- 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.

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.

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.

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.

Collaborators

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)