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Complex Fluids and Complex Flows
September 1, 2009 - June 30, 2010
**2009-2010 IMA Seminar on Complex Fluids and Complex Flows**

** Stirring and mixing: Topology, optimization, and walls**
** Transport and collective dynamics in suspensions of swimming
microorganisms**
** The generalized hydrodynamic theory - transient elasticity
and other examples**
** Transition in inertialess flows of viscoelastic fluids: the
role of uncertainty**
** On spider-man and film casting: the mathematics of free
liquid fibers and films in elongation**
** Are viscoelastic flows under control or out of control?**
** Turbulence transition in shear flows: what can we learn from
pipe flow??**
** Transport & Mixing in
Incompressible Fluid Flows**

September 23, 2009, 11:15am-12:15pm,
Lind Hall
305

Jean-Luc Thiffeault
(Department of Mathematics, University of Wisconsin – Madison
and IMA)

http://www.math.wisc.edu/~jeanluc/

**Stirring and mixing: Topology, optimization, and walls **

Abstract: I review various
aspects of current research, both experimental and
theoretical, on stirring and mixing in fluids. Three main
threads are
followed: 1) How topological features influence mixing
effectiveness;
2) How this leads to novel optimization methods; and 3) How one
has to
be mindful of wall effects, which can dramatically slow down
mixing.

September 30, 2009, 11:15am-12:15pm,
Lind Hall
305

Michael D. Graham
(Department of Chemical and Biological Engineering, University
of Wisconsin – Madison and IMA)

http://www.engr.wisc.edu/che/faculty/graham_michael.html

**Transport and collective dynamics in suspensions of swimming
microorganisms **

Abstract: A suspension of swimming organisms is an example of an active complex fluid. At the global scale, it has been suggested that swimming organisms such as krill can alter mixing in the oceans. At the laboratory scale, experiments with suspensions of swimming cells have revealed characteristic swirls and jets much larger than a single cell, as well as increased effective diffusivity of tracer particles. This enhanced diffusivity may have important consequences for how cells reach nutrients, as it indicates that the very act of swimming toward nutrients alters their distribution. The enhanced diffusivity has also been proposed as a scheme to improve transport in microfluidic devices and might be exploited in microfluidic cell culture of motile organisms or cells. The feedback between the motion of swimming particles and the fluid flow generated by that motion is thus very important, but is as yet poorly understood. In this presentation we describe theory and simulations of hydrodynamically interacting microorganisms that shed some light on the observations. In the dilute limit, simple arguments reveal the dependence of swimmer and tracer velocities and diffusivities on concentration. As concentration increases, we show that cases exist in which the swimming motion generates dramatically enhanced transport in the fluid. This transport is coupled to the existence of long-range correlations of the fluid motion. Furthermore, the mode of swimming matters in a qualitative way: microorganisms pushed from behind by their flagella are predicted to exhibit enhanced transport and long-range correlations, while those pulled from the front are not. A physical argument supported by a mean field theory sheds light on the origin of these effects. These results imply that different types of swimmers have very different effects on the transport of nutrients or chemoattractants in their environment; this observation may be related to the evolution of different modes of swimming.

October 7, 2009, 11:15am-12:15pm, EE/CS
3-180 (Note the change of
room)

Harald Pleiner
(Max Planck Institute for Polymer Research)

http://www.mpip-mainz.mpg.de/~pleiner/

**The generalized hydrodynamic theory - transient elasticity
and other examples **

Abstract: For modeling complex fluids (and more generally soft matter) on the phenomenological level a generalization of the well-known hydrodynamic method is proposed. It preserves the basic thermodynamic rules and linear response structure of ordinary hydrodynamics, but allows the handling of additional mesoscopic degrees of freedom that make those materials 'complex'. This is exemplified by discussing transient elasticity and applying it explicitly to the non-Newtonian behavior of polymers (and colloidal systems). Transient elasticity seems to be the defining physics for those systems and also for yield stress soft matter. As a second example true 2-fluid systems and the problems of their generalized hydrodynamics are briefly described.

October 21, 2009, 11:15am-12:15pm,
Lind Hall 305

Mihailo Jovanovic
(Department of Electrical & Computer Engineering, University of Minnesota)

http://www.umn.edu/~mihailo

**Transition in inertialess flows of viscoelastic fluids: the
role of uncertainty**

Abstract: In this talk a system theoretic approach is used to model and analyze the early stages of transition in inertialess channel flows of viscoelastic fluids. We argue that modeling of uncertainty, such as the approximate nature of polymer constitutive equations, is central to understanding the dynamics of viscoelastic fluids. Robustness with respect to uncertainty is quantified by induced norms from spatio-temporal body forces to components of velocity and polymer stress fluctuations. This input-output approach has strong connections to the analysis of pseudospectra of linear operators in Hilbert space, and it exhibits the importance of streamwise elongated flow patterns in viscoelastic fluids. For streamwise independent fluctuations, we establish an explicit unfavorable scaling of the L2-induced norms with the Weissenberg number. This suggests that small amount of modeling uncertainty can destabilize nominally stable dynamics and promote transition to elastic turbulence. We also demonstrate that small stability margins originate from the stretching of polymer stress fluctuations by a background shear and identify the spatial structure of the most amplified fluctuations. One of the main messages of this talk is that, at the level of velocity fluctuation dynamics, polymer stretching and the Weissenberg number in elasticity-dominated flows of viscoelastic fluids effectively play the role of vortex tilting and the Reynolds number in inertia-dominated flows of Newtonian fluids.

November 4, 2009, 11:15am-12:15pm,
Lind Hall 305

Thomas C. Hagen
(Department of Mathematical Sciences, University of Memphis)

http://www.msci.memphis.edu/~thagen/

**On spider-man and film casting: the mathematics of free
liquid fibers and films in elongation**

Abstract: In this lecture we give an overview of the mathematical theory of free liquid fibers and films of highly viscous liquids in fiber spinning and film casting. The governing equations to be discussed arise as the slender body approximation of the Navier-Stokes equations with moving boundary as 1D or 2D nonlinear coupled hyperbolic-elliptic systems of pdes. Topics of interest in this presentation include existence and uniqueness results, failure of fiber breakup in the purely viscous regime, and spectral determinacy/regularity of the linearized film equations. Some open questions will be motivated.

November 11, 2009, 11:15am-12:15pm,
Lind Hall 305

Michael Renardy
(Mathematics Department,
Virginia Tech)

http://www.math.vt.edu/people/renardym/

**Are viscoelastic flows under control or out of control?**

Abstract: Controllability refers to the ability to steer a system from a prescribed initial state to a desirable final state. The lecture will give an overview of recent results on the controllability of flows of viscoelastic fluids by means of a prescribed body force or prescribed motion of the boundary.

November 18, 2009, 11:15am-12:15pm,
Lind Hall 305

Bruno Eckhardt
(Physics Department, Philipps University Marburg)

http://www.physik.uni-marburg.de/de/forschung/komplexe-systeme/mitarbeiter/eckhardt.html

**Turbulence transition in shear flows: what can we learn from
pipe flow?**

Abstract: According to textbook wisdom, flow down a pipe becomes turbulent near a Reynolds number of about 2000. This simple statement misses many subtleties of the transition: the absence of a linear stability of the laminar flow, the sensitive dependence on perturbations that sometimes succeed and sometimes fail to induce turbulence and the unexpected observation that the turbulent state, once achieved, is not persistent but can decay. All these observations are compatible with the formation of a strange saddle in the state space of the system. I will focus on three aspects: on the appearance of 3-d coherent states, on the information contained in lifetime statistics and on results on the boundary between laminar and turbulent regions. They suggest a generic structuring of state space in flows where turbulent and laminar flow coexist, such as plane Couette flow, Poiseuille flow and perhaps even boundary layers.

January 21, 2010, 3:30pm-4:30pm,
Lind Hall 305

Charlie
Doering (University of
Michigan) and
Jean-Luc Thiffeault (University of
Wisconsin), (occasionally Wednesday as announced), 305 Lind
Hall

**Tag Team Tutorials: Transport & Mixing in
Incompressible Fluid Flows**

3:30pm Thursday (occasionally Wednesday as announced) 305 Lind
Hall

January 21 - April 8, 2010

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