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Viscoelastic Flow Computations

During many manufacturing operations, the nature of the flow and deformation experienced by the processed fluid significantly influences the alignment and stretch of polymer molecules. It is therefore essential to gain insight into the link between flow operating conditions and fluid microstructure. Most of the research on numerical methods for the solution of complex viscoelastic flows has concentrated on a purely macroscopic approach, where the equations of fluid dynamics are solved with plausible stress laws. While this approach is useful for understanding the influence of operating conditions on flow rates and stresses, it provides no insight into the fundamental process of molecular interaction with the flow. In the past few years, however, a number of novel micro-macro approaches have been proposed that provide direct insight into the connection between the flow induced microstructure and the imposed flow field. In this approach, the conservation equations are still solved on a macroscopic scale but the viscoelastic stresses are determined from microscopic physics where the polymer molecules are represented by coarse-grained microscopic models. Essentially, stochastic simulation techniques are used to describe the dynamics of these models, from which, information on local stresses can be obtained.

In our research, we have used the micro-macro approach to examine free-surface flows. Free surface flows are ubiquitous in a variety of commercial applications. They occur when a layer of liquid meets a gas at an interface, for instance, in coating, ink-jet printing, fibre spinning, and micropipetting. Frequently, these applications involve liquids that are viscoelastic, because of the presence of polymer as final product (as in coating) or as rheology modifier (as in ink-jet printing). Many of these flows are time dependent; their dynamics are controlled by the elasticity and capillarity of liquid. Modelling such flows requires computational methods that can describe and predict the molecular conformation of polymers, while simultaneously capturing accurately the shape of free surfaces. Development of such algorithms has been a significant focus of our research.

We have also used the spirit of the micro-macro approach to gain insight into the reasons for the breakdown of viscoelastic flow computations, which is typically observed under flow conditions where elastic effects become important. In particular, we have shown that the breakdown of finite element computations for the steady symmetric two-dimensional flow of dilute and ultradilute Oldroyd-B fluids around a cylinder in a channel arises due to a coil-stretch transition experienced by polymer molecules in the wake of the cylinder. This observation provides significant new insight into the origin of the High Weissenberg Number Problem, which is the major cause of our inability to compute the flow of viscoelastic fluids under physically realistic conditions.

Collaborators

1. M. Pasquali, Rice University

Funding

1. Monash Research Fund Postdoctoral Fellowships Scheme, Monash University
2. Cooperative Research Centre for Functional Communication Surfaces (CRC Smartprint)

Conference Presentations and Publications on this topic

3. M. Bajaj, M. Pasquali, and J. R. Prakash, "Coil-stretch transition and the breakdown of computations for viscoelastic fluid flow around a confined cylinder", J. Rheol., 52, 197-223 (2008).

2. M. Bajaj, J. R. Prakash, and M. Pasquali, "A Computational Study of the Effect of Viscoelasticity on Slot-Coating Flow of Dilute Polymer Solutions", J. Non-Newtonian Fluid Mech., 149, 104-123 (2008).

1. M. Bajaj, P. P. Bhat, J. R. Prakash, and M. Pasquali, "Multiscale Simulation of Viscoelastic Free Surface Flows", J. Non-Newtonian Fluid Mech., 140, 87-107 (2006). This paper appears in the "Top 25 Hottest Articles" in this area.


8. J. R. Prakash, Coil-stretch transition and the break down of continuum models, XVth International Workshop on Numerical Methods for Non-Newtonian Flows (IWNMNNF 2007) June 6-10, 2007, Rhodes, Greece.

7. M. Bajaj, M. Pasquali and J. R. Prakash, “Micro-Macro Simulation of Viscoelastic Flows at High Weissenberg Number using the Brownian Configuration Fields Method,” CHEMECA 2006, Auckland, New Zealand, 17 - 20 Sep., 2006.

6. P. P. Bhat, M. Bajaj, J. R. Prakash and M. Pasquali, Numerical analysis of the dynamics of stretching viscoelastic liquid filaments using the micro-macro Brownian Configurations Fields (BCF) method AIChE Annual Meeting, Oct. 30-Nov. 4 2005, Cincinnati, USA

5. M. Bajaj, P. P. Bhat, J. R. Prakash and M. Pasquali, Micro-macro Simulation of Transient Viscoelastic Free Surface Flows using the Brownian Configuration Fields Method, XIVth International Workshop on Numerical Methods for Non-Newtonian Flows Santa Fe, June 12 – 15, 2005, New Mexico U.S.A.

4. M. Bajaj, P. P. Bhat, A. Montesi, J. R. Prakash, and M. Pasquali, Micro-Macro Simulation of Viscoelastic Free Surface Flows, AIChE Annual Meeting, 7–12 November 2004, Austin, USA.

3. M. Bajaj, P. P. Bhat, J. R. Prakash, and Matteo Pasquali, “Micro-Macro simulation of viscoelastic free surface flows using the Brownian configuration fields method,” Fourteenth International Congress on Rheology, 22 Aug. - 27 Aug., 2004, Seoul, South Korea.

2. M. Bajaj, M. Pasquali, and J. R. Prakash, Micro-Macro Simulation of Viscoelastic Coating Flows, CRC Smartprint Conference, 6–7 July 2004, Melbourne, Australia.

1. M. Bajaj, J. R. Prakash, and M. Pasquali, Micro-Macro Simulation of Viscoelastic Hele-Shaw Flow, Moving Boundaries 2003, Seventh International Conference on Computational Modelling of Free and Moving Boundary Problems, 4 - 6 November 2003, Sante Fe, USA.