Jonathan J. L. Higdon
Contact Information:
e-mail:
phone: (217) 333-1479
fax: (217) 333-5052
195 Roger Adams Lab
MC-712, Box C-3
600 S. Mathews Ave.
Urbana, IL 61801
Professor
B.E.S., Johns Hopkins University, 1975
M.S.E., Johns Hopkins University, 1975
Ph.D., Cambridge University, 1978
- Presidential Young Investigator Award, National Science Foundation, 1984
- Prokasy Award for Excellence in Undergraduate Teaching, College of Liberal Arts & Sciences, University of Illinois, UC, 1988
- Stanley Corrsin Lectureship in Fluid Dynamics, Johns Hopkins University, 1993
Fluid Mechanics and Computational Algorithms
The goal of our research is to develop innovative
computational algorithms to extend the frontiers of computational
modeling in fluid mechanics and the dynamics of colloids and complex
fluids.
(1) Computational Modelling of Suspensions and Colloidal Systems.
Concentrated suspensions of small particles
present challenging research problems in many applications of scientific
and technological significance. These systems include paper manufacturing,
coating processes, paints, food products, ceramics, and bioparticulates
(including blood cells) as well as large macromolecules. We are
interested in the dynamics of these particulate systems under the
action of hydrodynamic, Brownian, and interparticle forces. Previous
studies have focused on the effects of Brownian and interparticle
forces but have had limited success in analyzing the strong hydrodynamic
interactions in concentrated systems. Accurate solution of the fluid
dynamic equations required O(N
3) operations, limiting
simulations to N = 100 particles or less. In our research, we have
reduced the computational cost to O(N ln N) operations, allowing
realistic simulations with systems having up to 25,000 particles.
With such large-scale systems, we are able to investigate a range
of interesting physical phenomena that have previously been beyond
the limits of computer simulation. We are currently pursuing research
on structure formation in suspensions, order-disorder transitions,
and the dynamics of nonspherical particles, such as platelets and
long flexible-particle chains.
(2) Large Scale Simulations of Multiphase Flow: Foams and Emulsions.
Multiphase flows of emulsions
and foams are encountered in a wide range of industrial processes.
Enhanced oil recovery processes and environmental remediation constitute
two important examples in which a multiphase mixture flows through
the complex interstitial spaces of a porous medium. Owing to the
complexity of the interfacial flows, many multiphase systems can
be analyzed only through experiment or computer simulation. Previously,
computational methods for solving the hydrodynamic equations required
O(MN)
2 operations, where N is the number of fluid droplets
and M is the number of computational elements per drop. As with
the particulate systems discussed above, this computational cost
placed severe limitation on the phenomena that could be studied
by direct simulation. In our research, we have developed a new algorithm,
having a computational cost O[MN ln(MN)]. Computer simulations with
this new algorithm promise to significantly extend our understanding
of multiphase flows of emulsions and foams. In two major research
thrusts, we are analyzing the rheology of multiphase fluid mixtures
in shear flows and studying the relative permeability of two fluid
phases in flow through porous media.
Selected Publications
Q.J. Meng and J.J.L. Higdon, "Large scale dynamic simulation of plate-like
particle suspensions. Part II: Brownian simulation," Journal of
Rheology, 52, 37-65 (2008).
Q.J. Meng and J.J.L. Higdon, "Large scale dynamic simulation of plate-like
particle suspensions. Part I: Non-Brownian simulation," Journal
of Rheology, 52, 1-36 (2008).
P. Dimitrakopoulos and J. J. L. Higdon, "On
the displacement of fluid bridges from solid surfaces
in viscous pressure-driven flows," Phys. Fluids.
15:3255 (2003).
D. R. Graham and J. J. L. Higdon, "Acoustic
stimulation of flow through porous media, Part 2.
Unsteady flow." J. Fluid Mech. 465:237-260 (2002).
D. R. Graham and J. J. L. Higdon, "Acoustic
stimulation of flow through porous media, Part 1.
Steady flow." J. Fluid Mech. 465:213-235 (2002).
P. Dimitrakopoulos and J. J. L. Higdon, "Displacement
of three dimensional fluid droplets from solid surfaces
in viscous pressure-driven flows", 435:327-350,
J. Fluid Mech. (2001).
D. R. Graham and J. J. L. Higdon, "Oscillatory
flow of droplets in capillary tubes. Part 2. Constricted tubes." J. Fluid Mech. 425:55-77 (2000).
D. R. Graham and J. J. L. Higdon, "Oscillatory
flow of droplets in capillary tubes. Part 1. Straight
tubes." J. Fluid Mech. 425:31-53 (2000).
