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Hypothesis Control of capillary flow through porous media has broad practical implications. However, achieving accurate and reliable control of such processes by tuning the pore size or by modification of interface wettability remains…
We propose a numerical approach to study the mechanics of a flowing bubble in a constraint micro channel. Using an open source two phase flow solver (Gerris, gfs.sourceforge.net) we compute solutions of the bubble dynamics (i.e. shape and…
In this paper, we propose a novel method for monocular depth estimation in dynamic scenes. We first explore the arbitrariness of object's movement trajectory in dynamic scenes theoretically. To overcome the arbitrariness, we use assume that…
In this paper, we present a novel interface-driven adaptive variational procedure using a fully Eulerian description of fluid-structure interaction. The proposed fully-Eulerian procedure involves a fixed background unstructured mesh on…
Microdrop impact and spreading phenomena are explored as an interface formation process using a recently developed computational framework. The accuracy of the results obtained from this framework for the simulation of high deformation…
Directed motion of liquid droplets is of considerable importance in various industrial processes. Despite extensive advances in this field of research, our understanding and the ability to control droplet dynamics at high temperature remain…
We consider two dimensional dispersions of droplets of isotropic phase in a liquid with an XY-like order parameter, tilt, nematic, and hexatic symmetries being included. Strong anchoring boundary conditions are assumed. Textures for a…
The dynamics of particles attached to an interface separating two immiscible fluids are encountered in a wide variety of applications. Here we present a combined asymptotic and numerical investigation of the fluid motion past spherical…
A mathematical model for the evolution of, and deposition from, a thin particle-laden droplet on an infinitely thick, isotropic, flooded, porous substrate with interconnected pores undergoing simultaneous evaporation and imbibition is…
We present a molecular dynamics study of the motion of cylindrical polymer droplets on striped surfaces. We first consider the equilibrium properties of droplets on different surfaces, we show that for small stripes the Cassie-Baxter…
We study the asymptotic behavior of the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of size $\varepsilon$ separated by distances $d_\varepsilon$ and the fluid fills the…
This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…
We present an effective method for simulating wall-bounded multiphase flows consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids with different densities, viscosities and pairwise surface tensions. The N-phase physical…
The immersed interface method (IIM) for fluid-structure interaction imposes discontinuities in the fluid stress along immersed boundaries that are generated by forces concentrated along those boundaries. For a viscous incompressible fluid,…
A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic liquid crystal fluid with stretching effect, which takes into account the geometrical shape of its molecules. This system…
In this note, we propose several unsolved problems concerning the irrotational oscillation of a water droplet under zero gravity. We will derive the governing equation of this physical model, and convert it to a quasilinear dispersive…
The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses…
In this article, we describe the instability of a contact line under nonequilibrium conditions mainly based on the results of our recent studies. Two experimental examples are presented: the self-propelled motion of a liquid droplet and…
We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is…
Droplet impact behavior has attracted much attention recently due to its academic significance and diverse industrial applications. This study employs the lattice Boltzmann method to simulate the impact of a droplet on a hydrophobic plate…