Weakly nonlinear shape oscillations of viscoelastic drops

Dino Zrnic, Günter Brenn*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Axisymmetric shape oscillations of a viscoelastic drop in a vacuum are studied by a weakly nonlinear analysis. The two-lobed initial drop deformation mode is studied. The Oldroyd-B model is used for characterizing the drop liquid rheological behaviour. The equations of motion and the solutions up to second order are developed, where elastic effects appear. Solutions of the characteristic equation are validated against the decay rate and frequency of damped shape oscillations of polymer solution drops in an acoustic levitator. The theory shows enhancing or dampening of the nonlinear behaviour and enhanced mode coupling, as compared with the Newtonian case. The study reveals an excess time in the prolate shape and a frequency change, together with a quasi-periodicity of the oscillations. The Fourier power spectra of traces of the drop north pole position in time show mode coupling as a nonlinear effect. At moderate stress-relaxation Deborah number, the resultant drop motion for large Ohnesorge number, suggesting aperiodic drop behaviour, may nonetheless be oscillatory, where the drop elasticity is owing to the liquid bulk elasticity instead of surface tension. A method is developed to predict the oscillatory or aperiodic behaviour of a drop of a given size from a rheologically characterized viscoelastic Oldroyd-B liquid.
Original languageEnglish
Article number20230887
JournalProceedings of the Royal Society A
Volume480
Issue number2295
DOIs
Publication statusPublished - 14 Aug 2024

Keywords

  • drop-shape oscillations
  • onset of aperiodic motion
  • quasi-periodic motion
  • viscoelastic liquid
  • weakly nonlinear analysis

ASJC Scopus subject areas

  • General Engineering
  • General Physics and Astronomy
  • General Mathematics

Fields of Expertise

  • Advanced Materials Science

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