Martin Ferer
Professor
B.S., University of Detroit, 1966
Ph.D., Univ. of Il. at Champaign-Urbana, 1972

West Virginia University
Department of Physics
PO Box 6315
Morgantown, WV 26506

Tel: (304)293-3422 ext. 1431
Fax: (304)293-5732
ferer@WVNVMS.WVNET.EDU

Fractal characteristics have now been observed for a number of seemingly disparate growth phenomena: the advance of a fluid/fluid interface during fluid flow, a variety of schemes for material deposition, the development and growth of cracks during a fracturing process, to name a few. As the field of fractal growth phenomena matures, the emphasis is shifting from merely cataloguing the unstable growth phenomena that obey a fractal geometry towards understanding what features of this growth phenomena cause the fractal character and what modifications will lead to a smoother, compact or Euclidean growth.

Our research on two phase flow in porous media has demonstrated a crossover from fractal to Euclidean advance of the fluid/fluid interface when the ratio of the viscosities between the two fluids is decreased from infinity, so that fractal flow occurs only when the displaced fluid is infinitely more viscous than the injected fluid. Furthermore, we have determined the time scale on which this fractal to compact crossover occurs, and we have characterized the way in which this characteristic crossover time varies with the ratio of the fluid viscosities. Since this characteristic time sets the time scale for the flow, it influences the flow in the regime of compact flow by determining the viscosity-ratio dependence of the usual density and current flow descriptors.

Currently, we are studying the fractal to compact crossover for flow in three-dimensional porous media, thereby extending the previous work in two-dimensional layers. We are also studying the effect of capillary pressure on the crossover. We are also studying models of the fracture of materials to determine what features of the model systems affect the fractal character of the fracture.

Recent Publications

Crossover from Capillary Fingering to Compact Invasion for Two-Phase
Drainage with Stable Viscosity Ratios M. Ferer,* Grant S. Bromhal, and
Duane H. Smith, Advances in Water Resources in press (2006).

2-D Network Model Simulations of Miscible Two-Phase Flow Displacements
in Porous Media: Effects of Heterogeneity and Viscosity; Kristen
Stevenson, Martin Ferer, Grant S. Bromhal, Jared Gump, Joseph Wilder,
Duane H. Smith, Physica A 367, 7-24 (2006).

Drainage Two-Phase Flow in Porous Media:Crossover from Capillary
Fingering to Compact Invasion, by M. Ferer,* Grant S. Bromhal, and Duane
H. Smith Physical Review E 71, #026303 (2005).

Miscible, Vertical Network Model 2-D Simulations of Two-Phase Flow
Displacements in Porous Media by Kristen Stevenson, Grant S. Bromhal,
Martin Ferer, Joseph Wilder, Duane H. Smith, Physica A 343 p 317(2004).

Crossover from capillary fingering to viscous fingering for immiscible
unstable flow: Experiment and Modeling by M. Ferer, Chuang Ji, Grant
S. Bromhal, Joshua Cook, Goodarz Ahmadi, Duane H. Smith, Phys. Rev. E 70
#016303, 7 pages (2004).

Fractal Dimensions of Invasion Percolation: the effect of aspect ratio,
by M. Ferer,, Grant S. Bromhal, and Duane H. Smith, Physica A 334, 22
(2004).

Pore-Level Modeling of Immiscible Drainage: Validation in the Invasion
Percolation and DLA Limits, M. Ferer, G. S. Bromhal, and Duane H.
Smith Physica A 319 11-35 (2003).

Cross-over from Invasion Percolation Fingering to Compact Flow:
Pore-Level Modeling of Drainage, by M. Ferer, Grant S. Bromhal, and
Duane H. Smith, Phys. Rev. E 67 Article # 051601 (12 pages) (2003).

Spatial Distribution of Avalanches: Their Role in Fingering, by M.
Ferer, Grant S. Bromhal, and Duane H. Smith, Physica A 311, 5 2002.

Patchy Cleaning of Rigid Gas Filters-Transient Regeneration Phenomena:
Comparison of Modeling to Experiment, Achim Dittler, M. Ferer, Pulkit
Mathur, P. Djuranovic, Gerhard Kasper, and Duane Smith Powder
Technology, 124, 55-66 (2002)

Filter Cake Removal Efficiency: Comparison of Modeling Results with
Experiment, M. Ferer and Duane H. Smith, Chemical Engineering Science
55, 5003-5011 (2000).
“The Transition from Continuous to Discontinuous Material Failure in a Simple Model of an Adhesive Layer”, M. Ferer and Duane H. Smith, Physical Review E, 57, 866 (1998).

“Modeling of Backpulse Filter Cleaning: The Small Particle Filter Cake Fragments”, M. Ferer and Duane H. Smith, Aerosol Science and Technology, 29, 246 (1998).

“Continuous Behavior in a Simple Model of the Adhesive Failure of a Layer”, M. Ferer and Duane H. Smith, Physical Review E 57, 866 (1998)