Rodica Borcia

Delayed coalescence of droplets with miscible liquids: Lubrication and phase field theories

Abstract.Mixing of droplets with a body of different liquids shows an interesting behavior for small contact angles at solid substrate. The droplets interact with each other, a liquid exchange appears between the approaching drops owing to surface tension gradients at the droplets interface. But the drops remain separated for some seconds (up to minutes), until the merging into a single drop occurs (Langmuir 24, 6395 (2008)). We investigate this phenomenon using lubrication approximation and phase field approach. For both methods, 2D quantitative computer simulations for delayed fusion of perfectly miscible thin liquid films/droplets with low contact angles are reported.

Can Vibrations Control Drop Motion

We discuss a mechanism for controlled motion of drops with applications for microfluidics and microgravity. The mechanism is the following: a solid plate supporting a liquid droplet is simultaneously subject to lateral and vertical harmonic oscillations. In this way the symmetry of the back-and-forth droplet movement along the substrate under inertial effects is broken and thus will induce a net driven motion of the drop. We study the dependency of the traveled distance on the oscillation parameters (forcing amplitude, frequency, and phase shift between the two perpendicular oscillations) via phase field simulations. The internal flow structure inside the droplet is also investigated. We make predictions on resonance frequencies for drops on a substrate with a varying wettability.

Controlled pattern formation in thin liquid layers.

We examine the fully nonlinear behavior of a thin liquid film on a hydrophobic/hydrophilic solid support in three dimensions using a phase field model. For flat homogeneous substrates, the stability of thin liquid layers is investigated under the action of gravity. The coarsening process at the solid boundary can be controlled on inhomogeneous substrates. On substrates chemically patterned in an adequate way with hydrophobic and hydrophilic spots, one can obtain stable, regular liquid droplets and even design liquid structures (PACS numbers: 47.54.-r, 68.18.Jk, and 05.70.Np).

A PHASE-FIELD DESCRIPTION OF SURFACE-TENSION-DRIVEN INSTABILITY

In this paper we report on 2D numerical simulations concerning linear and nonlinear evolution of surface-tension-driven instability in two-fluid systems heated from below using classical and phase-field models. In the phase-field formalism, one introduces an order parameter called phase-field function to characterize the phases thermodynamically. All the system parameters are assumed to vary continuously from one fluid bulk to another (as linear functions of the phase-field). The Navier–Stokes equation (with some extra terms) and the heat equation are written only once for the whole system. The evolution of the phase-field is described by the Cahn–Hilliard equation. In the sharp-interface limit the results found by the phase-field formalism recover the results given by the classical formulation.

On the coalescence of sessile drops with miscible liquids

Sessile drops sitting on highly wettable solid substrates fuse in qualitatively different ways after contact, depending on the surface tension gradients between the mixing droplets. In early time evolution the drop coalescence can be fast or delayed (intermittent). In long time evolution a secondary drop formation can occur. We study numerically droplet dynamics during coalescence in two and three spatial dimensions, within a phase field approach. We discuss criteria to distinguish different coalescence regimes. A comparison with recent experiments will be done.

CONVECTIVE PATTERNS IN LIQUID–VAPOR SYSTEMS WITH DIFFUSE INTERFACE

Recently, we have developed a phase field model to describe Marangoni convection with evaporation in a compressible fluid of van der Waals type away from criticality [Eur. Phys. J. B44 (2005)]. Using this model, we report now 2D fully nonlinear simulations where we emphasize the influence of evaporation on convective patterns.

Phase Field Modeling of Nonequilibrium Patterns on the Surface of a Liquid Film Under Lateral Oscillations at the Substrate

We use a phase field model which couples the generalized Navier–Stokes equation (including the Korteweg stress tensor) with the continuity equation for studying nonlinear pattern formation on the surface of a liquid film under (linear and circular) lateral harmonic vibrations at the solid substrate. First, we prove the thermodynamic consistency of our phase field model. Next, we present computer simulations in three spatial dimensions. We illustrate nonequilibrium patterns at the instability onset, confirming in this way the results recently reported in Phys. Rev. E 88, 023025 (2013). The lateral profiles of the deflected surface are compared with those reported in J. Fluid Mech. 686, 409 (2011) for Faraday instability excited by vertical harmonic vibrations at the bottom plate.

A phase field description of self-propulsion of twin sessile drops induced by surface tension gradients

We describe the self-propulsion of two sessile drops induced by surface tension gradients at the droplet interfaces using a three-dimensional phase field model. We study the problem for the low viscosity regime when the width of the connecting neck between the interacting drops increases linearly with increasing t1/2 and the merger is dominated by capillary forces. We investigate the dependence of the displacement achieved by self-propulsion on viscous shearing as well as the internal flow structure during the coalescence process.

Liquid layers on patterned surfaces

We examine numerically the behavior of liquid layers on horizontal patterned surfaces with hydrophobic and hydrophilic stripes. To this aim we use a phase field model as a mathematical tool with the density as the order parameter. The theoretical description is based on the Navier–Stokes equation with extra phase field terms and the continuity equation. The surface heterogeneity is controlled through the boundary conditions for the density field at the liquid–solid interface.

Numerical Simulations on Delayed Coalescence of Droplets in Confined Geometries

We investigate numerically the interaction between two sessile droplets with different perfectly miscible liquids. This application is motivated by recent experimental observations showing that for sufficiently small contact angles, a temporary non‐coalescence can occur after a lateral contact between drops [H. Riegler and P. Lazar, Langmuir 24, 6395 (2008)]. The theoretical framework is based on a phase field model previously developed for sessile drops in gas atmosphere on a horizontal solid substrate [R. Borcia et al., Phys. Rev. E 78, 066307 (2008)]. 2D numerical simulations are performed for closed systems (confined geometries) with different ratios between the surface and viscous forces. Depending on this ratio, different behaviors of delayed coalescence are observed from “chasing droplets” to “droplets repulsion.”