zheng, Z.: Numerical analysis of hollow droplet impacts on a dry flat surface. Int. J. Heat Mass Transf. 129, 753–763 (2019). https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.063
Li, D.S., Qiu, X.Q., Zheng, Z.W.: A Numerical Study on Hollow Droplets Impact onto a Solid Substrate. Adv. Mater. Res. 852, 501–505 (2014). https://doi.org/10.4028/www.scientific.net/amr.852.501
Liang, R., Chen, Z.: Dynamics for Droplets in Normal Gravity and Microgravity. Microgravity Sci. Technol. 21, 247–254 (2009). https://doi.org/10.1007/s12217-009-9156-2
Liu, X., Wang, Y., Wang, Z., Sun, H., Luan, Y.: Numerical investigation of two hollow cylindrical droplets vertically impacting on dry flat surface simultaneously. Phys. Fluids. 32, 113305 (2020). https://doi.org/10.1063/5.0024320
Patankar, S.V: Discretization Methods, (2018). https://doi.org/10.1201/9781482234213-3
Patel, V., Yadav, A., Sahoo, S., Thatoi, D., Winczek, J.: A novel fixed-grid interface-tracking algorithm for rapid solidification of supercooled liquid metal. Numer. Heat Transf. Part A Appl. 78, 306–320 (2020). https://doi.org/10.1080/10407782.2020.1791542
Patel, V., Yadav, A., Winczek, J.: Computational study of the effect of spray parameters on adhesion of splat on the stainless street substrate during the impact of molten zirconia droplet. Heat Mass Transf. (2022). https://doi.org/10.1007/s00231-022-03184-4
Planche, M.P., Costil, S., Verdy, C., Coddet, C.: Different spray processes for different Al2O3 coating properties. Appl. Phys. a. 99, 665–671 (2010). https://doi.org/10.1007/s00339-010-5586-3
Roisman, I.V., Opfer, L., Tropea, C., Raessi, M., Mostaghimi, J., Chandra, S.: Drop impact onto a dry surface: Role of the dynamic contact angle. Colloids Surfaces A Physicochem. Eng. Asp. 322, 183–191 (2008). https://doi.org/10.1016/j.colsurfa.2008.03.005
Shetabivash, H., Ommi, F., Heidarinejad, G.: Numerical analysis of droplet impact onto liquid film. Phys. Fluids. 26, 012102 (2014). https://doi.org/10.1063/1.4861761
Shinoda, K., Murakami, H.: Splat Morphology of Yttria-Stabilized Zirconia Droplet Deposited Via Hybrid Plasma Spraying. J. Therm. Spray Technol. 19, 602–610 (2010). https://doi.org/10.1007/s11666-009-9460-9
Shitanishi, K., Hasegawa, K., Kaneko, A., Abe, Y.: Study on Heat Transfer and Flow Characteristic Under Phase-Change Process of an Acoustically Levitated Droplet. Microgravity Sci. Technol. 26, 305–312 (2014). https://doi.org/10.1007/s12217-014-9401-1
Solonenko, O.P., Gulyaev, I.P., Smirnov, A.: V: Plasma processing and deposition of powdered metal oxides consisting of hollow spherical particles. Tech. Phys. Lett. 34, 1050–1052 (2008). https://doi.org/10.1134/s1063785008120183
Vadillo, D.C., Soucemarianadin, A., Delattre, C., Roux, D.C.D.: Dynamic contact angle effects onto the maximum drop impact spreading on solid surfaces. Phys. Fluids. 21, 122002 (2009). https://doi.org/10.1063/1.3276259
Yadav, A., Ghosh, A., Kumar, A.: Experimental and numerical study of thermal field and weld bead characteristics in submerged arc welded plate. J. Mater. Process. Technol. 248, 262–274 (2017). https://doi.org/10.1016/j.jmatprotec.2017.05.021
Yadav, A., Kumar, A., Gupta, P., Sinha, D.K.: Numerical study of temperature distributions and solidification pattern in the weld pool of arc welded plate. Defect Diffus. Forum. 392, 218–227 (2019). https://doi.org/10.4028/www.scientific.net/DDF.392.218
Yadav, A., Patel, R.V., Singh, C.P., Labhasetwar, P.K., Shahi, V.K.: Experimental study and numerical optimization for removal of methyl orange using polytetrafluoroethylene membranes in vacuum membrane distillation process. Colloids Surfaces A Physicochem. Eng. Asp. 635, (2022). https://doi.org/10.1016/j.colsurfa.2021.128070
Yin, H., Sibley, D.N., Thiele, U., Archer, A.J.: Films, layers, and droplets: The effect of near-wall fluid structure on spreading dynamics. Phys. Rev. E. 95, 023104 (2017). https://doi.org/10.1103/PhysRevE.95.023104
Yokoi, K., Vadillo, D., Hinch, J., Hutchings, I.: Numerical studies of the influence of the dynamic contact angle on a droplet impacting on a dry surface. Phys. Fluids. 21, 72102 (2009). https://doi.org/10.1063/1.3158468
Yonemoto, Y., Kunugi, T.: Analytical consideration of liquid droplet impingement on solid surfaces. Sci. Rep. 7, 2362 (2017). https://doi.org/10.1038/s41598-017-02450-4
Yoon, I., Shin, S.: Maximal spreading of droplet during collision on particle: Effects of liquid viscosity and surface curvature. Phys. Fluids. 33, 083310 (2021). https://doi.org/10.1063/5.0058816
Acknowledgements
The CSIR-CSMCRI PRIS number for this manuscript is 080/2022. The comments from anonymous reviewers and the editor have greatly improved the content.
Funding
This research received no external funding.
Author information
Authors and Affiliations
Contributions
V.P. and A.Y.—Conceptualization, Methodology, Visualization, Investigation, Data curation, Writing—original draft, Writing—review & editing S.S. and D.T.—Visualization.
Corresponding author
Ethics declarations
Competing of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Ethics approval
Not applicable.
Consent to Participate
Not applicable.
Consent for Publication
We here give our consent to publish the paper in this journal.
Conflicts of Interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This artcile belongs to the Topical Collection: The effect of gravity on non-equilibrium processes in fluids
Guest Editors: Tatyana Lyubimova, Valentina Shevtsova
Rights and permissions
About this article
Cite this article
Patel, V., Yadav, A., Sahoo, S. et al. Numerical Study on the Effect of Dynamic Contact Angle on Air Entrapment and Spreading of a Hollow Droplet Impacting on a Surface. Microgravity Sci. Technol. 34, 39 (2022). https://doi.org/10.1007/s12217-022-09960-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12217-022-09960-5