FCF Research Group
Areas of Research

Instabilities and Nonlinear Dynamics of Polymeric Fluid Flows

Turbulence and Coherent Structures in Polymer Solutions

Fluid turbulence is often referred to as the last great unsolved problem of classical physics. Despite the importance of turbulence in varied scientific fields, the phenomenon is still poorly understood. One attempt at gaining a better understanding of turbulence focuses on the coherent structures seen in both experiment and direct numerical simulation (DNS) of fluid flows. Recent research by F. Waleffe and others has found exact stationary (in a moving frame) solutions to the Navier-Stokes equation that are linked to the coherent structures observed in turbulence. The study of these exact coherent states leads to a better understanding of the coherent structures and their role in the dynamics of turbulence.

The research in our group focuses on how these exact coherent states are affected by rheologically complex additives, such as polymers. It has been known since the 1940's that the addition of a very small amount of polymer (10-500 ppm) to a simple fluid can produce dramatic effects in turbulent flow without appreciably changing the properties measured in laminar flow. One of the more industrially important effects is drag reduction, the suppression of skin friction in turbulent flow due to additives. By studying the effect of polymers on these coherent states, we hope to gain a better understanding of the mechanisms responsible for drag reduction.

The image above shows an "exact coherent state" in plane Couette flow (see Stone, P. A. and Graham, M. D., Phys. Fluids, 15, 1247-1256 (2003) for details). This flow captures the dominant structure of the turbulent buffer region: wavy streaks in the streamwise direction flanked by counter-rotating vortices

Movie showing the suppression of viscoelastic Dean flow instability by oscillatory axial shear flow (click here).

Snapshot of an azimuthal cross-section of the destabilizing disturbance of viscoelastic circular Couette flow with superimposed axial pressure driven flow.

Elasticity-Driven Instabilities in Polymeric Liquids

Polymer processing applications, especially coating processes, are susceptible to instabilities that arise purely from the elasticity of the polymeric liquid. We are working to gain a better fundamental understanding of instabilities and nonlinear dynamics in polymeric flows, as well as to develop strategies for suppressing them. Examples of our recent work in this area are as follows:

• Prediction of the existence of stationary, spatially localized, "point defect" vortex pair patterns in viscoelastic circular Couette flow. These solutions are very strongly localized, are isolated in parameter space from the trivial solutions in Couette flow, exist for large and even infinite wavelengths, and show a hysteretic character in the Weissenberg number, similar to experimentally observed "diwhirl" patterns. These new patterns may comprise, along with oscillatory patterns arising via linear instability, the fundamental building blocks of complex spatiotemporal dynamics in polymeric flows.
• Theoretical prediction that addition of a relatively weak steady or oscillatory flow in the direction transverse to the main flow can lead to significant stabilization of flow. We have elucidated, using asymptotic analysis and full numerical simulations, the detailed mechanism underlying the stabilization. In effect, the very elasticity that drives instability can also be used to suppress it.
• Elucidation of a novel mechanism for viscoelastic free surface instabilities like those observed in the filament stretching rheometer, an important new device for characterizing elastic polymer solutions. The mechanism we have described may also play a role in other polymer flow phenomena, such as the knife-edged shape of the rear of a bubble rising in a viscoelastic fluid.
• Complete exact solution of the normal mode stability problem for viscoelastic plane Couette flow, including the modes in the continuous spectrum. The stress fields are not integrable, explaining some of the numerical difficulties and spurious instabilities found in transient computations of viscoelastic flows.

Wall Slip and Viscoelastic Flow Instability

In extrusion of polymer melts and solutions, flow instabilities occur that lead to undesirable distortions of the surface; experiments link these instabilities to slip of the polymeric liquid relative to the solid surfaces of the extruder. Both the mechanisms of slip at the molecular level (e.g. desorption and disentanglement) and its consequences at the macroscopic level have been active and controversial research topics in the last decade. Recent work by our group in this area includes:

• Prediction of a new mechanism for flow-induced enhancement of concentration fluctuations in concentrated polymer solutions. We have shown theoretically that in flows with slip, an instability develops at high shear rate that leads to large concentration fluctuations localized near the polymer/solid interface. This result captures the main features of recent and previously unexplained experimental observations in polystyrene solutions. This new mechanism may be of practical importance in processing of entangled polymeric materials.
• Establishment of criteria for determining whether or not a given mathematical model of slip in polymer flow will lead to small scale (short wavelength) flow instabilities, and in particular, demonstrating that a particular model that we developed leads to flow instability, agreeing qualitatively with experimentally observed trends.
• Demonstration of the role of stress-induced desorption of polymer chains in the transition from weak to strong slip.

Flow and Transport Fundamentals for Complex Fluids

Microstructural and Multiscale Simulations of Polymeric Liquids in Flow (with J. J. de Pablo)

Microfluidic devices such as those used in DNA sequencing typically involve the transport of a complex fluid through a geometry whose dimensions are on the order of the underlying microstructure (DNA molecules, blood cells, proteins, etc.)  Consider, for example, the flow cell shown at right, which was built in collaboration with D. C. Schwartz.  In this case, the microstructure is fluorescently stained 300 micron DNA molecules.  The width of the channel ranges from 50 microns down to 25 microns, or 1/12th of the length scale of the microstructure.  When analyzing or designing  these devices, one is concerned with overall fluid properties (pressure drop required for a given flow rate) as well as microstructural detail (wall adsorption, diffusion, and configuration of the microstructure).

In general, processes which involve the transport of complex materials contain a wide spectrum of time and length scales, and the level of description used to model the process depends on the information one wishes to obtain.  Choices range from atomistic descriptions, which are unable to resolve the long length and time scales of realistic problems, to purely continuum descriptions, in which one ``gives up'' molecular detail in favor of a closed-form relation.

We, in collaboration with Professor Juan J. de Pablo, take an intermediate approach, in which the microstructure is represented via Brownian dynamics, while the fluid is treated as a thermal continuum which acts on the microstructure through the local velocity gradient tensor and a sequence of random fluctuations.  The microstructure in turn acts on the fluid through its contribution to the stress tensor.  These multiscale, or ``Micro-Macro'', simulations allow one to retain important molecular level information, and still resolve the time and length scales of the overall process.

Movie showing mixing enhancement in a microchannel through electrochemical method (click here).

Flow and Transport Driven by Tunable Surfactants (with N. L. Abbott)

Marangoni effects are caused by the gradients in the surface tension over the surface.  A number of factors can contribute to the surface tension gradients.  For example, gradients in the temperature, solvent concentration, or electric potential can create gradients in the surface tension.  It occurs in many settings, such as crystal growth, alloy melting, film wetting, and the condensation of immunocompetent mixtures.  Recent years have seen a resurgence in interest in Marangoni flows because of their potential importance for control of fluid motions at the scales characteristic of microfluidic devices.  In particular, the present study is motivated in part by recent demonstrations that electrochemical methods can be used to transform a redox-active surfactant (e.g. FTMA) between states that differ in surface activity and thereby achieve active control of a variety of interfacial phenomena, including Marangoni flows. 

The broad goal of this research project will mainly focus on how to use redox-active surfactant's ``tunability" to explore the possibility of integration the surface tension driven flows into microfluidic units for mixing enhancement, separation, transportation, and analysis.