Modeling of the collision of a concentrated suspension droplet with a substrate


Аuthors

Zharikov D. S.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: dimazharikov10@gmail.com

Abstract

This study presents a numerical investigation of the impact of a dilatant suspension droplet on a solid surface, accounting for the non-Newtonian flow behavior. Accurate prediction of the behavior of concentrated suspensions under impact and rapid mechanical loading is important for applications such as functional coating deposition, spraying of industrial formulations, and the development of impact-resistant materials based on shear-thickening fluids. The aim of this study is to investigate the effect of shear thickening on the deformation and spreading dynamics of a dilatant suspension droplet upon impact with a solid surface, as well as to assess the applicability of the numerical approach to practical engineering and industrial applications. The Volume of Fluid (VOF) method was used to model the two-phase flow. The dependence of effective viscosity on the local shear rate was implemented using a user-defined function (UDF), while the transport of a history-dependent variable was modeled using a user-defined scalar (UDS). Suspensions with different volume fractions of the dispersed phase were considered, with rheological parameters determined from experimental data. The numerical results show that accounting for shear thickening improves the prediction of droplet shape evolution and its interaction with a solid surface. Comparison with the data reported in the original study further supports the applicability of the numerical approach. 
The results can be used in further numerical simulations of the impact of concentrated non-Newtonian suspension droplets on solid surfaces, particularly in the development of protective and impact-absorbing materials, where deformation, spreading, and energy dissipation under rapid mechanical loading play an important role.

Keywords:

rheology; droplet impact; suspension; numerical modeling; shear thickening; Navier-Stokes equations

References

  1. Ye Q., Tiedje O., Shen B., Domnick J. Impact of viscous droplets on dry and wet substrates for spray painting processes // Fluids. 2025. Vol. 10, no. 5. Article no. 131. DOI: 10.3390/fluids10050131.
  2. Mundo Ch., Sommerfeld M., Tropea C. Droplet-wall collisions: experimental studies of the deformation and breakup process // International Journal of Multiphase Flow. 1995. Vol. 21, no. 2. P. 151–173.
  3. Derby B. Inkjet printing of functional and structural materials: fluid property requirements, feature stability, and resolution // Annual Review of Materials Research. 2010. Vol. 40. P. 395–414.
  4. Kim J. Spray cooling heat transfer: The state of the art // International Journal of Heat and Fluid Flow. 2007. Vol. 28, no. 4. P. 753–767.
  5. Boyer F., Sandoval-Nava E., Snoeijer J. H., Dijksman J. F., Lohse D. Drop impact of shear thickening liquids // Physical Review Fluids. 2016. Vol. 1, no. 1. Article no. 013901. DOI: 10.1103/PhysRevFluids.1.013901.
  6. Rioboo R., Tropea C., Marengo M. Outcomes from a drop impact on solid surfaces // Atomization and Sprays. 2001. Vol. 11, no. 2. P. 155–165.
  7. Josserand C., Thoroddsen S. T. Drop impact on a solid surface // Annual Review of Fluid Mechanics. 2016. Vol. 48. P. 365–391.
  8. Grishaev V., Iorio C. S., Dubois F., Amirfazli A. Complex drop impact morphology // Langmuir. 2015. Vol. 31, no. 36. P. 9833–9844. DOI: 10.1021/acs.langmuir.5b02162.
  9. Piskunov M. V., Semyonova A. E., Khomutov N. A., Ashikhmin A. E., Yanovsky V. A. Effect of rheology and interfacial tension on spreading of emulsion drops impacting a solid surface // Physics of Fluids. 2021. Vol. 33, no. 8. Article no. 083309. DOI: 10.1063/5.0059079.
  10. Ashikhmin A., Khomutov N., Volkov R., Piskunov M., Strizhak P. Effect of monodisperse coal particles on the maximum drop spreading after impact on a solid wall // Energies. 2023. Vol. 16, no. 14. Article no. 5291. DOI: 10.3390/en16145291.
  11. Hirt C. W., Nichols B. D. Volume of fluid (VOF) method for the dynamics of free boundaries // Journal of Computational Physics. 1981. Vol. 39, no. 1. P. 201–225.
  12. Brackbill J. U., Kothe D. B., Zemach C. A continuum method for modeling surface tension // Journal of Computational Physics. 1992. Vol. 100, no. 2. P. 335–354.
  13. Lunkad S. F., Buwa V. V., Nigam K. D. P. Numerical simulations of drop impact and spreading on horizontal and inclined surfaces // Chemical Engineering Science. 2007. Vol. 62, no. 24. P. 7214–7224.
  14. Vozhakov I. S., Misyura S. Y., Morozov V. S., Piskunov M. V., Piskunova A. E., Orlova E. G., Mullyadzhanov R. I. High-speed droplet impact on solid surfaces: review on the prospects of modeling fluid flow // Experiments in Fluids. 2025. Vol. 66, no. 3. Article no. 65. DOI: 10.1007/s00348-025-03996-0.
  15. Brown E., Jaeger H. M. Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming // Reports on Progress in Physics. 2014. Vol. 77, no. 4. Article no. 046602. DOI: 10.1088/0034-4885/77/4/046602.
  16. Seto R., Mari R., Morris J. F., Denn M. M. Discontinuous shear thickening of frictional hard-sphere suspensions // Physical Review Letters. 2013. Vol. 111, no. 21. Article no. 218301. DOI: 10.1103/PhysRevLett.111.218301.
  17. Wyart M., Cates M. E. Discontinuous shear thickening without inertia in dense non-Brownian suspensions // Physical Review Letters. 2014. Vol. 112, no. 9. Article no. 098302. DOI: 10.1103/PhysRevLett.112.098302.
  18. Guémas M., Marín A. G., Lohse D. Drop impact experiments of non-Newtonian liquids on micro-structured surfaces // Soft Matter. 2012. Vol. 8, no. 41. P. 10725–10731. DOI: 10.1039/C2SM26230D.
  19. Patankar S. V. Numerical heat transfer and fluid flow. Boca Raton: CRC Press, 2018. 214 p.
  20. Youngs D. L. Time-dependent multi-material flow with large fluid distortion // Numerical Methods for Fluid Dynamics / ed. by K. W. Morton, M. J. Baines. New York: Academic Press, 1982. P. 273–285.
  21. Hoffman R. L. A study of the advancing interface. I. Interface shape in liquid-gas systems // Journal of Colloid and Interface Science. 1975. Vol. 50, no. 2. P. 228–241. DOI: 10.1016/0021-9797(75)90225-8.
  22. Kistler S. F. Hydrodynamics of wetting // Wettability / ed. by J. C. Berg. New York: Marcel Dekker, 1993. P. 311–429.
  23. Mobaseri A., Kumar S., Cheng X. Maximum spreading of impacting shear-thinning and shear-thickening drops // Proceedings of the National Academy of Sciences of the United States of America. 2025. Vol. 122, no. 22. Article no. e2500163122. DOI: 10.1073/pnas.2500163122.
  24. Crawford N. C., Popp L. B., Johns K. E., Caire L. M., Peterson B. N., Liberatore M. W. Shear thickening of corn starch suspensions: Does concentration matter? // Journal of Colloid and Interface Science. 2013. Vol. 396. P. 83–89. DOI: 10.1016/j.jcis.2013.01.024.
  25. Cho J. H., Griese A. H., Peters I. R., Bischofberger I. Lasting effects of discontinuous shear thickening in cornstarch suspensions upon flow cessation // Physical Review Fluids. 2022. Vol. 7, no. 6. Article no. 063302. DOI: 10.1103/PhysRevFluids.7.063302.
  26. Popinet S. An accurate adaptive solver for surface-tension-driven interfacial flows // Journal of Computational Physics. 2009. Vol. 228, no. 16. P. 5838–5866. DOI: 10.1016/j.jcp.2009.04.042.


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