How fluids move depend on what they are made of - their constituents.  Thus while all fluid flows conserve mass and obey Newton's second law of motion, they generate internal stresses differently dependent on how the flow distorts, deforms, or rearranges the constituents of the fluid. This material-dependent property is described by the constitutive equation - the simplest cases lead to Euler's equation or the Navier-Stokes equation. In the case of polymer fluids, the equation is more complicated - and typically so is the flow.
We investigate the even more unusual fluid dynamics of wormlike micellar fluids - that is, fluids comprised of tubelike aggregations of surfactant molecules. These surfactants are amphiphilic molecules with a single carbon tail (hydrophobic), typically 16 carbons long, and a polar headgroup (hydrophilic). Above a critical concentration (the Critical Micelle Concentration, or CMC), these molecules will aggregate in solution to form micellar spheres, with a typical diameter of several Angstroms. The introduction of certain organic counterions drives a geometric transition of the spherical micelles to cylindrical tubes. These cylindrical micelles can grow to be long (to almost one micron) and flexible. While these long tubes play the same role as polymers in adding elasticity to the fluid, they are also subject to breaking and re-forming while flowing - and even at rest. The importance of these effects relative to the standard viscoelasticity can be adjusted via temperature or chemical concentration.
We have found surprising new instabilities, and modifications to previously known instabilities. The flow of wormlike micellar fluids thus provides an important distinguishing case for testing the role of microscopic dynamics to the macroscopic hydrodynamics.


Faculty and Postdocs

  • Andrew Belmonte,  Associate Professor, Dept of Mathematics, Penn State
  • Enrique Soto,  Postdoctoral Associate, Dept of Mathematics, Penn State
Students involved
  • Andong He, PhD student (mathematics), Penn State
  • Theresa Tauscher, undergraduate (astronomy), Penn State
Former Students and Postdocs involved
  • Benjamin Akers (undergraduate): Graduate student, Department of Mathematics, University of Wisconsin Madison
  • Josh Gladden,  Assistant Professor, Department of Physics, University of Mississippi
  • Torben Grumstrup (Master's, Mechanical Engineering): Fermi National Accelerator Laboratory, Batavia, IL
  • Nestor Handzy (PhD): Postdoctoral researcher, Weizmann Institute, Rehovot, Israel
  • Anand Jayaraman (postdoc): Postdoc, Department of Mathematics, Duke University
  • Thomas Podgorski (postdoc): CNRS at Laboratoire de Spéctrométrie Physique, Université de Grenoble, France
  • Linda Smolka (PhD): Assistant Professor, Department of Mathematics, Bucknell University
  • Michael Sostarecz (PhD): Visiting Assistant Professor, Department of Physics, Monmouth College


  • T. Grumstrup and A. Belmonte, ``Elastic splash of two Newtonian liquids"  Physics of Fluids 19, 091109 (2007)  pdf   (Winning entry,  * 2007 Gallery of Fluid Motion * )

  • J. R. Gladden and A. Belmonte, ``Motion of a viscoelastic micellar fluid around a cylinder: flow and fracture."  Physical Review Letters 98, 224501 (2007)  pdf

  • T. Podgorski, M. C. Sostarecz, S. Zorman, and A. Belmonte, ``Fingering instabilities of a reactive micellar interface''  Physical Review E 76, 016202[1--6] (2007)  pdf

  • B. Akers and A. Belmonte, ``Impact dynamics of a solid sphere falling into a viscoelastic micellar fluid,''  Journal of Non-Newtonian Fluid Mechanics 135, 97-108 (2006).  pdf

  • M. C. Sostarecz and A. Belmonte, ``Beads-on-string phenomena in wormlike micellar fluids,''  Physics of Fluids 16, L67-L70 (2004).  pdf

  • N. Z. Handzy and A. Belmonte, ``Oscillatory rise of bubbles in wormlike micellar fluids with different microstructures,''  Physical Review Letters 92, 124501-4 (2004).  pdf

  • L. B. Smolka and A. Belmonte, ``Drop pinch-off and filament dynamics of wormlike micellar fluids,''  Journal of Non-Newtonian Fluid Mechanics 115, 1-25 (2003).  pdf

  • A. Jayaraman and A. Belmonte, ``Oscillations of a solid sphere falling through a wormlike micellar fluid,''  Physical Review E 67, 65301-4 (2003).  pdf

  • T. Podgorski and A. Belmonte, ``Surface folds during the penetration of a viscoelastic fluid by a sphere,''  Journal of Fluid Mechanics 460, 337-348 (2002).  pdf

  • A. Belmonte, ``Self-oscillations of a cusped bubble rising through a micellar solution,''  Rheologica Acta 39, 554-559 (2000).  pdf

Related sites:
  • Rheology of wormlike micelles, by J-F Berret
  • What is rheology anyway?  by F. A. Morrison
  • Worm-like micelles stir up a storm   by Peter Olmsted

  • Department of Mathematics