Skip to main content
SpringerLink
Log in

Numerical predictions of bubble growth in viscoelastic stretching filaments

  • Original Contribution
  • Published:
Rheologica Acta Aims and scope Submit manuscript

Abstract

In this study, we investigate the growth of bubbles within predominately extensional-deformation flows of thin film stretching form. This involves more than one free-surface to the flow (multiple surfaces), typically as inner (bubble) and outer (filament) boundaries that introduces fluid–gas interfacial treatment. Various bubble initial states and locations may be considered. The problem is discretised in space–time through a hybrid-finite element/volume pressure-correction formulation, coupled with an arbitrary Lagrangian–Eulerian (ALE) coupled with VOF scheme to track domain-mesh and free-surface movement. We contrast these results against the results from a complete ALE algorithm. Various fluid-filament materials have been considered, covering such properties as constant viscosity fluids (Newtonian), low-polymeric/high-solvent viscosity Boger-type (Oldroyd-B) fluids and high-polymeric/low-solvent viscosity elastic-type fluids (Oldroyd-B and Phan-Thien/Tanner). Numerical solutions are presented in terms of comparison between algorithms (ALE versus hybrid ALE/VOF), shapes (bubble shapes, filament shapes), contours of extra-stress (magnitude and location), mid-filament radius and extensional viscosity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • Eggers J (1997) Nonlinear dynamics and breakup of free-surface flows. Rev Mod Phys 69:865–929

    Article  CAS  ADS  Google Scholar 

  • Foggler H, Goddard JD (1970) Collapse of spherical cavities in viscoelastic fluids. J Non-Newton Fluid Mech 13:1135–1141

    Google Scholar 

  • Foteinopoulou K, Mavrantzas VG, Tsamopoulos J (2004) Numerical simulation of bubble growth in Newtonian and viscoelastic filaments undergoing stretching. J Non-Newton Fluid Mech 122:177–200

    Article  MATH  CAS  Google Scholar 

  • Foteinopoulou K, Mavrantazas VG, Tsamopoulos J (2005) Numerical simulation of multi-bubble growth in filaments undergoing stretching. In: 5th GRACM international congress on computational mechanics, Limassol, 29 June–1 July

  • Foteinopoulou K, Mavrantazas VG, Tsamopoulos J (2006) Numerical simulation of multi-bubble growth in Newtonian filaments undergoing stretching. Phys Fluids 18:042106

    Article  ADS  CAS  Google Scholar 

  • Kim C (1994) Collapse of spherical bubbles in Maxwell fluids. J Non-Newton Fluid Mech 55:37–58

    Article  CAS  Google Scholar 

  • Lister JR, Stone HA (1998) Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys Fluids 10:2758–2764

    Article  MATH  CAS  MathSciNet  ADS  Google Scholar 

  • Matallah H, Banaai MJ, Sujatha KS, Webster MF (2006) Modelling filament stretching flows with strain-hardening models and sub-cell approximations. J Non-Newton Fluid Mech 134:77–104

    Article  MATH  CAS  Google Scholar 

  • McKinley GH, Sridhar T (2002) Filament-stretching rheometry of complex fluids. Annu Rev Fluid Mech 34:375–415

    Article  MathSciNet  ADS  Google Scholar 

  • Miller E, Clasen C, Rothstein JP (2009) The effect of step-stretch parameters on capillary breakup extensional rheology (CaBER) measurements. Rheol Acta 48:625–639

    Article  CAS  Google Scholar 

  • Rasmussen HK, Hassager O (1999) Three-dimensional simulations of viscoelastic instability in polymeric filaments. J Non-Newton Fluid Mech 82:189–202

    Article  MATH  CAS  Google Scholar 

  • Ryskin G (1990) Dynamics and sound emission of a spherical cavitation bubble in a dilute polymer solution. J Fluid Mech 218:239–263

    Article  MATH  CAS  ADS  Google Scholar 

  • Papanastasiou AC, Scriven LE, Macosko CW (1984) Bubble growth and collapse in viscoelastic liquids analysed. J Non-Newton Fluid Mech 16:53–75

    Article  MATH  CAS  Google Scholar 

  • Pearson G, Middleman S (1977) Elongational flow behaviour of viscoelastic liquids, part I. Modelling of bubble collapse; part II. Definition and measurement of apparent elongational viscosity. AIChE J 23:714–725

    Article  CAS  Google Scholar 

  • Sizaire R, Legat V (1997) Finite element simulation of a filament stretching extensional rheometer. J Non-Newton Fluid Mech 71:89–107

    Article  CAS  Google Scholar 

  • Sujatha KS, Matallah H, Banaai J, Webster MF (2006) Computational predictions for viscoelastic filament stretching flows: ALE methods and free-surface techniques (CM and VOF). J Non-Newton Fluid Mech 137:81–102

    Article  MATH  CAS  Google Scholar 

  • Sujatha KS, Matallah H, Banaai J, Webster MF (2008) Modelling step-strain filament-stretching (CaBER-type) using ALE techniques. J Non-Newton Fluid Mech 148:109–121

    Article  MATH  CAS  Google Scholar 

  • Yao M, McKinley GH (1998) Numerical simulation of extensional deformations of viscoelastic liquid bridges in filament stretching devices. J Non-Newton Fluid Mech 74:47–88

    Article  MATH  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of non-Newtonian Fluid Mechanics, School of Engineering, Swansea University, Singleton Park, SA2 8PP, Swansea, UK

    K. S. Sujatha, H. Matallah, M. F. Webster & P. R. Williams

Authors
  1. K. S. Sujatha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Matallah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. F. Webster
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. R. Williams
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. F. Webster.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sujatha, K.S., Matallah, H., Webster, M.F. et al. Numerical predictions of bubble growth in viscoelastic stretching filaments. Rheol Acta 49, 1077–1092 (2010). https://doi.org/10.1007/s00397-010-0493-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00397-010-0493-2

Keywords

Search

Navigation