Martin R. Maxey Professor of Applied Mathematics, Professor of Engineering, Director of Fluid Mechanics, Turbulence and Computation

Professor Maxey completed his undergraduate and graduate education at the University of Cambridge and received his Ph.D. in Applied Mathematics and Theoretical Physics in 1979. In 1977, he was a pre-doctoral research fellow in the Geophysical Fluid Dynamics Summer Program at Woods Hole Oceanographic Institute. He held a post-doctoral position in the Department of Mechanics and Materials Science at the Johns Hopkins University and subsequently was a lecturer in the Department of Chemical Engineering at Johns Hopkins. He joined the Division of Applied Mathematics at Brown University in 1982. He is presently Professor of Applied Mathematics and Engineering and since 1991 has served as Director of the Center for Fluid Mechanics, Turbulence and Computation. He is a member of the editorial board for the International Journal of Multiphase Flow, an associate editor for Fluid Dynamics Research, and is a fellow of the American Physical Society.

Brown Affiliations

Research Areas

scholarly work

D. Liu, M.R. Maxey and G.E. Karniadakis, 2005. Simulations of dynamic self-assembly of paramagnetic microspheres in confined microgeometries. J. Micromech. Microeng. 15, 2298-2306.

E. Keaveny, I. Pivkin, M. Maxey and G.E. Maxey, 2005. A comparative study between dissipative particle dynamics and molecular dynamics for simple- and complex geometry flows. J. Chem. Phys. 123, 104107.

E. Climent, M.R. Maxey and G.E. Karniadakis, 2004. Dynamics of self-assembled chaining in magnetorheological fluids. Langmuir 20, 507-513.

D. Liu, M. Maxey and G.E. Karniadakis, 2004. Modeling and optimization of colloidal micro-pumps. J. Micromech. Microeng. 14, 567-575.

S. Lomholt and M.R. Maxey, 2003. Force coupling method for particles sedimenting in a channel: Stokes flow. J. Comp. Physics 184, 381-405.

S. Dance and M.R. Maxey, 2003. Incorporation of lubrication effects into the force-coupling method for particulate two-phase flow. J. Comp. Phys. 189, 212-238.

J. Xu, M.R. Maxey and G.E. Karniadakis, 2002. Numerical simulation of turbulent drag reduction using micro-bubbles. J. Fluid Mech. 468, 271-281.

D. Liu, M.R. Maxey and G.E. Karniadakis, 2002. A fast method for particulate microflows. J. Microelectromechanical Systems 11, 691-702.

E. Climent and M.R. Maxey, 2001. Numerical simulations of random suspensions at finite Reynolds numbers. Int. J. Multiphase Flow 29, 579-601.

S. Lomholt, B. Stenum and M.R. Maxey, 2001. Experimental verification of the force coupling method for particulate flows. Int. J. Multiphase Flow 28, 225-246.

M.R. Maxey and B.K. Patel, 2001. Localized force representations for particles sedimenting in Stokes flow, Int. J. Multiphase Flow 27, 1603-1626.

E.J. Chang and M.R. Maxey, 1995. Accelerated motion of rigid spheres in unsteady flow at low to moderate Reynolds number. Part II - Accelerated motion, J. Fluid Mech. 303, 133-153.

E.J. Chang and M.R. Maxey, 1994. Accelerated motion of rigid spheres in unsteady flow at low to moderate Reynolds number. Part I - Oscillatory motion, J. Fluid Mech. 277, 347-379.

L-P. Wang and M.R. Maxey, 1993. The motion of microbubbles in a forced isotropic and homogeneous turbulence, Applied Scientific Res. 51, 291-296.

L-P. Wang and M.R. Maxey, 1993. Settling velocity and concentration distribution of heavy particles in homogeneous, isotropic turbulence, J. Fluid Mech. 256, 27-68.

G.R. Ruetsch and M.R. Maxey, 1992. The evolution of small-scale structures in homogeneous isotropic turbulence, Phys. Fluids A 4, 2747-2766.

G. Ruetsch and M.R. Maxey, 1991. Small-scale feature of vorticity and passive scalar fields in homogeneous isotropic turbulence, Phys. Fluids A 3, 1587-1597.

M.R. Maxey, 1990. On the advection of spherical and nonspherical particles in a nonuniform flow, Phil. Trans. R. Soc. (London) A 333, 289-307.

S. Balachandar and M.R. Maxey, 1989. Methods for evaluating fluid velocities in spectral simulations of turbulence, J. Comp. Phys. 83, 96-125.

M.R. Maxey, 1987. The motion of small spherical particles in a cellular flow field, Phys. Fluids 30, 1915-1928.

M.R. Maxey, 1987. The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields, J. Fluid Mech. 174, 441-465.

M.R. Maxey and S. Corrsin, 1986. Gravitational settling of aerosol particles in randomly oriented cellular flow fields, J. Atmos. Sci. 43, 112-1134.

M.R. Maxey and J.J. Riley, 1983. Equation of motion for a small rigid sphere in a nonuniform flow, Phys. Fluids 26, 883-889.


research overview

Professor Maxey's research in fluid dynamics is focused on dispersed two-phase flows such as suspensions of particles in liquids. Current applications of interest include self-assembly in micro-scale flows, swimming of single cell organisms and blood flow. Other research areas include turbulent flows and mixing with applications to physical and geophysical systems.

research statement

Recent research projects include methods for turbulent drag reduction, the manipulation of small paramagnetic particles with magnetic fields to form self-assembled structures in a suspension, active suspensions of microorganisms or artificial swimmers, and problems relating to the transport and coagulation of platelets in blood flow. In these projects, we have developed direct numerical simulations and theoretical models that characterize the microstructure and help understand the overall processes.

In a Defense Advanced Research Projects Agency (DARPA) sponsored project aimed at reducing drag on ship hulls, we have been studying the dynamics of micro-bubbles injected into turbulent shear flows and how these may alter the near-wall flow. The technique of micro-bubble injection is known to work in laboratory experiments but there has been little theory as to how drag reduction is achieved or how it might be scaled. Previously we had provided the first demonstration of drag reduction through a direct numerical simulation. We have developed new simulations for spatially-developing channel flows that now provide a direct basis for comparison with experiments. Our simulations have further identified bubble-bubble contacts as an important factor in bubble dispersion, which in turn controls the persistence of drag reduction. Drag reduction may be enhanced by the presence of a gas film at the walls. Papers on this work were presented at the 2nd Int. Symp. Seawater Drag Reduction, held in Busan, South Korea in 2005.

With National Science Foundation support, we are studying the dynamics of paramagnetic beads in suspensions. These beads (~ 1 micron in size) are commonly used in biomedical testing and can be treated to respond to biochemical agents. When in suspension they can be manipulated by magnetic fields to form self-assembled structures such as chains that can be used in micro-devices to create optical filters, or as flow pumps and actuators. They can be used also to produce mixing in a fluid, or for manipulating individual cells in biomedical applications. We have developed new simulation methods to accurately predict the interactions between magnetic beads. We have demonstrated the strong role of 3D-geometry of the flow device on the chains that form, and verified these results against available experiments. We are presently investigating the effects of unsteady or rotating magnetic fields. Surface physics and short-range interactions play a role too. We have been using molecular dynamics (MD) simulations and the dissipative particle dynamics (DPD) to investigate the link between these nano-scale and mescopic features to link them to larger scale simulations.

In a new project, we are studying the dynamics of platelet coagulation in blood flow in both large blood vessels and in small capillaries.

funded research

Current Awards

National Science Foundation – CBET - Particulate and Multiphase Processes Program, Jan 2004 – Dec 2007, $307,968. P.I. (co-P.I. G. Karniadakis) Simulation of Magnetorheological Fluids: Microdevices and Self-Assembled Structures.

National Science Foundation – DMS - Multiscale Modeling: BBB, Sep 2005 – Aug 2008, $640,475. Co-P.I. (P.I. G.E. Karniadakis and co-P.I. P.D. Richardson) A Stochastic Molecular Dynamics Method for Multiscale Modeling of Blood Platelet Phenomena. (Award DMS-0506312)

Completed Awards

National Science Foundation - ATM8310136, Nov. 1984 - Feb. 1988. Study of the fallout and dispersion of particles in turbulence and random fields.

National Air and Space Administration, with L.Sirovich, 1986-1987. Problems in fluid dynamics.

DARPA, University Research Initiative, L. Sirovich-Director, Oct. 1986 - March 1992. Analysis, Prediction and Control of Turbulent Flows.

DoD, DURIP equipment grant for computer systems, (with L. Sirovich, E. Meiburg). Oct. 1988 - Sept. 1989.

Office of Naval Research - ARI on Dynamics of Bubbly Flows, Nov. 1990-Oct. 1993. The dynamics of bubbly flows and the modification of turbulence by microbubbles.

National Science Foundation - DMS 9205227, Sept. 1992-Feb. 1994, Principal Investigator (Co-P.I.'s, C. Jones, D. McClure, L. Sirovich). Mathematical Sciences Computing Research Environments.

Office of Naval Research - ARI on Dynamics of Bubbly Flows, Nov. 1993-April 1996. The dynamics of bubbly flows and the modification of turbulence by microbubbles.

National Science Foundation - STI-9413819, Academic Research Infrastructure Program. Co-P.I. (P.I. G. Karniadakis), Oct. 1994-Sept. 1995. Acquisition of a parallel supercomputer.

National Science Foundation - CTS9424169 - Fluid, Particulate and Hydraulic Systems Program, May 1995-April 1998, $218,723. Interactions of finite-sized particles and turbulence in dispersed two-phase flow.

National Science Foundation - DMS9628601, (with G. Karniadakis, D. Gottlieb, C. Jones and D. McClure), Aug. 1996-July 1997, $40,000. Mathematical Sciences Computing Research Environments.

National Science Foundation - CTS9619232 - Fluid, Particulate and Hydraulic Systems Program, Co-P.I. (P.I. G. Karniadakis), Sept. 1997 - Aug. 1998, $60,000. A new model for turbulence based on the hydrodynamics - electromagnetism analogy.

National Center for Microgravity Research, USRA 4500-03, Sept. 1998- Oct. 1999, $39,675. Initial investigation of particle interactions and dispersed two-phase flow under low gravity conditions.

DARPA, ATO – Friction Drag Technologies Program, MDA972-01-C-0024, March 2001 – September 2003, $928,858 ($671,521 at Brown University). P.I., with G. Karniadakis and B. Caswell co-PI's at Brown University. Microbubble and microbubble/polymer turbulent drag reduction.

DARPA, ATO – Friction Drag Technologies Program, subcontract through ARL – Penn State Univ., November 2003 – June 2006, $499,448. P.I. (co-P.I. G. Karniadakis) at Brown University. Multiscale physical modeling for micro-bubble drag reduction at high Reynolds numbers. (RFP 04-15)