Martin R Maxey
Martin R Maxey
Professor of Applied Mathematics (Research), Professor Emeritus of Engineering, Professor Emeritus of Applied Mathematics
Overview
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
Publications
| Howard, Amanda A., Maxey, Martin R. "Simulation study of particle clouds in oscillating shear flow." Journal of Fluid Mechanics, vol. 852, 2018, pp. 484-506. |
| Cui, Francis R., Howard, Amanda A., Maxey, Martin R., Tripathi, Anubhav. "Dispersion of a suspension plug in oscillatory pressure-driven flow." Physical Review Fluids, vol. 2, no. 9, 2017. |
| Trask, Nathaniel, Maxey, Martin, Kim, Kyungjoo, Perego, Mauro, Parks, Michael L., Yang, Kai, Xu, Jinchao. "A scalable consistent second-order SPH solver for unsteady low Reynolds number flows." Computer Methods in Applied Mechanics and Engineering, vol. 289, 2015, pp. 155-178. |
| Yeo, Kyongmin, Maxey, Martin R. "Dynamics and rheology of concentrated, finite-Reynolds-number suspensions in a homogeneous shear flow." Physics of Fluids, vol. 25, no. 5, 2013, pp. 053303. |
| Reddy, Sheila M. W., Wentz, Allison, Aburto-Oropeza, Octavio, Maxey, Martin, Nagavarapu, Sriniketh, Leslie, Heather M. "Evidence of market-driven size-selective fishing and the mediating effects of biological and institutional factors." Ecological Applications, vol. 23, no. 4, 2013, pp. 726-741. |
| Morse, Michael, Huang, Athena, Li, Guanglai, Maxey, Martin R., Tang, Jay X. "Molecular Adsorption Steers Bacterial Swimming at the Air/Water Interface." Biophysical Journal, vol. 105, no. 1, 2013, pp. 21-28. |
| Li, Guanglai, Bensson, James, Nisimova, Liana, Munger, Daniel, Mahautmr, Panrapee, Tang, Jay X., Maxey, Martin R., Brun, Yves V. "Accumulation of swimming bacteria near a solid surface." Physical Review E, vol. 84, no. 4, 2011. |
| Rosa, B., Wang, L.-P., Maxey, M.R., Grabowski, W.W. "An accurate and efficient method for treating aerodynamic interactions of cloud droplets." Journal of Computational Physics, vol. 230, no. 22, 2011, pp. 8109-8133. |
| MAXEY, MARTIN R. "Biomimetics and cilia propulsion." J. Fluid Mech., vol. 678, 2011, pp. 1-4. |
| Maxey, M., Yeo, K. "Flow Modulation by Finite Size Particles: From Stokes Suspensions to Turbulence." 6th AIAA Theoretical Fluid Mechanics Conference, 2011. |
| YEO, KYONGMIN, MAXEY, MARTIN R. "Numerical simulations of concentrated suspensions of monodisperse particles in a Poiseuille flow." J. Fluid Mech., vol. 682, 2011, pp. 491-518. |
| Nisimova, Liana, Bensson, James, Li, Guanglai, Maxey, Martin, Tang, Jay X. "Tracking Bacterial Swimming Near a Solid or Air Surface." Biophysical Journal, vol. 100, no. 3, 2011, pp. 599a. |
| Yeo, Kyongmin, Maxey, Martin R. "Anomalous diffusion of wall-bounded non-colloidal suspensions in a steady shear flow." EPL, vol. 92, no. 2, 2010, pp. 24008. |
| YEO, KYONGMIN, MAXEY, MARTIN R. "Dynamics of concentrated suspensions of non-colloidal particles in Couette flow." J. Fluid Mech., vol. 649, 2010, pp. 205. |
| Gerritsma, Marc, van der Steen, Jan-Bart, Vos, Peter, Karniadakis, George. "Dynamics of Self-Assembled Chaining in Magnetorheological Fluids." Langmuir, vol. 20, no. 22, 2010, pp. 8333-8363. |
| Yeo, K., Dong, S., Climent, E., Maxey, M.R. "Modulation of homogeneous turbulence seeded with finite size bubbles or particles." International Journal of Multiphase Flow, vol. 36, no. 3, 2010, pp. 221-233. |
| Yeo, Kyongmin, Maxey, Martin R. "Ordering transition of non-Brownian suspensions in confined steady shear flow." Physical Review E, vol. 81, no. 5, 2010. |
| Yeo, Kyongmin, Maxey, Martin R. "Rheology and ordering transitions of non-Brownian suspensions in a confined shear flow: Effects of external torques." Physical Review E, vol. 81, no. 6, 2010. |
| Yeo, Kyongmin, Maxey, Martin R. "Simulation of concentrated suspensions using the force-coupling method." Journal of Computational Physics, vol. 229, no. 6, 2010, pp. 2401-2421. |
| Liu, D., Keaveny, E.E., Maxey, M.R., Karniadakis, G.E. "Force-coupling method for flows with ellipsoidal particles." Journal of Computational Physics, vol. 228, no. 10, 2009, pp. 3559-3581. |
| Luo, Xian, Maxey, Martin R., Karniadakis, George Em. "Smoothed profile method for particulate flows: Error analysis and simulations." Journal of Computational Physics, vol. 228, no. 5, 2009, pp. 1750-1769. |
| Dobrushkin, V. A., Maxey, M. "An improved boundary element formulation for the motion of spherical bubbles." Diff Equat, vol. 44, no. 9, 2008, pp. 1305-1312. |
| Keaveny, Eric E., Maxey, Martin R. "Interactions between comoving magnetic microswimmers." Physical Review E, vol. 77, no. 4, 2008. |
| Keaveny, Eric E., Maxey, Martin R. "Modeling the magnetic interactions between paramagnetic beads in magnetorheological fluids." Journal of Computational Physics, vol. 227, no. 22, 2008, pp. 9554-9571. |
| Luo, Xian, Maxey, Martin R., Karniadakis, George E. "Smoothed Profile Method for Particulate Two-Phase Flow." Volume 1: Symposia, Parts A and B, 2008. |
| KEAVENY, ERIC E., MAXEY, MARTIN R. "Spiral swimming of an artificial micro-swimmer." J. Fluid Mech., vol. 598, 2008. |
| Climent, Eric, Yeo, Kyongmin, Maxey, Martin R., Karniadakis, George E. "Dynamic Self-Assembly of Spinning Particles." Journal of Fluids Engineering, vol. 129, no. 4, 2007, pp. 379. |
| XU, JIN, DONG, SUCHUAN, MAXEY, MARTIN R., KARNIADAKIS, GEORGE E. "Turbulent drag reduction by constant near-wall forcing." J. Fluid Mech., vol. 582, 2007, pp. 79. |
| Kunz, Robert F., Gibeling, Howard J., Maxey, Martin R., Tryggvason, Gretar, Fontaine, Arnold A., Petrie, Howard L., Ceccio, Steven L. "Validation of Two-Fluid Eulerian CFD Modeling for Microbubble Drag Reduction Across a Wide Range of Reynolds Numbers." Journal of Fluids Engineering, vol. 129, no. 1, 2007, pp. 66. |
| Abbas, Micheline, Climent, Eric, Simonin, Olivier, Maxey, Martin R. "Dynamics of bidisperse suspensions under Stokes flows: Linear shear flow and sedimentation." Physics of Fluids, vol. 18, no. 12, 2006, pp. 121504. |
| Keaveny, Eric E., Pivkin, Igor V., Maxey, Martin, Em Karniadakis, George. "A comparative study between dissipative particle dynamics and molecular dynamics for simple- and complex-geometry flows." The Journal of Chemical Physics, vol. 123, no. 10, 2005, pp. 104107. |
| Stephens, Monica Y., Oglesby, Robert J., Maxey, Martin. "A One-Dimensional Mixed Layer Ocean Model for Use in Three-Dimensional Climate Simulations: Control Simulation Compared to Observations." Journal of Climate, vol. 18, no. 13, 2005, pp. 2199-2221. |
| Maxey, M.R., Dong, S., Xu, J., Karniadakis, G.E. "Simulations for Microbubble Drag Reduction (MBDR) at High Reynolds Numbers." 2005 Users Group Conference (DOD-UGC'05), 2005. |
| Liu, D, Maxey, M R, Karniadakis, G E. "Simulations of dynamic self-assembly of paramagnetic microspheres in confined microgeometries." J. Micromech. Microeng., vol. 15, no. 12, 2005, pp. 2298-2308. |
| Dong, Suchuan, Xu, Jin, Maxey, Martin, Karniadakis, George. "Slippery Issues in Microbubble Drag Reduction." 43rd AIAA Aerospace Sciences Meeting and Exhibit, 2005. |
| Dance, S. L., Climent, E., Maxey, M. R. "Collision barrier effects on the bulk flow in a random suspension." Physics of Fluids, vol. 16, no. 3, 2004, pp. 828. |
| Liu, Dong, Maxey, Martin, Karniadakis, George. "Dynamic Self-Assembly in Confined Micro-Domains." Fluids Engineering, 2004. |
| Liu, D, Maxey, M, Karniadakis, G E. "Modeling and optimization of colloidal micro-pumps." J. Micromech. Microeng., vol. 14, no. 4, 2004, pp. 567-575. |
| Dong, Suchuan, Liu, Dong, Maxey, Martin R, Karniadakis, George Em. "Spectral distributed Lagrange multiplier method: algorithm and benchmark tests." Journal of Computational Physics, vol. 195, no. 2, 2004, pp. 695-717. |
Research
Research Overview
Research Statement
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
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)
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.
OTHER PUBLICATIONS
Background
Education and Training
| Year | Degree | Institution |
|---|---|---|
| 1979 | PhD | University of Cambridge |
| 1977 | MA | University of Cambridge |
| 1974 | BA | University of Cambridge |
Honors and Awards
Japan Society for the Promotion of Science, Invited Research Fellow, 1997.
Rayleigh Essay Prize, University of Cambridge, 1977.
Research Scholarship and College Prize, Trinity Hall, Cambridge, 1975.
Scholarship and College Prize, Trinity Hall, Cambridge, 1972 and 1973.
Affiliations
Collaborators
| Name | Title |
|---|---|
| Karniadakis, George | Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics, Professor of Engineering |
Affiliations
American Physical Society
American Society of Mechanical Engineers
Sigma Xi
Society for Industrial and Applied Mathematics (SIAM)
Society of Rheology
Editorial Board ââ'¬â International Journal of Multiphase Flow
Teaching
Teaching Overview
Mathematical methods of applied mathematics
Teaching
| APMA 0330 - Methods of Applied Mathematics I, II |
| APMA 0360 - Applied Partial Differential Equations I |
| APMA 1930P - Mathematics and Climate |
| APMA 2420 - Fluid Mechanics II |
| ENGN 2820 - Fluid Mechanics II |