Interfacial flows and instabilities (free drops, jets, core-annular,
rod-annular flows):
- self-similarity solution on pinch-off and cusp formation in
Stokes flow
- breakup and drop formation with contaminated surface, e.g.
surfactants(soluble or insoluble);
- breakup and drop formation in external electric fields (electrohydrodynamics)
- interaction of multiple drops in electric fields
- wall/topological structure effect on interfacial flow
stabilities (Floquet-Bloch analysis, Fourier-Floquet-Hill
method)
- stability of a viscoelastic liquid thread
Asymptotic modeling/analysis:
- a slender leaky dielectric drop/bubble
- a slender viscous liquid thread immersed in another viscous
fluids
- thin film coating between cylindrical tubes (modified Hammond
and Kuramoto-Sivashinsky equations e.g.)
Electrochemical physics (Poisson-Nernst-Planck (PNP) system)
- boundary layer analysis in transport problem with flow
- variational approach when considering ion particle size?
Scientific computing (fast and accurate boundary integral method for
Yukawa or Modified Helmholtz kernel)
- fast summation of periodic Green's function of Laplace kernel
and Stokeslets (with geometry confinement possibly)
- hybrid method (boundary integral + boundary layer
approximation) for drops with soluble surfactant and thin Debye
layers in electric fields
- evaluation of the axisymmetric kernel (using the
one-dimensional fast algorithm by PG Martinsson? Fourier series
based on FFM?)
Modeling and simulation in math biology:
- tissue morphogenesis (modeling and simulation in dorsal
closure)
- fetal cardiovascular circulation and brain ECoG modeling in
labor
- cortical spread depression (CSD) with electrodiffusion
- PAR/GTPase protein polarity (in C-elegans, drosophila embryo
e.g.)