Mathematical Analysis of Viscoelastic Flows

Mathematical Analysis of Viscoelastic Flows

Author: Michael Renardy

Publisher: SIAM

Published: 2000-01-01

Total Pages: 113

ISBN-13: 9780898719413

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This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.


Flow Behavior and Instabilities in Viscoelastic Fluids

Flow Behavior and Instabilities in Viscoelastic Fluids

Author: Boyang Qin

Publisher:

Published: 2018

Total Pages: 0

ISBN-13:

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The flow of complex fluids, especially those containing polymers, is ubiquitous in nature and industry. From blood, plastic melts, to airway mucus, the presence of microstructures such as particles, proteins, and polymers, can impart nonlinear material properties not found in simple fluids like water. These rheological behaviors, in particular viscoelasticity, can give rise to flow anomalies found in industrial settings and intriguing transport dynamics in biological systems. The first part of my work focuses on the flow of viscoelastic fluids in physical systems. Here, I investigate the flow instabilities of viscoelastic fluids in three different geometries and configurations. Realized in microfluidic channels, these experiments mimic flows encountered in technology spanning the oil extraction, pharmaceutical, and chemical industries. In particular, by conducting high-speed velocimetry on the flow of polymeric fluid in a micro-channel, we report evidence of elastic turbulence in a parallel shear flow where the streamline is without curvature. These turbulent-like characteristics include activation of the flow at many time scales, anomalous increase in flow resistance, and enhanced mixing associated with the polymeric flow. Moreover, the spectral characteristics and spatial structures of the velocity fluctuations are different from that in a curved geometry. Measured using novel holographic particle tracking, Lagrangian trajectories show spanwise dispersion and modulations, akin to the traveling waves in the turbulent pipe flow of Newtonian fluids. These curvature perturbations far downstream can generate sufficient hoop stresses to sustain the flow instabilities in the parallel shear flow. The second part of the thesis focuses on the motility and transport of active swimmers in viscoelastic fluids that are relevant to biological systems and human health. In particular, by analyzing the swimming of the bi-flagellated green algae Chlamydomonas reinhardtii in viscoelastic fluid, we show that fluid elasticity enhances the flagellar beating frequency and the wave speed. Yet the net swimming speed of the alga is hindered for fluids that are sufficiently elastic. The origin of this complex response lies in the non-trivial change in flagellar gait due to elasticity. Numerical simulations show that such change in gait reduces elastic stress build up in the fluid and increases efficiency. These results further illustrate the complex coupling between fluid rheology and swimming gait in the motility of micro-organisms and other biological processes such as mucociliary clearance in mammalian airways.


Advances in Heat Transfer

Advances in Heat Transfer

Author: Young I. Cho

Publisher: Academic Press

Published: 2011-11-28

Total Pages: 459

ISBN-13: 0123815290

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Advances in Heat Transfer fills the information gap between regularly scheduled journals and university-level textbooks by providing in-depth review articles over a broader scope than in journals or texts. The articles, which serve as a broad review for experts in the field, will also be of great interest to non-specialists who need to keep up-to-date with the results of the latest research. This serial is essential reading for all mechanical, chemical and industrial engineers working in the field of heat transfer, graduate schools or industry. Provides an overview of review articles on topics of current interest Bridges the gap between academic researchers and practitioners in industry A long-running and prestigious series