John H. CushmanUniversity Distinguished Professor of Earth and Atmospheric Science
Professor of Mathematics
Office Address: Math Sciences Building, Rm 816 and Civil Engineering Biulding Rm 3223
Mailing Address: Purdue University
Earth and Atmospheric Sciences
550 Stadium Mall Drive
West Lafayette, IN 47907-2051
Phone: (765) 494-8040 or (765) 494-3258
The focus of Professor Cushman's research is the physics of fluids in porous media, over time/space scales ranging from picoseconds/angstroms to years/miles. Problems of special interest are (i) species separation and phase change in micropores, (ii) dispersion in media with continuously evolving heterogeneity, (iii) swelling colloidal systems, (iv) reservoir-scale dispersion of environmental contaminants in natural geological media, (v) transconjugation of genes between microbes their evolution in the environment, and (vi) developing theories for the evolution of earths plates. Some past and present examples are presented below.
- Species separation and phase change in micropores
- Dispersion in media with continuously evolving heterogeneity
- Swelling colloidal systems
- Reservoir-scale dispersion of environmental contaminants in natural geologic media
- Tranconjugation of genes between microbes and their evolution in the environment
- Developing theories of the evolution of the earths plates
- Tracking the paths of microbes
|Species separation and phase change in micropores||Consider a fluid contained in a pore
that pore is only a few fluid-molecular diameters wide in at least one
dimension. Such fluids are of importance in condensed matter physics
(model systems for the study of critical phenomena), in biology
(protein folding and transport through membranes), in engineering and
materials science (nanotechnologies), and in environmental science
(chemical adsorption on soil colloids). Computational statistical
mechanical experiments carried out by Cushman's group enhance our
understanding of such fluids. Even a fluid as simple as a rare gas
mixture displays an extremely rich and anomalous behavior when confined
to a structured planar system of width on the order of a few
The fluid's phase diagram is changed, its transport coefficients are
radically altered from those in the fluids bulk phase, and it becomes
inhomogeneous and anisotropic. The properties of the fluid depend in a
complex way on
the initial structure of the liquid, the structure and commensurability
of the confining walls, the wall-fluid interaction, the separation of
walls, asperities within the pore walls, and, if the pore-fluid is in
equilibrium with its bulk-phase, then the pore-fluid depends strongly
on the bulk-phase composition.
|If a porous medium looks
inhomogeneous at every scale on which it can be viewed, then it is said
to have continuously evolving heterogeneity. Many natural geologic
media, and more generally fractal
porous media, are of this category. By using nonequilibrium statistical
Cushman's group developed general theories of conservative chemical
in this type of system. The theories are non-Markovian, but they reduce
their appropriate Fickian counterparts in the asymptotic limits.
these theories can be applied to turbulent bulk-phase dispersion as
as to fluids in porous media.
|Swelling porous media
include many natural soils, baked foodstuffs (chips, cookies, pasta,
breads), many drug delivery substrates, and body tissues. Cushman's
group has provided the
first correct derivations and statements of Darcy's and Fick's laws for
systems. The group showed that contrary to classical belief, flow in
systems is not driven by gradients in pressure and external fields
gravity) alone, but is also driven by changes in Helmholz free energy
volume fraction (the "interaction" potential). This result is of major
in problems of drying that involve crust formation in soils and food
The Cushman group also provided rational definitions for the
capillary and swelling (disjoining) pressures in such systems.
swelling pressure gives rise to the well-known exponential swelling law
applied at equilibrium. Most recently Cushman's group has developed
for coupled heat and mass transfer and swelling systems which include
Large-scale heterogeneities in an aquifers hydraulic and chemical character play a fundamental role in the evolution of contaminants in the environment. The work of Cushman's group shows that uncertainty in the parameters that characterize an aquifer give rise to spatially and temporally nonlocal constitutive laws for chemical transport. When computationally implemented, these laws often lead to different conclusions regarding groundwater contamination scenarios than those commonly employed by litigators and by the Environmental Protection Agency when enforcing environmental regulations.
Coming soon: Animation
Reservoir-scale dispersion of
environmental contaminants in
natural geologic media
Our group focus is on horizontal transfer of extra chromosomal DNA between microbes via mobile elements (plasmids or other transposable elements). Specifically we are interested in visualization of the process on the micron scale, it's evolution in the environment and in developing a mechanistic model to predict the evolution of the genes in the recipient population.
Plate tectonics has changed the way earth scientists look at the surface of the Earth. It has recently become clear that there are broad zones of deformation within what were once thought to be the earths rigid plates. Our group is focusing on finding theories of such deformation, and more generally of the formation and evolution of the plates themselves. We are attacking this problem with numerical models based on micromorphic continuum theories, and a generalized "statistical mechanics" of the lithosphere and mantle.
Developing theories of the evolution of the earths plates
Tracking the paths of microbes
The ability to characterize the Lagrangian trajectories will allow for the incorporation of microbial motility into models of porous media, but first Lagrangian trajectories of real experiments must be gathered. The video below was created from a video by Howard Berg by using particle tracking velocimetry to trace the path of the microbes. Several different points on each microbe were used. This is a first trial in gathering Lagrangian trajectories of microbes. Particle tracking velocimetry was also used in the experiments related to the general theories for inhomogeneous systems.
Click here to see the video
- Park*, M. and J. H. Cushman (2006) On upscaling operator-stable Levy motions in fractal porous media. J. Comp. Phys. 217:159-165.
- Park*, M.,
N. Kleinfelter* and J. H. Cushman (2006) Renormalizing chaotic dynamics in fractal porous media with application to microbe motility. Geophysical Research Letters, 33, L01401.
- Park*, M.,
N. Kleinfelter* and J. H. Cushman (2005) Scaling laws and Fokker-Planck equations for 3-dimensional porous media with fractal mesoscale. , 4(4): 1233-1244. SIAM Multiscale Modeling and Simulation
- Park*, M., N. Kleinfelter* and J. H. Cushman (2005) Scaling laws and dispersion equations for Levy particles in 1-dimensional fractal porous media., Physical Review E, 72, 056305: 1-7.
- Kleinfelter*, N., M. Moroni*, and J. H. Cushman (2005) Application of a finite-size Lyapunov exponent to particle tracking velocimetry in fluid mechanics experiments. Physical Review E, 72, 056306: 1-12.
- Cushman, J. H., M. Park*,
N. Kleinfelter*, and M. Moroni* (2005) Super-diffusion via Levy Lagrangian velocity processes. Geophysical Research Letters, 32 (19) L19816: 1-4.
- Axtell*, N.K., M. Park* and J.H. Cushman (2005) Micromorphic fluid in an elastic porous body: Blood flow in tissues. Int. J. Multiscale Computational Engineering. 3(1).
- Cushman, J. H., L.S. Bennethum* and P.P. Singh* (2004) Toward rational design of drug delivery substrates: I. Mixture theory for two-scale biocompatible polymers.
J. Multiscale Modeling and Simulation 2(2): 302-334. SIAM
- Cushman, J. H., P.P. Singh* and L.S. Bennethum* (2004) Toward rational design of drug delivery substrates: II. Mixture theory for three-scale biocompatible polymers and a computational example.
J. Multiscale Modeling and Simulation 2(2): 335-357. SIAM
- Singh*, P.P., D. Maier, J.H. Cushman and O.H. Campanella (2004) Effect of viscoelastic relaxation on fluid transport in foods. Part II: Imbibition and drying of seeds. J. Math. Biol. 49: 1-19.
- Singh*, P.O., D.E. Maier, J.H. Cushman, K. Haghighi and C. Corvalan (2004) Effect of viscoelastic relaxation on fluid transport in foods. Part I: Solution of the general transport equation. J. Math. Biol. 49: 20-34.
- Cushman, J.H. and J.E. Curry* (2004) The complex behavior of simple fluids in nanoscale restricted geometrics. In Dynamics and Friction in Sub-micron Scale Confined Systems (ed) Y. Braiman, ACS Symposium Series 882: 157.
- Su*, Z., J.E. Curry* and J.H. Cushman (2003) Tunable diffusion of OMCTS and cyclohexane monolayers in mica slit pores. J. Chem. Phys. 118:1417-1422.
- Cushman, J.H., L.S. Bennethum* and B.X. Hu* (2002) A primer on upscaling methods for porous media. Adv. Water Resour. 25:1043-1067.
- Stroud*, W., J. Curry*, and J.H. Cushman (2001) Capillary condensation and snapoff in nanoscale contacts. Langmuir 17(3):688-698.
- Cushman, J.H. and M. Moroni* (2001) Statistical mechanics with 3D-PTV experiments in the study of anomalous dispersion: Part I. Theory. Phys. Fluids 13(1):75-80.
*, M. and J.H. Cushman (2001) Statistical mechanics with 3D-PTV experiments in the study of anomalous dispersion: Part II. Experiment. Phys. Fluids 13(1):81-91. Moroni
- Murad*, M.A. and J.H. Cushman (2000) Thermomechanical theories for swelling porous media with microstructure. Int. J. Eng. Sci. 38:517-564.
- Bennethum*, L.S. and J.H. Cushman (1996) Multiscale hybrid mixture theory for swelling systems. Part I: Balance laws. Int. J.
Sci. 34(2):125-145. Eng.
- Bennethum*, L.S. and J.H. Cushman (1996) Multiscale hybrid mixture theory for swelling systems. Part II: Constitutive theory. Int. J.
Sci. 34(2):147-169. Eng.
- Curry*, J. and J.H. Cushman (1995) Nanophase coexistence and sieving in binary mixtures confined between corrugated walls. J. Chem. Phys. 103:2132-2139.
- Curry*, J. and J.H. Cushman (1995) Binary mixtures of simple fluids in structured slit-micropores. Mol. Phys. 85(1):173-192.
- Curry*, J.E., Zhang*, F., J.H. Cushman, M. Schoen*, D.J. Diestler (1994) Transiently coexisting nanophases in ultrathin films confined between corrugated walls. J. Chem. Phys. 101(12):10824-10832.
- Schoen*, M., D.J. Diestler, J.H. Cushman (1994) Stratification-induced order-disorder phase transitions in molecularly thin confined films. J. Chem. Phys. 101(8):6865-6873.
- Schoen*, M., D.J. Diestler, J.H. Cushman (1994) Fluids in Micropores IV. The behavior of molecularly thin confined films in the Grand Isostress Ensemble. J. Chem. Phys. 100(10):7707-7717.
- Diestler, D.J., M. Schoen*, J.H. Cushman (1993) On thermodynamic stability of confined thin films under shear. Science 262:545-547.
- Lee*, K.-K., F.-W. Deng*, J.H. Cushman (1993) Multiscale adaptive estimation of the conductivity field using head and tracer data. Stoch. Hydrol. Hyd. 7(1):66-82.
- Schoen*, M., D.J. Diestler, J.H. Cushman (1993) Isostress-isostrain ensemble Monte Carlo simulation of second-order phase transitions in a confined monolayer fluid. Molecular Physics 78:1097-1115.
- Cushman, J.H. (1990) Molecular Scale Lubrication, Nature 347(6290):227-228.
- Schoen*, M., C.L. Rhykerd*, Jr., D.J. Diestler, and J.H. Cushman (1989) Shear Forces in Molecularly Thin Films, Science 245:1223-1225.
- Schoen*, M., J.H. Cushman, D.J. Diestler, and C.L. Rhykerd*, Jr. (1988) Fluids in Micropores, II. Self-Diffusion of a Simple Classical Fluid in a Slit-Pore, J. Chem. Phys. 88(2):1394-1406.
- Rhykerd*, Jr., C.L., M. Schoen*, D.J. Diestler, and J.H. Cushman (1987), Epitaxy in Simple Classical Fluids in Micropores and Near Solid Surfaces, Nature 330(3):461-463.
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