Supplementary material from "Weakly nonlinear shape oscillations of viscoelastic drops" ...

• Main Authors: Zrnic, Dino, Dr. Brenn, Günter
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: The Royal Society 2024
• Subjects: Fluid mechanics and thermal engineering not elsewhere classified; North Pole
• Online Access: https://dx.doi.org/10.6084/m9.figshare.c.7399609.v1; https://rs.figshare.com/collections/Supplementary_material_from_Weakly_nonlinear_shape_oscillations_of_viscoelastic_drops_/7399609/1

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 characterising the drop liquid rheological behavior. 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 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 to 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 ...