Viscoelastic fluids

Vesicles are locally-inextensible fluid membranes that can
sustain bending. We consider the dynamics of flows of
vesicles suspended in Stokesian fluids. We use a boundary
integral formulation for the fluid that results in a set of
nonlinear integro-differential equations for the vesicle dynamics.
The motion of the vesicles is determined by balancing
the nonlocal hydrodynamic forces with the elastic
forces due to bending and tension. Numerical simulations
of such vesicle motions are quite challenging. On one hand,

Keywords: Oldroyd-B, viscoelastic, instabilities,
mixing

The problem of coupling microscopic and continuum-level descriptions of
complex fluids
when the microscopic system exhibits slow relaxation times is
considered. This type of
problem arises whenever the fluid exhibits significant memory effects.
The main difficulty
in this type of multiscale computation is the initialization of
microscopic configurations and
establishing the duration of microscopic evolution that has to be
computed before a continuum
time step can be taken. Density estimation theory is applied to

Traditional hydrodynamic stability studies infer stability of a flow from
a computation of eigenvalues of the linearized system. While this is well
justified for the Navier-Stokes equations, no rigorous result along these lines
is known for general systems of partial differential equations; indeed there are
counterexamples for lower order perturbations of the wave equations. This lecture
will discuss how recent results on advective equations can be applied to creeping

Under the proper conditions, surfactant molecules can self-assemble into
wormlike micelles, resembling slender rods, can entangle and impart
viscoelasticity to the fluid. The behavior of wormlike micelles solutions
is similar to that of polymer solutions. The primary difference being that,
unlike covalently bound polymers, micelles are continuously breaking and
reforming under Brownian fluctuations and the imposed shear or extensional
flow field. In this talk, we will discuss the behavior of a series of

This talk will provide an overview of our recent work on
amplification of disturbances in channel flows of
viscoelastic fluids. Even if a standard linear stability
(i.e., modal) analysis predicts that a particular flow is
stable, the question of the sensitivity of the flow to
various disturbances remains. If disturbances to the
linearized governing equations are sufficiently amplified
over a finite time interval, then nonlinearities may become
important and cause transition to a more complex flow state.

Direct Numerical Simulations (DNS) of turbulent viscoelastic channel flows
typically generate a tremendous volume of information (terabytes per run.
Data reduction is therefore essential in order to allow for an efficient
processing of the data, let alone its preservation for future studies.
However, previous attempts, using a projection of the velocity to the top
Karhunen-Loeve (K-L) modes, failed to produce velocity fields that could
generate the DNS conformation field adequately. In an effort to rectify

Ability to manipulate equilibrium self-assembly and dynamical self-organization in nonlinear systems is of central importance to the success of many emerging technologies. This seminar will focus on flow instability and pattern formation in complex fluids, i.e., fluids with internal microstructure such as solutions/melts of polymers, surfactant/colloidal gels and suspensions.

Keywords: Elasticity, viscoelastic instability, nonlinear transitions,
drag-reducing polymers

Abstract: Taylor-Couette flow (i.e., flow between concentric, rotating
cylinders) has long served as a paradigm for studies of
hydrodynamic stability. For Newtonian fluids, the rich cascade
of transitions from laminar, Couette flow to turbulent flow
occurs through a set of well-characterized flow states that
depend on the Reynolds numbers of both the inner and outer

In this talk results of pressure gradient vs. volume flow rate calculations over a wide range of oscillatory frequencies for oscillatory tube flow of healthy human blood are performed using the non-homogeneous hemorheological model of Moyers-Gonzalez et al. [M.A. Moyers-Gonzalez, R.G. Owens, J. Fang, A non-homogeneous constitutive model for human blood. Part I. Model derivation and steady flow, J. Fluid Mech. 617 (2008) 327–354]. Results at low (2 Hz) oscillatory frequencies are shown to be in close conformity to the experimental data of Thurston [G.B.