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Numerical analysis of the drop impact onto a liquid film of non-linear viscoelastic fluids

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Abstract

This paper numerically analyzes the crown formation due to a plane two-dimensional drop impact onto a pre-existing film in a viscoelastic fluid. The finite volume method is applied to solve the governing equations, and the volume of fluid technique is utilized to track the liquid’s free surface. Here, the non-linear Giesekus model is used as the constitutive equation for the viscoelastic phase. The formation and temporal evolution of the crown’s parameters are evaluated using fluid elasticity and non-linear viscometric functions. The results show that a rise in the Weissenberg number, the viscosity ratio, the Weber number, and the mobility factor of the viscoelastic fluid leads to an increase in both the dimensionless height and radius of the crown, while increasing the Bond number leads to a decrease in the growth of the crown’s dimensions. Moreover, by increasing the film’s thickness, the crown’s height increases, while the crown’s radius decreases. One of the main findings of the present study is that the fluid’s elasticity and surface tension forces enhance the crown’s propagation.

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Abbreviations

\(Bo\) :

The Bond number

\(D\) :

The drop’s diameter

\(\bf g\) :

Acceleration of gravity

\(h\) :

The film’s thickness

\(H\) :

The dimensionless thickness of the film

\(p\) :

Pressure

\(R\) :

The crown’s radius

\(Re\) :

The Reynolds number

\(t\) :

Time

\(U_{0}\) :

The drop’s velocity

\(\bf {\bf \text{v}}\) :

The velocity vector

\(Z\) :

The crown’s height

\(We\) :

The Weber number

\(Wi\) :

The Weissenberg number

\(\alpha\) :

The mobility factor

\(\beta\) :

The viscosity ratio

\(\phi\) :

The volume fraction

\(\eta\) :

The viscosity

\(\kappa\) :

The interface’s curvature

\(\lambda\) :

The relaxation time

\(\rho\) :

The density

\(\sigma\) :

Surface tension

\(\bf \uptau\) :

Stress tensor

\(p\) :

Polymer

\(s\) :

Solvent

References

  1. Rieber M, Frohn A (1999) A numerical study on the mechanism of splashing. Int J Heat Fluid Flow 20(5):455–461

    Article  Google Scholar 

  2. Nikolopoulos N, Theodorakakos A, Bergeles G (2005) Normal impingement of a droplet onto a wall film: a numerical investigation. Int J Heat Fluid Flow 26(1):119–132

    Article  Google Scholar 

  3. Coppola G, Rocco G, de Luca L (2011) Insights on the impact of a plane drop on a thin liquid film. Phys Fluids 23(2):022105

    Article  Google Scholar 

  4. Guo Y, Lian Y, Sussman M (2016) Investigation of drop impact on dry and wet surfaces with consideration of surrounding air. Phys Fluids 28(7):073303

    Article  Google Scholar 

  5. Raman KA, Jaiman RK, Lee TS, Low HT (2015) On the dynamics of crown structure in simultaneous two droplets impact onto stationary and moving liquid film. Comput Fluids 107:285–300

    Article  MathSciNet  Google Scholar 

  6. Worthington AM (1908) A study of splashes. Longmans, Green, and Company, New York

    Google Scholar 

  7. Manzello SL, Yang JC (2002) An experimental study of a water droplet impinging on a liquid surface. Exp Fluids 32(5):580–589

    Article  Google Scholar 

  8. Rein M (1993) Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dyn Res 12(2):61–93

    Article  Google Scholar 

  9. Rein M (1995) Wave phenomena during droplet impact. In: Morioka S, Van Wijngaarden L (eds) IUTAM symposium on waves in liquid/gas and liquid/vapour two-phase systems. Springer, Dordrecht, pp 171–190

    Chapter  Google Scholar 

  10. Cossali GE, Coghe A, Marengo M (1997) The impact of a single drop on a wetted solid surface. Exp Fluids 22(6):463–472

    Article  Google Scholar 

  11. Wang A-B, Chen C-C (2000) Splashing impact of a single drop onto very thin liquid films. Phys Fluids 12(9):2155–2158

    Article  Google Scholar 

  12. Rioboo R, Bauthier C, Conti J, Voué M, De Coninck J (2003) Experimental investigation of splash and crown formation during single drop impact on wetted surfaces. Exp Fluids 35(6):648–652

    Article  Google Scholar 

  13. Yarin AL, Weiss DA (2006) Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity. J Fluid Mech 283:141–173

    Article  Google Scholar 

  14. Levin Z, Hobbs PV (1971) Splashing of water drops on solid and wetted surfaces: hydrodynamics and charge separation. Philos Trans R Soc Lond Ser A Math Phys Sci 269(1200):555–585

    Google Scholar 

  15. Cossali GE, Marengo M, Coghe A, Zhdanov S (2004) The role of time in single drop splash on thin film. Exp Fluids 36(6):888–900

    Article  Google Scholar 

  16. Josserand C, Zaleski S (2003) Droplet splashing on a thin liquid film. Phys Fluids 15(6):1650–1657

    Article  Google Scholar 

  17. Trujillo MF, Lee CF (2001) Modeling crown formation due to the splashing of a droplet. Phys Fluids 13(9):2503–2516

    Article  MathSciNet  Google Scholar 

  18. Roisman IV, Tropea C (2002) Impact of a drop onto a wetted wall: description of crown formation and propagation. J Fluid Mech 472:373–397

    Article  MathSciNet  Google Scholar 

  19. Mukherjee S, Abraham J (2007) Crown behavior in drop impact on wet walls. Phys Fluids 19(5):052103

    Article  Google Scholar 

  20. Lampe J, DiLalla R, Grimaldi J, Rothstein JP (2005) Impact dynamics of drops on thin films of viscoelastic wormlike micelle solutions. J Nonnewton Fluid Mech 125(1):11–23

    Article  Google Scholar 

  21. Tomé MF, Grossi L, Castelo A, Cuminato JA, McKee S, Walters K (2007) Die-swell, splashing drop and a numerical technique for solving the Oldroyd B model for axisymmetric free surface flows. J Nonnewton Fluid Mech 141(2):148–166

    Article  Google Scholar 

  22. Tomé MF, McKee S, Walters K (2010) A computational study of some rheological influences on the “splashing experiment.” J Nonnewton Fluid Mech 165(19):1258–1264

    Article  Google Scholar 

  23. Izbassarov D, Rosti ME, Ardekani MN, Sarabian M, Hormozi S, Brandt L, Tammisola O (2018) Computational modeling of multiphase viscoelastic and elastoviscoplastic flows. Int J Numer Meth Fluids 88(12):521–543

    Article  MathSciNet  Google Scholar 

  24. Komeili Birjandi A, Norouzi M, Kayhani MH (2017) A numerical study on drop formation of viscoelastic liquids using a nonlinear constitutive equation. Meccanica 52(15):3593–3613

  25. Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39(1):201–225

    Article  Google Scholar 

  26. Berberović E, van Hinsberg NP, Jakirlić S, Roisman IV, Tropea C (2009) Drop impact onto a liquid layer of finite thickness: dynamics of the cavity evolution. Phys Rev E 79(3):036306

    Article  MathSciNet  Google Scholar 

  27. Habla F, Marschall H, Hinrichsen O, Dietsche L, Jasak H, Favero JL (2011) Numerical simulation of viscoelastic two-phase flows using openFOAM®. Chem Eng Sci 66(22):5487–5496

    Article  Google Scholar 

  28. Shonibare O (2017) Numerical simulation of viscoelastic multiphase flows using an improved two-phase flow solver. PhD dissertation, Michigan Technological University. https://doi.org/10.37099/mtu.dc.etdr/382

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    M. R. Rezaie, M. Norouzi & M. H. Kayhani

  2. Chemical Engineering Department, Laval University, Quebec, G1V 0A6, Canada

    S. M. Taghavi

Authors
  1. M. R. Rezaie
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  2. M. Norouzi
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  3. M. H. Kayhani
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  4. S. M. Taghavi
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Correspondence to M. Norouzi.

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Appendices

Appendix 1

The MATLAB code for image processing of the results is as follows:

figure a
figure b

Appendix 2

Figure 20 illustrates that the volumes of the two phases are conserved.

Fig. 20
figure 20

Time variation in the volume fraction

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Rezaie, M.R., Norouzi, M., Kayhani, M.H. et al. Numerical analysis of the drop impact onto a liquid film of non-linear viscoelastic fluids. Meccanica 56, 2021–2038 (2021). https://doi.org/10.1007/s11012-021-01363-x

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