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 Eric
S. G. Shaqfeh
Professor of Chemical Engineering and
Mechanical Engineering, Associate Chair of Chemical Engineering
Department of Chemical Engineering
Stauffer III, Rm. 207
723-3764
eric@chemeng.stanford.edu
Ph. D., Stanford University, 1986. Francois
N. Frenkiel Award, 1989, APS/DFD; National Science Foundation
Presidential Young Investigator, 1990-1995; David and Lucile Packard
Fellow, 1991-1996; Camille and Henry Dreyfus Teacher-Scholar Award,
1994; W.M. Keck Foundation Teaching Excellence Award, 1994; Curtis
W. McGraw Award, 1998, ASEE; Ernest Thiele Lecturer, Notre Dame,
1999; Fellow of the American Physical Society, 2000; Van Ness
Lecturer, RPI, 2001
Transport Mechanics of Complex Fluids
Our research program includes the study of different areas associated
with transport in complex fluids including: a) the occurrence
of purely elastic instabilities in polymer flows, b) the micro-dynamics
of polymer molecules, including DNA, in nonequilibrium transport,
and c) the flow behavior of fiber suspensions. Our approach
in these areas includes developing large scale simulations (including
both Brownian dynamics and continuum simulation) of poorly understood
phenomena and then couple these to detailed experiments to elucidate
the important physics in a variety of processes. Ongoing large
projects in these areas include an examination of elastic effects
in coating instabilities, studies of DNA dynamics in mixed flows
with application to scission and sequencing, investigations of
the separation of complex macromolecules in Brownian ratchets
and fabricated post arrays, and molecular simulation of turbulent
drag reduction by polymers and fibers.
" Ribbing"
or "Fingering" in the Flows of Highly Elastic Liquids
(Funded by 3M Corp. and NSF Chemical and Thermal Sciences Division;
Collaboration with Prof. Bamin Khomami, Washington University,
St. Louis)
Careful experiments have demonstrated
that elasticity in flowing liquids can dramatically destabilize
fluid displacement flows common to coating applications. The resulting
"fingers" or "ribs" at the air-fluid interface (as shown below)
result in non-uniform displacement or coating, and render operating
regimes of such processes inaccessible. These instabilities have
been demonstrated, in certain instances, to be "purely elastic"
and therefore qualitatively different than those found in flowing
Newtonian fluids, as they are driven by the intrinsic elasticity
of a polymer solution or melt. Our group has examined elastic
instabilities in a variety of contexts for more than a decade,
and recent large scale simulations of the coating process demonstrate
that the instabilties are at least partially associated with the
formation of elastic boundary layers at the free surface, i.e.
the air-fluid displacement interface. These boundary layers result
in large shape distortion in the bubble and ultimately in sharp
"cusped" interfaces that are harbingers of spanwise breakup and
subsequent fingering.
The Dynamics of Fiber Suspensions in Sedimentation
(Funded by the ACS-PRF; Collaboration with Elizabeth Guazzelli,
ESPCI, Marseille, FRANCE)
For more than a decade, our group has examined the dynamics of
nonBrownian fiber suspensions noting that the flow dynamics under
all types of situations is qualitatively different than that found
in suspensions of spheres. The simplest difference comes in the
effect of hydrodynamic interactions where a given high aspect
ratio fiber can interact with many of its neighbors before it
ever interacts with its opposite end (!). Such semi-dilute fiber
suspensions have properties which are dramatically different than
their Newtonian suspending fluid even at remarkably small volume
fraction. A second profound effect in fiber suspensions is associated
with the mobility or drag coffiecient depending on orientation
for fibers, and thus in sedimentation, fibers move rapidly in
directions perpendicular as well as parallel to gravity.
The consequence of this for a sedimenting suspension of fibers
is that the suspension does not remain homogeneous but spontaneously
forms "clumps" or "packets" which settle more quickly than an
isolated fiber. We have discovered by simulation and theory, as
well as by detailed experiment, that there is a region of particle
concentration where the average sediment velocity is actually
larger than the isolated particle rate. This finding brings new
meaning to the phrase "hindered settling function"! This sedimentation
velocity in suspension is therefore critically dependent on the
"clumps" which form in the suspension. Thus new simulations and
experiments are being developed to understand the formation of
concentration inhomogeneities in these simple suspension flows.
DNA Dynamics in Mixed Flows and in Micro- and Macro- Devices
(Funded by the Center of Polymer Interfaces and Molecular Assemblages,
CPIMA and the NSF Chemical and Thermal Sciences Division; Collaboration
with Prof. Steve Chu, Physics and Applied Physics, Stanford University)
The dynamics of DNA, as both a probe for polymer
dynamics in flow and as a research area of great importance to
industries associated with biosensors and lab-on-a-chip devices,
has been an ongoing theme in our research group for more than
five years. The research begins with the development of detailed
Brownian dynamic models for DNA dynamics in a variety of well-characterized
flow fields which are validated with single molecule flourescence
microscopy originating in the Chu group. This combination has
allowed the description of new physical principles governing these
dynamics under highly nonequilibrium conditions, including the
tumbling dynamics and fluctuation dynamics of molecules in a wide
range of planar flows with varying ratios of strain and vorticity.
These flows designated as "mixed" flows span the behavior from
purely vortical flow to purely straining motion. The dynamics
is most interesting near the "critical point" known as simple
shear flow where the straining and vorticity are exactly balanced.
For flows near this point the configurational "phase transition"
is associated with large fluctuations that can be examined in
a detailed manner both computationally and experimentally.
Mixed flows are literally everywhere as a local condition in
common complex processing flows and one of the most important
such flows is contraction flow which is used as a means of cleaving
DNA for subsequent sequencing applications. The ongoing development
of an accurate scission model for this process is just one of
the applications of our knowledge that we are developing in collaboration
with the Stanford Genomic Center.
Our materials center known as CPIMA
is focussed on the interfacial properties of polymers as well
as their interfacial dynamics. Our developing DNA model has thus
been applied to understand new DNA microdevices including post
arrays for separation, Brownian ratchets and the rheology in ultrathin
gaps. Simulating these nonequilibrium processes where the statistical
mechanics of unbound molecules is not applicable, allows for the
understanding of the new important physical principles that govern
these processes. Two primary examples are demonstrated in the
figures below. The first illustrates "hairpin" dynamics associated
with the unravelling of chains around posts as they interact.
These dynamics are critical to understanding the relative mobilities
of molecules as they are passed through post arrays and this mobility
difference can allow for separation under certain conditions.
Remarkably these dynamics are very similar to drop breakup in
fixed fiber beds, where in this example, the dynamics of a drop
wrapping around a fiber is key to understanding the breakup mechanism.
(This is another project in our group which is examined via dynamic
simulations using boundary integral techniques).A second interesting
piece of physics is that associated with the change in nonequilibrium
chain dynamics when a polymer is constrained to a gap of thickness
comparable to its radius of gyration. The movie below shows that
such constraint reduces the net chain extension in flows even
for stretch in the direction parallel to the walls.
Moreover the chain relaxation time associated with end-to-end
relaxation is lengthened considerably in these ultra-thin gaps.
A Molecular Simulation of Turbulent Drag Reduction by Flexible
Polymers and/or Fibers
(Funded by DARPA; joint with Parviz Moin, Sanjiva Lele, and Godfrey
Mungal; Mechanical Engineering and the Center for Turbulence Research,
Stanford University)
In a new project that combines all the expertise in the group,
we have forged a collaboration with the Center for Turbulence
Research to develop a molecular simulation of turbulent drag reduction
including the effects of a number of different added micro-elements
(e.g. flexible polymers and/or rigid fibers). Note that drag reduction
is a 50 year old problem associated with originally with the name
Thoms as the Thoms phenomena, where the addition of even very
small (i.e. 5 ppm) of polymeric material can cause the reduction
of turbulent drag by 80% in fully developed boundary layer and
channel flows. The origins of this reduction at a molecular level
are still the subject of heated debate. However, our research
using a combination of Brownian dynamics simulations and coupled
continuum solver (the so-called micro-macro method) allows
for a direct numerical simulation of the phenomena using realistic
molecular models that have been benchmarked in our ongoing research
program associated with developing Brownian dynamic simulations
of model polymers. As an initial step "uncoupled" calculations
in which detailed molecular models are simulated in their configuration
change and stretch in simulations of "Minimal Channel Flows",
(i.e. the smallest computational unit necessary to maintain wall
bounded turbulence) has been accomplished. These simulations yield
insight into the molecular origins regarding the mechanism of
stress production in the turbulent flow polymeric solutions at
ultra-dilute concentrations. An experimental team at Stanford
headed by Godfrey Mungal is working with our simulation team to
directly examine our flow predictions using 3-dimensional DPIV
and direct stress measurements in channel turbulence.
Representative Publications
Grillet, A., B. Yang, B. Khomami, and E.S.G. Shaqfeh, "The modelling
of viscoelastic lid-driven cavity flows using finite element simulations''
J. NonNewtonian Fluid Mech, 88 pp. 99-131 (1999)
Levinson, J.A., E.S.G. Shaqfeh, A.V. Hamza and M. Balooch,
''The Ion-assisted Etching and Profile Development of Silicon
in Molecular and Atomic Chlorine'', J. Vac. Sci. Technol. B 18(1)
Jan/Feb pp. 172-190 (2000)
Hur, J., E.S.G. Shaqfeh and R.G. Larson, "Brownian dynamics simulations
of single DNA chains in simple shear flow'', J. Rheol. 44(4) July/August
713-742 (2000)
Grillet, A.M., E.S.G. Shaqfeh, and B. Khomami, "Observations
of the Viscoelastic Instabilities in Lid Driven Cavity Flow'',
J. NonNewtonian Fluid Mech.,94, p. 15 (2000)
Babcock, H., D. Smith, J. Hur, E.S.G. Shaqfeh, S. Chu, "Relating
the Microscopic and Macroscopic Response of a Polymeric Fluid
in a Shearing Flow'', Phys. Rev. Lett. 85, 2018-2021, (2000)
Hur, J., E.S.G. Shaqfeh, H. Babcock, D. Smith, S. Chu, "The dynamics
of dilute and semidilute DNA solutions in the startup of shear
flow'', Journal of Rheology 45, 421-450, (2001)
Kwan T., Woo, N., and E.S.G. Shaqfeh, "An Experimental and Simulation
Study of Dilute Polymer Solutions in Exponential Shear Flow: Comparison
to Uniaxial and Planar Extensional Flows'', Journal of Rheology,
45, pp.321-349 (2001)
Somasi, M., Komami, B., Woo, N., Hur, J. and E.S.G. Shaqfeh,
"Brownian Dynamics Simulations of Bead-Rod and Bead-Spring Chains:
Numerical Algorithms and Coarse Graining Issues'', (J. NonNewtonian
Fluid Mech., submitted, 8/6/2001)
Butler, J. and E.S.G. Shaqfeh, "Dynamic simulations of the inhomogeneous
sedimentation of rigid fibers'', (J. Fluid Mech., accepted, 9/2001)
Babcock, H., R. Teixeira, J. Hur, E.S.G. Shaqfeh, and S. Chu,
"Single Molecule Observation of the Coil-Stretch Transition
in Mixed Flows, (Science, submitted 8/2001)
Hur, J., E.S.G. Shaqfeh, H. Babcock, S. Chu, "The Dynamics
and Configurational Fluctuations of Single DNA Chains in Linear
Mixed Flows'', (Phys. Rev. Lett., submitted 8/2001)
Schorr, P.A., T.C.B. Kwan, S.M. Kilbey II, and E.S.G. Shaqfeh,
"Shear forces between tethered polymer chains as a function of
compression, sliding velocity, and solvent quality'', (Macromolecules,
submitted 7/2001)
Olson, D.J., J.M. Johnson, P.D. Patel, E.S.G. Shaqfeh, S.G.
Boxer, and G.G. Fuller, "Electrophoresis of DNA Adsorbed to a
Cationic Supported Bilayer'', (Langmuir, accepted 8/2001)
Ph.D. Students with Undergraduate Institution
Alex Gweo-Kai Lee, University
of Texas at Austin
Prateek Dinesh Patel, Washington
University at St. Louis
Nathan "Jung" Woo, Univ.
of California at Berkeley
Charles Martin Schroeder, Carnegie
Mellon University
Rodrigo Esquivel Teixiera, Georgia
Tech
Gandharv Bhatara, Indian
Institute of Technology, New Delhi
John Paschkewitz, M.I.T.
Post-Doctoral Student
Joseph "Seok" Hur, BSE Seoul
National University, Korea, MS and PhD Stanford University
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