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






























































































































































































  • Complex fluids and materials
  • Active matter
  • Liquid crystal physics
  • Nonlinear elasticity
  • Fluid-structure interaction
  • Soft robotics
  • Biological flows and biomedicine
  • High performance computing 


1.  Soft colloids

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.  Active matter

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.
* Active cellular matter   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.
* Control of active matter through confinement   To effectively control the collective dynamics in various internally-driven systems, it is critical to manipulate the emergent coherent structures. One way of doing this is to tune the suspension concentration and the amount of chemical fuels. Alternatively, we can take advantage of the particle interactions, either individually or collectively, with obstacles and geometric boundaries to manipulate the system more directly. By trapping active suspensions (such as Pusher swimmers or Quincke rollers) within the straight and curved boundaries, stable flow patterns, such as unidirectional circulations, traveling waves, density shocks, and rotating vortices, have already been constructed. More interestingly, active nematic flows under soft confinement by surface tension are able to generate internal flows to break symmetry and drive the whole-body movement.

3.  Numerical methods and theoretical models

Modeling and simulation of fluid-structure interaction problems in complex fluids environement is very challenging, especially when the objects are moving or deforming. Furthermore, it becomes more and more important to develop and integrate hybrid algorithms that combine computational fluid dynamics techniques and stochastic methods to perform large-scale simulations, together with coarse-grained modeling, to reveal the multiscale physics in novel soft matter systems.
* 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.
* Fictitious domain method  We have been developing a fictitious domain (FD)/active muscle model that can handle active swimming of soft robots through periodic nonlinear elastic deformations that are actuated by distributing active stresses or strains on desired locations. The key idea of FD method is to virtually extend the exterior fluid field into the material domain where a distribution of pseudo body forces are employed to enforce the structural movement through Lagrange multipliers.
* 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.
* Continuum models for active fluids  For biological and synthetic fluids, their physical properties are determined by many-body hydrodynamic interactions between tens of thousands of suspended microstructures. Although direct simulations are possible, it is much more convenient to model the complex fluids through continuum models. At small Reynolds number, we investigate suspensions of the rod-like microparticles that are of different shapes, material properties, and activities. Their suspension mechanics is then investigated by using either (microscopic) Doi-Onsager models or coarse-grained (macroscopic) liquid crystal models.
Funding Support
      National Science Foundation
            CAREER (PMP CBET): No. 1943759
            Comput Math: No. 1619960
            Fluid Dyn. : No. 1702987
      MSU's Strategic Partnership Grants (SPG)