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Currently, there are several ongoing research projects that cover the following areas:

  • Complex fluids and materials
  • Active matter
  • Computational fluid dynamics
  • Liquid crystal physics
  • Cell mechanics
  • Fluid-structure interaction
  • Electrohydrodynamics
  • Microfluidics
  • Fast summation methods 

Research highlights

1.  Soft particles

Microscopic soft particles are commonly found in nature and engineeringapplications. Examples include red blood cells, fluid vesicles and microgel particles. When placed in a liquid, soft particles can readily undergo large deformations to accommodate the hydrodynamic forces, which in turn has a significant impact on the macroscopic rheological properties of the mixture.
* Shear flow   We consider a suspension of elastic solid particles in a viscous liquid. The particles are assumed to be neo-Hookean and can undergo finite deformation. When placed in a shear flow, three types of motion - steady-state, trembling and tumbling - are found. The rheological properties generally exhibit shear-thinning behavior, and can even show negative intrinsic viscosity for sufficiently soft particles.

* Extensional flow   We investigate the dynamics and rheology of neo-Hookean elastic particles in a viscous extensional flow under Stokes flow condition. When subjected to an extensional field, an initially ellipsoidal particle stretches and rotates simultaneously, tending to deform into another stable ellipsoidal shape. However, the steady-state solutions may not exist when the particle stiffness is very lower. The rheology study shows that the suspension exhibits strain-thickenning effect, similar to some polymer blends.
* Electrohydrodynamics of soft particle   We study the dynamics of a long elastic particle undergoing electrophoresis. The particle is elliptical in shape and is initially aligned with its major axis perpendicular to the direction of a uniformly applied electric field. The particle tends to curl up at its ends and arches in the middle. After a transient deformation, the particle migrates at Helmholtz-Smoluchowski velocity.

2.  Biofilament assemblies

As a new branch of complex fluids, active matter is composed of self-driven constitutes with emergence of nonequilibrium physics. Despite the difference in composition, all these active systems orchestrate cooperative actions across various length and time scales. They are commonly featured by collective motions, order transitions, and anomalous fluctuations and mechanical properties, accompanying energy conversion from one form to another. Typical systems include cytoskeletal networks, synthetic microswimmers, bacterial suspensions, etc.
* Microtubules (MTs) and molecular motors   Microtubules and motor-proteins are the building blocks of self-organized subcellular structures such as the mitotic spindle and the centrosomal microtubule array. They are ingredients in new "bioactive" liquid-crystalline fluids that are powered by ATP, and driven out of equilibrium by motor-protein activity to display complex flows and defect dynamics. We develop a multiscale theory for such systems. Brownian dynamics simulations of polar microtubule ensembles, driven by active crosslinks, are used to study microscopic organization and the stresses created by microtubule interactions. This identifies two polar-specific sources of active destabilizing stress: polarity-sorting and crosslink relaxation. We develop a Doi-Onsager theory that captures polarity sorting, and the hydrodynamic flows generated by polar-specific active stresses. In simulating experiments of active flows on immersed surfaces, the model exhibits turbulent dynamics and continuous generation and annihilation of disclination defects. Analysis shows that the dynamics follows from two linear instabilities, and gives characteristic length- and time-scales.

3.  Simulation methods for fluid-structure interactions

Numerical simulation of flow over a rigid or flexible body with complex immersed boundary is a challenging problem in computational fluid dynamics. When the objects are moving, The computation becomes even more expensive and time consuming to achieve high accuracy. Moreover, due to the multiscale nature of the complex fluids, it is desired to develop and integrate numerical methods to resolve physics across temporal and spatial scales. Our group works on both theoretical and numerical methods in the general category of complex fluids.
* Arbitrary Lagrangian-Eulerian finite element  We develop a new finite element method with moving mesh technique to solve the dynamics of elastic particles deforming in a viscous shear flow. In comparison with the previous treatments, we solve the unknown variables in both fluid and solid phase are the velocity, pressure and stress simultaneously. In this method, consistent time integration schemes and discretizing methods can be employed for all physical variables, eventually leading to a linear system which can be solved by efficient iterative schemes with appropriate preconditioners.
* Hybrid Cartesian/immersed boundary method We propose an improved hybrid Cartesian/immersed boundary method based on ghost point treatment. A second-order Taylor series expansion is used to evaluate the values at the ghost points, and an inverse distance weighting method to interpolate the values due to its properties of preserving local extrema and smooth reconstruction. The present method effectively eliminates numerical instabilities caused by matrix inversion and flexibly adopts the interpolation in the vicinity of the boundary.
* Mesoscopic methods for complex fluids  For biological and synthetic fluids, their mechanical and dynamical properties are determined by many-body hydrodynamic interactions between tens of thousands of suspended microstructures. Although direct simulations are possible, sometimes it is more convenient to model these complex fluids using mesoscopic continuum models. At small Reynolds number, we investigate the suspensions of rod-like particles of different shapes, material properties, and activities. The corresponding suspension mechanics is then investigated using a Doi-Onsager theory that is constructed upon the Smoluchowski-Stokes equations.


       Michael J. Shelley (Courant Institute)
             Howard H. Hu (Penn)
             Pedro Ponte Castañeda (Penn)
             David Saintillan (UCSD)
 Meredith D. Betterton (UC Boulder)
             Matthew A. Glaser (UC Boulder)