• Simulation of tissue morphogenesis
  • Cell mechanics: collective migration, fluidization and activation
  • Tear film breakup in healthy and infected eyes
  • Dynamics of moving contact lines
  • Morphology of sheared foam
  • Interfacial dynamics in complex fluids
  • Self-assembly of micro-particles and droplets

  • When a liquid-liquid interface intersects a solid substrate, a three-phase contact line (or wetting line) is formed. This is perhaps the most notorious and intransigent problem in multiphase flows since the conventional Navier-Stokes formulation, with no-slip boundary condition on the substrate, runs into a singularity at the contact line. In recent years we have explored the use of phase-field models to compute moving contact lines. The advantages include a more rational regularization of the singularity (in terms of Cahn-Hilliard diffusion), and the ease in capturing moving and deforming interfaces as well as their coalescence or breakup. We are interested in fundamental physical and numerical issues of this approach, as well as applications.

    (Fig. 1. In the lotus effect, the superhydrophobicity of the surface stems from the hierarchical surface roughness. Images from Wikipedia.)

    In applications, a particularly interesting set of problems involve the pinning and movement of contact lines on textured and superhydrophic substrates. The lotus leaf epitomizes nature's application of the basic principle (Fig. 1 above). Laboratory experiments showed the possibility of attaining very large drag reduction and apparent slip on micro-textured substrates. Our recent simulation has attributed these to the depinning of contact lines at the edge of micro-pits or ridges. In particular, a continuous gas film may form on the substrate that completely insulates and lubricates the liquid. The movie in Fig. 2 illustrates the sub-optimal situation when the gas film (blue) breaks up to form a bubble that is pushed along by the flowing liquid (red). Motivated by water transport problems in proton-exchange membrane fuel cells, we are applying similar ideas to air-water flows in porous media, modeled as micropores of varying cross-sections (Fig. 3).


    Fig. 2. Evolution of the gas-liquid interface on a substrate textured with grooves and ridges. Only one period of the spatial pattern is shown.

    Fig. 3. Annular-droplet flow in an axisymmetric micropore with periodic constrictions. Only one period of the spatial pattern is shown.

    The dynamics of moving contact lines also figures prominently in the locomotion of surface dwelling creatures such as water striders and water spiders. We carried out a simulation of the rowing motion of a single leg of a water strider, modeled as a 2D hydrophobic cylinder that rows on the water surface. The movie below illustrates a single cycle of the rowing, with colors indicating the magnitude of vorticity.


    (Fig. 4. Rowing of the leg of a water strider simulated as a 2D cylinder. Note the meniscus ahead of the leg in the driving stroke and the surface waves generated, as well as the detachment of the leg in the recovery stroke. The contact angle on the cylinder is 120°.)

Department of ChBE / Department of Mathematics / Fluids Lab / James J. Feng / Research