Modeling liquid droplet impact on a micropillar-arrayed viscoelastic surface via mechanically averaged responses

References

• Basso, B. C., & Bostwick, J. B. (2020). Splashing on soft elastic substrates. Langmuir, 36(49), 15010–15017. https://doi.org/10.1021/acs.langmuir.0c02500
   PubMed Web of Science ®Google Scholar
• Bell, J. B., Colella, P., & Glaz, H. M. (1989). A second-order projection method for the incompressible Navier-Stokes equations. Journal of Computational Physics, 85(2), 257–283. https://doi.org/10.1016/0021-9991(89)90151-4
   Web of Science ®Google Scholar
• Boisly, M., Schuldt, S., Kästner, M., Schneider, Y., & Rohm, H. (2016). Experimental characterisation and numerical modelling of cutting processes in viscoelastic solids. Journal of Food Engineering, 191, 1–9. https://doi.org/10.1016/j.jfoodeng.2016.06.019
   Web of Science ®Google Scholar
• Bussmann, M., Mostaghimi, J., & Chandra, S. (1999). On a three-dimensional volume tracking model of droplet impact. Physics of Fluids, 11(6), 1406–1417. https://doi.org/10.1063/1.870005
   Web of Science ®Google Scholar
• Choi, M., Son, G., & Shim, W. (2017). Numerical simulation of droplet impact and evaporation on a porous surface. International Communications in Heat and Mass Transfer, 80, 18–29. https://doi.org/10.1016/j.icheatmasstransfer.2016.11.002
   Web of Science ®Google Scholar
• Christensen, R. (2012). Theory of viscoelasticity: An introduction. Elsevier.
   Google Scholar
• Chyasnavichyus, M., Young, S. L., & Tsukruk, V. V. (2014). Probing of polymer surfaces in the viscoelastic regime. Langmuir, 30(35), 10566–10582. https://doi.org/10.1021/la404925h
   PubMed Web of Science ®Google Scholar
• Drapaca, C. S., Sivaloganathan, S., & Tenti, G. (2007). Nonlinear constitutive laws in viscoelasticity. Mathematics and Mechanics of Solids, 12(5), 475–501. https://doi.org/10.1177/1081286506062450
   Web of Science ®Google Scholar
• Du, P., Cheng, C., Lu, H., & Zhang, X. (2013). Investigation of cellular contraction forces in the frequency domain using a PDMS micropillar-based force transducer. Journal of Microelectromechanical Systems, 22(1), 44–53. https://doi.org/10.1109/JMEMS.2012.2213070
   Web of Science ®Google Scholar
• Dupont, J. B., & Legendre, D. (2010). Numerical simulation of static and sliding drop with contact angle hysteresis. Journal of Computational Physics, 229(7), 2453–2478. https://doi.org/10.1016/j.jcp.2009.07.034
   Web of Science ®Google Scholar
• Findley, W. N., Lai, J. S., Onaran, K., & Christensen, R. M. (1977). Creep and relaxation of nonlinear viscoelastic materials with an introduction to linear viscoelasticity. Journal of Applied Mechanics, 44(2), 364–364. https://doi.org/10.1115/1.3424077
   Google Scholar
• Ghezelbash, F., Liu, S., Shirazi-Adl, A., & Li, J. (2022). Blood clot behaves as a poro-visco-elastic material. Journal of the Mechanical Behavior of Biomedical Materials, 128, 105101. https://doi.org/10.1016/j.jmbbm.2022.105101
   PubMed Web of Science ®Google Scholar
• Gong, L., Pan, D., & Wang, X. (2021). Finite element modeling of the viscoelastic contact for a composite micropillar. Mechanics of Advanced Materials and Structures, 28(5), 537–549. https://doi.org/10.1080/15376494.2019.1578011
   Web of Science ®Google Scholar
• Guo, Y., Wei, L., Liang, G., & Shen, S. (2014). Simulation of droplet impact on liquid film with CLSVOF. International Communications in Heat and Mass Transfer, 53, 26–33. https://doi.org/10.1016/j.icheatmasstransfer.2014.02.006
   Web of Science ®Google Scholar
• Howland, C. J., Antkowiak, A., Castrejón-Pita, J. R., Howison, S. D., Oliver, J. M., Style, R. W., & Castrejón-Pita, A. A. (2016). It's harder to splash on soft solids. Physical Review Letters, 117(18), 184502. https://doi.org/10.1103/PhysRevLett.117.184502
   PubMed Web of Science ®Google Scholar
• Jepsen, R. A., Yoon, S. S., & Demosthenous, B. (2006). Effects of air on splashing during a large droplet impact: Experimental and numerical investigations. Atomization and Sprays, 16(8), 981–996. https://doi.org/10.1615/AtomizSpr.v16.i8
   Web of Science ®Google Scholar
• Kohlrausch, F. (1863). Ueber die elastische nachwirkung bei der torsion. Annalen Der Physik, 195(7), 337–368. https://doi.org/10.1002/(ISSN)1521-3889
   Google Scholar
• Laan, N., De Bruin, K. G., Bartolo, D., Josserand, C., & Bonn, D. (2014). Maximum diameter of impacting liquid droplets. Physical Review Applied, 2(4), 044018. https://doi.org/10.1103/PhysRevApplied.2.044018
   Web of Science ®Google Scholar
• Langley, K. R., Castrejón-Pita, A. A., & Thoroddsen, S. T. (2020). Droplet impacts onto soft solids entrap more air. Soft Matter, 16(24), 5702–5710. https://doi.org/10.1039/D0SM00713G
   PubMed Web of Science ®Google Scholar
• Lazan, B. J. (1968). Damping of materials and members in structural mechanics. Pergamon Press LTD.
   Google Scholar
• Lee, H. G., & Kim, J. (2015). Two-dimensional Kelvin-Helmholtz instabilities of multi-component fluids. European Journal of Mechanics, B/Fluids, 49, 77–88. https://doi.org/10.1016/j.euromechflu.2014.08.001
   Web of Science ®Google Scholar
• Lee, J. B., Laan, N., De Bruin, K. G., Skantzaris, G., Shahidzadeh, N., Derome, D., Carmeliet, J., & Bonn, D. (2015). Universal rescaling of drop impact on smooth and rough surfaces. Journal of Fluid Mechanics, 786, R4. https://doi.org/10.1017/jfm.2015.620
   Web of Science ®Google Scholar
• Liu, J., Vu, H., Yoon, S. S., Jepsen, R. A., & Aguilar, G. (2010). Splashing phenomena during liquid droplet impact. Atomization and Sprays, 20(4), 297–310. https://doi.org/10.1615/AtomizSpr.v20.i4
   Web of Science ®Google Scholar
• Mandre, S., & Brenner, M. P. (2012). The mechanism of a splash on a dry solid surface. Journal of Fluid Mechanics, 690, 148–172. https://doi.org/10.1017/jfm.2011.415
   Web of Science ®Google Scholar
• Mishra, A., & Patra, N. R. (2018). Time-dependent settlement of pile foundations using five-parameter viscoelastic soil models. International Journal of Geomechanics, 18(5), 04018020. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001122
   Web of Science ®Google Scholar
• Mori, T., & Tanaka, K. (1973). Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 21(5), 571–574. https://doi.org/10.1016/0001-6160(73)90064-3
   Google Scholar
• Nguyen, S. T., Vu, M. H., Vu, M. N., & Nguyen, T. N. (2017). Generalized Maxwell model for micro-cracked viscoelastic materials. International Journal of Damage Mechanics, 26(5), 697–710. https://doi.org/10.1177/1056789515608231
   Web of Science ®Google Scholar
• Osher, S., & Sethian, J. A. (1988). Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79(1), 12–49. https://doi.org/10.1016/0021-9991(88)90002-2
   Web of Science ®Google Scholar
• Parizi, H. B., Rosenzweig, L., Mostaghimi, J., Chandra, S., Coyle, T., Salimi, H., Pershin, L., McDonald, A., & Moreau, C. (2007). Numerical simulation of droplet impact on patterned surfaces. Journal of Thermal Spray Technology, 16(5-6), 713–721. https://doi.org/10.1007/s11666-007-9122-8
   Web of Science ®Google Scholar
• Pasandideh-Fard, M., Qiao, Y. M., Chandra, S., & Mostaghimi, J. (1996). Capillary effects during droplet impact on a solid surface. Physics of Fluids, 8(3), 650–659. https://doi.org/10.1063/1.868850
   Web of Science ®Google Scholar
• Popinet, S. (2003). Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries. Journal of Computational Physics, 190(2), 572–600. https://doi.org/10.1016/S0021-9991(03)00298-5
   Web of Science ®Google Scholar
• Popinet, S. (2009). An accurate adaptive solver for surface-tension-driven interfacial flows. Journal of Computational Physics, 228(16), 5838–5866. https://doi.org/10.1016/j.jcp.2009.04.042
   Web of Science ®Google Scholar
• Rambausek, M., Mukherjee, D., & Danas, K. (2022). A computational framework for magnetically hard and soft viscoelastic magnetorheological elastomers. Computer Methods in Applied Mechanics and Engineering, 391, 114500. https://doi.org/10.1016/j.cma.2021.114500
   Web of Science ®Google Scholar
• Rioboo, R., Marengo, M., & Tropea, C. (2002). Time evolution of liquid drop impact onto solid, dry surfaces. Experiments in Fluids, 33(1), 112–124. https://doi.org/10.1007/s00348-002-0431-x
   Web of Science ®Google Scholar
• Rioboo, R., Tropea, C., & Marengo, M. (2001). Outcomes from a drop impact on solid surfaces. Atomization and Sprays, 11(2), 12–165. https://doi.org/10.1615/AtomizSpr.v11.i2
   Web of Science ®Google Scholar
• Schapery, R. A. (1962). Approximation methods of transform inversion for viscoelastic stress analysis. Proc Fourth USNat Congr Appl Mech, 2, 1075. https://www.researchgate.net/publication/243783018_Approximate_Methods_of_Transform_Inversion_for_Viscoelastic_Stress_Analysis
   Google Scholar
• Stow, C. D., & Hadfield, M. G. (1981). An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 373(1755), 419–441. https://doi.org/10.1098/rspa.1981.0002
   Google Scholar
• Temam, R. (2001). Navier-Stokes equations: Theory and numerical analysis. American Mathematical Society.
   Google Scholar
• Thoroddsen, S. T., & Sakakibara, J. (1998). Evolution of the fingering pattern of an impacting drop. Physics of Fluids, 10(6), 1359–1374. https://doi.org/10.1063/1.869661
   Web of Science ®Google Scholar
• Wang, M. Y., Wang, X., & Guo, D. (2003). A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 192(1-2), 227–246. https://doi.org/10.1016/S0045-7825(02)00559-5
   Web of Science ®Google Scholar
• Weisensee, P. B., Tian, J., Miljkovic, N., & King, W. P. (2016). Water droplet impact on elastic superhydrophobic surfaces. Scientific Reports, 6(1), 1–9. https://doi.org/10.1038/srep30328
   PubMedGoogle Scholar
• Wildeman, S., Visser, C. W., Sun, C., & Lohse, D. (2016). On the spreading of impacting drops. Journal of Fluid Mechanics, 805, 636–655. https://doi.org/10.1017/jfm.2016.584
   Web of Science ®Google Scholar
• Wineman, A. (2009). Nonlinear viscoelastic solids – a review. Mathematics and Mechanics of Solids, 14(3), 300–366. https://doi.org/10.1177/1081286509103660
   Web of Science ®Google Scholar
• Wu, Z., & Cao, Y. (2017). Dynamics of initial drop splashing on a dry smooth surface. PloS One, 12(5), e0177390. https://doi.org/10.1371/journal.pone.0177390
   PubMed Web of Science ®Google Scholar
• Xu, L., Zhang, W. W., & Nagel, S. R. (2005). Drop splashing on a dry smooth surface. Physical Review Letters, 94(18), 184505. https://doi.org/10.1103/PhysRevLett.94.184505
   PubMed Web of Science ®Google Scholar