Convective and absolute instability of viscoelastic liquid jets

Alhushaybari, Abdullah (2020). Convective and absolute instability of viscoelastic liquid jets. University of Birmingham. Ph.D.

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The instability, and subsequent disintegration, of a column of fluid is of interest in a wide variety of growing applications. Despite over 200 years of scientific scrutiny, the instability of a liquid jet remains an active area of study for many researchers from a wide range of scientific disciplines. The last few decades have seen a growth in novel techniques for examining the absolute instability of liquid jets, in many such cases, these methods are intractable. In this thesis, the convective and absolute instability of a viscoelastic liquid jet falling under gravity is examined for axisymmetrical disturbances. We use the upper-convected Maxwell model to provide a mathematical description of the dynamics of a viscoelastic liquid jet. An asymptotic approach, based on the slenderness of the jet, is used to obtain the steady-state solutions. By considering traveling wave modes, we derive a dispersion relationship relating the frequency to the wavenumber of disturbances which is then solved numerically using the Newton-Raphson method. We show the effect of changing a number of dimensionless parameters on convective and absolute instability. In this work, we use a mapping technique developed by Kupfer et al. (1987) to find the cusp point in the complex frequency plane and its corresponding saddle point (the pinch point) in the complex wavenumber plane for absolute instability. The convective/absolute instability boundary is identified for various parameter regimes. We then extend this by including the effect of the surrounding gas, using insoluble surfactants, and immersing the viscoelastic jet into another viscoelastic fluid.

Type of Work: Thesis (Doctorates > Ph.D.)
Award Type: Doctorates > Ph.D.
Licence: All rights reserved
College/Faculty: Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department: School of Mathematics
Funders: None/not applicable
Subjects: Q Science > QA Mathematics


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