Shahriar Afkhami

A mesh-dependent model for applying dynamic contact angles to VOF simulations

Typical VOF algorithms rely on an implicit slip that scales with mesh refinement, to allow contact lines to move along no-slip boundaries. As a result, solutions of contact line phenomena vary continuously with mesh spacing; this paper presents examples of that variation. A mesh-dependent dynamic contact angle model is then presented, that is based on fundamental hydrodynamics and serves as a more appropriate boundary condition at a moving contact line. This new boundary condition eliminates the stress singularity at the contact line; the resulting problem is thus well-posed and yields solutions that converge with mesh refinement. Numerical results are presented of a solid plate withdrawing from a fluid pool, and of spontaneous droplet spread at small capillary and Reynolds numbers.

Deformation of a hydrophobic ferrofluid droplet suspended in a viscous medium under uniform magnetic fields

The effect of applied magnetic fields on the deformation of a biocompatible hydrophobic ferrofluid drop suspended in a viscous medium is investigated numerically and compared with experimental data. A numerical formulation for the time-dependent simulation of magnetohydrodynamics of two immiscible non-conducting fluids is used with a volume-of-fluid scheme for fully deformable interfaces. Analytical formulae for ellipsoidal drops and near-spheroidal drops are reviewed and developed for code validation. At low magnetic fields, both the experimental and numerical results follow the asymptotic small deformation theory. The value of interfacial tension is deduced from an optimal fit of a numerically simulated shape with the experimentally obtained drop shape, and appears to be a constant for low applied magnetic fields. At high magnetic fields, on the other hand, experimental measurements deviate from numerical results if a constant interfacial tension is implemented. The difference can be represented as a dependence of apparent interfacial tension on the magnetic field. This idea is investigated computationally by varying the interfacial tension as a function of the applied magnetic field and by comparing the drop shapes with experimental data until a perfect match is found. This estimation method provides a consistent correlation for the variation in interfacial tension at high magnetic fields. A conclusion section provides a discussion of physical effects which may influence the microstructure and contribute to the reported observations.

Field-induced motion of ferrofluid droplets through immiscible viscous media

The motion of a hydrophobic ferrofluid droplet placed in a viscous medium and driven by an externally applied magnetic field is investigated numerically in an axisymmetric geometry. Initially, the drop is spherical and placed at a distance away from the magnet. The governing equations are the Maxwell equations for a non-conducting flow, momentum equation and incompressibility. A numerical algorithm is derived to model the interface between a magnetized fluid and a non-magnetic fluid via a volume-of-fluid framework. A continuum-surface-force formulation is used to model the interfacial tension force as a body force, and the placement of the liquids is tracked by a volume fraction function. Three cases are studied. First, where inertia is dominant, the magnetic Laplace number is varied while the Laplace number is fixed. Secondly, where inertial effects are negligible, the Laplace number is varied while the magnetic Laplace number is fixed. In the third case, the magnetic Bond number and inertial effects are both small, and the magnetic force is of the order of the viscous drag force. The time taken by the droplet to travel through the medium and the deformations in the drop are investigated and compared with a previous experimental study and accompanying simpler model. The transit times are found to compare more favourably than with the simpler model.

Numerical investigation of elongated drops in a microfluidic T-junction

We present a combined numerical and asymptotic approach for modeling droplets in microchannels. The magnitude of viscous forces relative to the surface tension force is characterized by a capillary number, Ca, which is assumed to be small. The numerical results successfully capture existing asymptotic solutions for the motion of drops in unconfined and confined flows; examples include the analytic Stokes flow solution for a two-dimensional inviscid bubble placed in an unbounded parabolic flow field and asymptotic formulas for slender bubbles and drops in confined flows. An extensive investigation of the accuracy of the computations is presented to probe the efficacy of the methodology and algorithms. Thereafter, numerical simulations are presented for droplet breakup in a symmetric microfluidic T-junction. The results are shown to support a proposed mechanism for breakup, driven by a pressure drop in a narrow gap between the droplet and the outer channel wall, which was formally derived in the limit Ca1/5...

Hierarchical Nanoparticle Ensembles Synthesized by Liquid Phase Directed Self-Assembly

A liquid metal filament supported on a dielectric substrate was directed to fragment into an ordered, mesoscale particle ensemble. Imposing an undulated surface perturbation on the filament forced the development of a single unstable mode from the otherwise disperse, multimodal Rayleigh-Plateau instability. The imposed mode paved the way for a hierarchical spatial fragmentation of the filament into particles, previously seen only at much larger scales. Ultimately, nanoparticle radius control is demonstrated using a micrometer scale switch.

Directed assembly of one- and two-dimensional nanoparticle arrays from pulsed laser induced dewetting of square waveforms.

The directed assembly of arrayed nanoparticles is demonstrated by dictating the flow of a liquid phase filament on the nanosecond time scale. Results for the assembly of Ni nanoparticles on SiO2 are presented. Previously, we have implemented a sinusoidal perturbation on the edge of a solid phase Ni, thin film strip to tailor nanoparticle assembly. Here, a nonlinear square waveform is explored. This waveform made it possible to expand the range of nanoparticle spacing-radius combinations attainable, which is otherwise limited by the underlying Rayleigh-Plateau type of instability. Simulations of full Navier-Stokes equations based on volume of fluid method were implemented to gain further insight regarding the nature of instability mechanism leading to particle formation in experiments.

A volume of fluid method for simulating fluid/fluid interfaces in contact with solid boundaries

In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit inclusion of the fluid/solid interaction forces into the governing equations. We show that the interaction forces lead to a partial wetting condition and in particular to a natural definition of the equilibrium contact angle. We present two numerical methods to discretize the interaction forces that enter the model; these two approaches differ in complexity and convergence. To validate the computational framework, we consider the application of these models to simulate two-dimensional drops at equilibrium, as well as drop spreading. We demonstrate that the model, by including the underlying physics, captures contact line dynamics for arbitrary contact angles. More generally, the approach permits novel means to study contact lines, as well as a diverse range of phenomena that previously could not be addressed in direct simulations.

Comparison of Navier-Stokes simulations with long-wave theory: Study of wetting and dewetting

The classical long-wave theory (also known as lubrication approximation) applied to fluid spreading or retracting on a solid substrate is derived under a set of assumptions, typically including small slopes and negligible inertial effects. In this work, we compare the results obtained by using the long-wave model and by simulating directly the full two-phase Navier-Stokes equations employing a volume-of-fluid method. In order to isolate the influence of the small slope assumption inherent in the long-wave theory, we present a quantitative comparison between the two methods in the regime where inertial effects and the influence of gas phase are negligible. The flow geometries that we consider include wetting and dewetting drops within a broad range of equilibrium contact angles in planar and axisymmetric geometries, as well as liquid rings. For perfectly wetting spreading drops we find good quantitative agreement between the models, with both of them following rather closely Tanners law. For partially wet...

A volume-of-fluid formulation for the study of co-flowing fluids governed by the Hele-Shaw equations

We present a computational framework to address the flow of two immiscible viscous liquids which co-flow into a shallow rectangular container at one side, and flow out into a holding container at the opposite side. Assumptions based on the shallow depth of the domain are used to reduce the governing equations to one of Hele-Shaw type. The distinctive feature of the numerical method is the accurate modeling of the capillary effects. A continuum approach coupled with a volume-of-fluid formulation for computing the interface motion and for modeling the interfacial tension in Hele-Shaw flows is formulated and implemented. The interface is reconstructed with a height-function algorithm. The combination of these algorithms is a novel development for the investigation of Hele-Shaw flows. The order of accuracy and convergence properties of the method are discussed with benchmark simulations. A microfluidic flow of a ribbon of fluid which co-flows with a second liquid is simulated. We show that for small capillary...

Instability of nano- and microscale liquid metal filaments: Transition from single droplet collapse to multidroplet breakup

We carry out experimental and numerical studies to investigate the collapse and breakup of finite size, nano- and microscale, liquid metal filaments supported on a substrate. We find the critical dimensions below which filaments do not break up but rather collapse to a single droplet. The transition from collapse to breakup can be described as a competition between two fluid dynamic phenomena: the capillary driven end retraction and the Rayleigh-Plateau type instability mechanism that drives the breakup. We focus on the unique spatial and temporal transition region between these two phenomena using patterned metallic thin film strips and pulsed-laser-induced dewetting. The experimental results are compared to an analytical model proposed by Driessen et al. and modified to include substrate interactions. In addition, we report the results of numerical simulations based on a volume-of-fluid method to provide additional insight and highlight the importance of liquid metal resolidification, which reduces inertial effects.