Taehun Lee

Coalescence-induced jumping of droplet: Inertia and viscosity effects

The problem of coalescence-induced self-propelled jumping of droplet is studied using three-dimensional numerical simulation. The focus is on the effect of inertia and in particular the effect of air density on the behavior of the merged droplet during jumping. A lattice Boltzmann method is used for two identical, static micro-droplets coalescing on a homogeneous substrate with contact angle ranging from 0∘ to 180∘. The results reveal that the effect of air density is significant on detachment of the merged droplet from the substrate at the later stage of the jumping process; the larger the air density, the larger the jumping height of the droplet. Analysis of streamlines and vorticity contours is performed for density ratios ranging from 60 to 800. These show a generation of vortical structures inside and around the droplet. The intensity of these structures gets weaker after droplet departure as the air inertia is decreased. The results are also presented in terms of phase diagrams of the merged droplet jumping for different Ohnesorge numbers (Oh) and surface wettabilities for both small and large density ratios. The critical value of contact angle where the merged droplet jumps away from the substrate is independent of density ratio and has a value around 150∘. However, the critical value of Oh depends on both density ratio and wettability of the surface for contact angles greater than 150∘. In this range of contact angle, the diagrams show two distinct dynamical regimes for different density ratios, namely, inertial and viscous regimes.

Multiscale liquid drop impact on wettable and textured surfaces

The impact of microscopic liquid drops on solids with a variety of surface characteristics is studied using numerical simulations. The focus is on relatively low impact velocities leading to bouncing or spreading drops, and the effects of wettability. Molecular dynamics and lattice Boltzmann simulation methods are used for nanometer-sized and continuum drops, respectively, and the results of the two methods are compared in terms of scaled variables. We consider surfaces which are flat, curved or pillared, with either homogeneous interactions or cross-shaped patterns of wettability. In most situations we observe similar drop behavior at both length scales; the two methods agree best at low impact velocities on wettable surfaces while discrepancies are most pronounced for strongly hydrophobic surfaces and for higher velocities.

Effects of initial conditions on the simulation of inertial coalescence of two drops

A numerical study has been performed using a lattice Boltzmann method (LBM) for an incompressible binary fluid based on the Cahn-Hilliard diffuse interface approach to investigate the effects of initial conditions on the early stages of inertial coalescence. We focus on the effects of starting the simulation with two drops connected by a small finite contact radius, and two drops separated by a small finite distance, on the growth dynamics of the liquid bridge connecting the drops. For initially connected drops, we observed a slower initial growth of the bridge radius, and for initially separated drops, we found that, because of the diffuse interface dynamics, the bridge evolution is sensitive to the value of the initial separation between the drops.

Dynamics of viscous coalescing droplets in a saturated vapor phase

The dynamics of two liquid droplets coalescing in their saturated vapor phase are investigated by Lattice Boltzmann numerical simulations. Attention is paid to the effect of the vapor phase on the formation and growth dynamics of the liquid bridge in the viscous regime. We observe that the onset of the coalescence occurs earlier and the expansion of the bridge initially proceeds faster when the coalescence takes place in a saturated vapor compared to the coalescence in a non-condensable gas. We argue that the initially faster evolution of the coalescence in the saturated vapor is caused by the vapor transport through condensation during the early stages of the coalescence.

A new splitting scheme to the discrete Boltzmann equation for non-ideal gases on non-uniform meshes

We present a novel numerical procedure for solving the discrete Boltzmann equations (DBE) on non-uniform meshes. Our scheme is based on the Strang splitting method where we seek to investigate two-phase flow applications. In this note, we investigate the onset of parasitic currents which arise in many computational two-phase algorithms. To the best of our knowledge, the results presented in this work show, for the first time, a spectral element discontinuous Galerkin (SEDG) discretization of a discrete Boltzmann equation which successfully eliminates parasitic currents on non-uniform meshes. With the hope that this technique can be used for applications in complex geometries, calculations are performed on non-uniform mesh distributions by using high-order (spectral), body-fitting quadrilateral elements. Validation and verification of our work is carried out by comparing results against the classical 2D YoungLaplace law problem for a static drop.

Coalescence-induced jumping of immersed and suspended droplets on microstructured substrates

The coalescence-induced jumping of liquid droplets on superhydrophobic structured substrates is investigated numerically using a three-dimensional multiphase lattice Boltzmann method. The numerical experiments on evolution of droplets during jumping process show higher jumping velocity and height from superhydrophobic substrates structured with a periodic array of square pillars, than flat superhydrophobic substrates with an equilibrium contact angle of . The results further reveal a strong effect of pillars on the vertical jumping velocity and the final quasi-equilibrium height of the merged droplet as a function of air and liquid viscosity, as well as air inertia. As for substrate wettability, it is found that, compared to the flat superhydrophobic substrate, the critical contact angle where the merged droplet jumps away from substrate is reduced for pillared substrate and is about . It is also observed that the droplet initial placement on a substrate with a square array of pillars has an important effect on the spontaneous jumping of the coalesced droplet, and a Wenzel–Cassie wetting transition upon coalescence is observed for droplets that are initially immersed within the pillars.