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NONLINEAR STABILITY ANALYSIS OF VISCOUS NEWTONIAN AND NON-NEWTONIAN VISCOELASTIC SHEETS

by KONGARA VEERA VENKATA, SATYA SRINIVASU

Abstract (Summary)
A model for instability and breakup of a planar liquid sheet injected in a co-flowing air stream is presented. Both viscous Newtonian and viscoelastic non-Newtonian liquid sheets are considered. The Jeffery’s model is used to describe the viscoelastic behavior of the liquid. A perturbation expansion method, with the initial magnitude of the disturbance as the perturbation parameter, is used to analyze the sheet stability characteristics. The unperturbed liquid sheet is considered to move at a uniform axial velocity. The temporal evolution of the sheet in response to a small disturbance imposed on its surface is tracked until sheet breakup. The model is validated by comparing our predictions with other theoretical analyses available in literature for several limiting cases. Further validation is carried out by comparing the predictions with breakup length measurements available in the literature for sheets injected in still air as well as in co-flowing air stream. Earlier instability analyses based on a linear theory predict that the non-Newtonian liquid sheets are always more unstable compared to Newtonian sheets under identical flow conditions. However, this is not consistent with experimental observations where non-Newtonian sheet have been found to be more stable compared to Newtonian sheets under certain conditions. The present nonlinear model correctly captures this sheet breakup behavior. Results show that the breakup lengths of the viscoelastic sheets are higher than that of the viscous Newtonian sheets until a certain Weber number and the behavior is reversed at higher Weber numbers. This behavior is observed for a liquid sheet emanating in stagnant air as well as in a co-flowing air stream. The initial disturbance amplitude has a significant effect on the breakup length and as the initial disturbance amplitude increases the breakup length of the sheets decreases. For viscoelastic sheets the sheet breakup length increases with decreasing time constant ratio at low Weber numbers. However, the behavior is opposite at higher Weber numbers. For low liquid Weber number, the Ohnesorge number has only marginal effect on the breakup of viscoelastic sheets.
Bibliographical Information:

Advisor:

School:University of Cincinnati

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:nonlinear atomization viscoelastic

ISBN:

Date of Publication:01/01/2006

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