Kevin Connington

Flow patterns in the sedimentation of an elliptical particle

We study the dynamics of a single two-dimensional elliptical particle sedimenting in a Newtonian fluid using numerical simulations. The main emphasis in this work is to study the effect of boundaries on the flow patterns observed during sedimentation. The simulations were performed using a multi-block lattice Boltzmann method as well as a finite-element technique and the results are shown to be consistent. We have conducted a detailed study on the effects of density ratio, aspect ratio and the channel blockage ratio on the flow patterns during sedimentation. As the channel blockage ratio is varied, our results show that there are five distinct modes of sedimentation: oscillating, tumbling along the wall, vertical sedimentation, horizontal sedimentation and an inclined mode where the particle sediments with a non-trivial orientation to the vertical. The inclined mode is shown to form a smooth bridge between the vertical and horizontal modes of sedimentation. For narrow channels, the mode of sedimentation is found to be sensitively dependent on the initial orientation of the particle. We present a phase diagram showing the transitions between the various modes of sedimentation with changing blockage ratio of the channel.

Lattice Boltzmann simulations of forced wetting transitions of drops on superhydrophobic surfaces

The behavior of drops on superhydrophobic surfaces is of interest from an engineering point of view. As it can be difficult to probe some of the more subtle phenomena by experiment, numerical simulations can be illuminating. Many research efforts have utilized the lattice Boltzmann method to glean important conclusions about the nature of this subject, but only few have done so while eliminating the phenomenon of spurious currents and employing drop densities greater than approximately ten times that of the gas density. This paper presents a new implementation of boundary conditions for the complex geometry found in simulations of drops on superhydrophobic surfaces, which extends an existing model that has been shown to eliminate spurious currents. We validate our model by comparison with experiments, and demonstrate that spurious currents are eliminated for the density ratio encountered in a water/air system. We further discuss the issue of numerical resolution for a problem that possesses such a naturally large separation of scales, and we present a comparison between two- and three-dimensional simulations. We find that an adequate resolution, which may be difficult to achieve, must be given to capture the appropriate transition from the Cassie to the Wenzel state for the case of forced wetting under gravity. Furthermore, the form of our boundary condition may be extended to cover other types of complex geometry not included here.

Interaction of fluid interfaces with immersed solid particles using the lattice Boltzmann method for liquid-gas-particle systems

Due to their finite size and wetting properties, particles deform an interface locally, which can lead to capillary interactions that dramatically alter the behavior of the system, relative to the particle-free case. Many existing multi-component solvers suffer from spurious currents and the inability to employ components with sufficiently large density differences due to stability issues. We developed a liquid-gas-particle (LGP) lattice Boltzmann method (LBM) algorithm from existing multi-component and particle dynamics algorithms that is capable of suppressing spurious currents when geometry is fixed while simulating components with liquid-gas properties. This paper presents the LGP algorithm, with several code validations. It discusses numerical issues raised by the results and the conditions under which the algorithm is most useful. The previously existing particle dynamics algorithm was augmented to capture surface tension forces arising from the interface, which was validated for the case of a 2D capillary tube. Using the full algorithm, a particle situated in a region of bulk fluid in an otherwise quiescent situation remained in its original location, indicating that spurious currents were suppressed. A particle brought into the interface of a drop (without gravity) achieved its expected depth of immersion into the drop, demonstrating that all aspects of the code work together to produce the correct equilibrium state when a particle is in the interface. As in an experiment, two particles on a flat interface approached each other due to capillary effects. The simulation approach velocity was faster than that of the experiment, but agreed qualitatively, achieving the same equilibrium state. Given the validations and the favorable, though imperfect, experimental comparison, this algorithm can be a useful tool for simulating LGP systems. The motion of particles normal to the interface can be considered reliable, and the motion tangent to the interface can be considered qualitatively accurate, leading to the correct equilibrium state.