Related papers: Gradient flow formulation and second order numeric…
Surfactants have important effects on the dynamics of droplets on solid surfaces, which has inspired many industrial applications. Phase-field surfactant model with moving contact lines (PFS-MCL) has been employed to investigate the complex…
We present a method to simulate non-coalescing impacts and rebounds of droplets onto the free surface of a liquid bath, together with new experimental data, focused on the low-speed impact of droplets. The method is derived from first…
Condensation is an important aspect of many flow applications due to the universal presence of humidity in the air at ambient conditions. For direct numerical simulations of such flows, simulating the gas phase as a mixture characterized by…
In this work, we investigate an original strategy in order to derive a statistical modeling of the interface in gas-liquid two-phase flows through geometrical variables. The con- tribution is two-fold. First it participates in the…
Walking droplets -- millimetric oil droplets that self-propel across the surface of a vibrating fluid bath -- exhibit striking emergent statistics that remain only partially understood. In particular, in a variety of experiments, a robust…
We examine theoretically the effects of random topographical substrates on the motion of two-dimensional droplets via appropriate statistical approaches. Different random substrate families are represented as stationary random functions.…
A new mechanism for the passive removal of drop on a horizontal surface is described that does not require pre-fabrication of a surface energy gradient. The method relies upon the preparation of alternate hydrophilic/hydrophobic stripes on…
The evolution of a closed two-dimensional surface driven by both mean curvature flow and a reaction--diffusion process on the surface is formulated into a system, which couples the velocity law not only to the surface partial differential…
Active contour models based on partial differential equations have proved successful in image segmentation, yet the study of their geometric formulation on arbitrary geometric graphs is still at an early stage. In this paper, we introduce…
This work has explored interface evolution and pinch-off mechanism of the droplet formation in two-phase flow through cross-flow microfluidic device. The two-dimensional mathematical model equations have been solved using the finite element…
We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the…
We consider the 2D stochastic Ising model evolving according to the Glauber dynamics at zero temperature. We compute the initial drift for droplets which are suitable approximations of smooth domains. A specific spatial average of the…
In this paper a numerical methodology for surface tension modeling is presented, with an emphasis on the implementation in the OpenFOAM framework. The methodology relies on a combination of (i) a well-balanced approach based on the Ghost…
A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here…
In this paper we prove that in $\mathbb R^3$ the minimizing movement solutions for mean curvature motion of droplets, obtained in [Bellettini, Kholmatov: J. Math. Pure Appl. (2018)], coincide with the smooth mean curvature flow of droplets…
We report an experimental investigation of the spontaneous motion of liquid droplets on soft gels with a crosslinking gradient. By systematically adjusting the spatial difference in crosslinking density, we observed that millimeter-sized…
Super hydrophobic surfaces have been the focus of research in the recent years.One of the reasons for this is the self cleaning property of these surfaces which emerges from the ability of the droplets to roll freely over them.However…
We introduce a system of shallow water-type equations to model laboratory experiments of particle-laden flows. We explore homogeneous liquid-solid suspensions of fine, non-cohesive, monodisperse glass beads which propagate as an equivalent…
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…
The single droplet under shear is a foundational problem in fluid mechanics. In computational fluid dynamics, the two-dimensional (2D) formulation offers advantages in both computational efficiency and relevance, yet its theoretical…