A moving, solidifying interface that grows by the instantaneous adsorption of a diffusing solute is described by the classic one-sided “Stefan problem” [15, 19]. More generally, the behavior of precipitate growth can depend on both surface kinetics and bulk drift of the depositing species. We generalize the Stefan problem and its interface boundary condition to explicitly account for both surfa...

The facet-engineered surface and interface design for photocatalytic materials has been proven as a versatile approach to enhance their photocatalytic performance. This review article encompasses some recent advances in the facet engineering that has been performed to control the surface of mono-component semiconductor systems and to design the surface and interface structures of multi-componen...

We propose a practical numerical framework for free surface flows with surface tension force. The numerical framework consists of the CLSVOF (coupled level set and volumeof-fluid) method, the THINC/WLIC (tangent of hyperbola for interface capturing/weighted line interface calculation) scheme, multi-moment methods (CIP-CSL and VSIAM3) and the density-scaled CSF (continuum surface force) model. W...

A simple model for the interfacial free energy of a semicoherent interface is used to develop expressions for interface stresses, which are surface thermodynamic quantities associated with solid–solid interfaces. An analysis of the thermodynamics of thin film epitaxy is presented that incorporates the effects of free surface and interface stresses, and an expression for the critical thickness f...

We succeeded in fabrication of a free accessible microchannel using an air-liquid interface. To pattern the air-liquid interface in the microfluidic chip, we utilized nano-geometric surface which encloses micropatterned massive nanopillars to enhance the wettability of the surface, which was fabricated by using the hybrid mask lithography technique. Novelties of this paper are shown as follows....

Morphological instabilities are common to pattern formation problems such as the non-equilibrium growth of crystals and directional solidiication. Very small perturbations caused by noise originate convoluted interfacial patterns when surface tension is small. The generic mechanisms in the formation of these complex patterns are present in the simpler problem of a Hele-Shaw interface. Amid this...

Morphological instabilities are common to pattern formation problems such as the non-equilibrium growth of crystals and directional solidification. Very small perturbations caused by noise originate convoluted interfacial patterns when surface tension is small. The generic mechanisms in the formation of these complex patterns are present in the simpler problem of a Hele-Shaw interface. Amid thi...

In this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unkn...