Development of a Moving Front Kinetic Monte Carlo Algorithm to Simulate Moving Interface Systems

Abstract

Moving interfaces play vital and crucial roles in a wide variety of different natural, technological, and industrial processes, including solids dissolution, capillary action, sessile droplet spreading, and superhydrophobicity. In each of these systems, the fundamental process behaviour is entirely dependent on the interface and on the underlying physics governing its movement. As a result, there is significant interest in studying and developing models to capture the behaviour of these moving interface systems over a wide variety of different applications. However, the simulation techniques used to model moving interfaces are limited in their application, as the molecular-level models are unable to simulate interface behaviour over large spatial and temporal scales, whereas the large-scale modeling techniques cannot account for the nanoscale processes that govern the interface behaviour or the molecular-scale fluctuations and deviations in the interface. Furthermore, methods developed to bridge the gap between the two scales are prone to error-induced force imbalances at the interface that can result in fictitious behaviour. In order to overcome these challenges, this study developed a novel kinetic Monte Carlo (kMC)-based modelling technique referred to as Moving Front kMC (MFkMC) to adequately and efficiently capture the molecular-scale events and forces governing the moving interface behaviour over large length and timescales. This framework was designed to capture the movement of transiently-varying interfaces in a kinetic-like manner so that its movement can be described using Monte Carlo sampling. The MFkMC algorithm accomplishes this task by evaluating the behaviour of the interfacial molecules and assigning kinetic Monte Carlo-style rate equations that describe the transition probability that a molecule would advance into the neighbouring phase, displacing an interfacial molecule from the opposing phase and thus changing the interface. The proposed algorithm was subsequently used to capture the moving interface behaviour within crystal dissolution, capillary rise, and sessile droplet spreading on both smooth and superhydrophobic surfaces. The individual system models for each application were used to analyze the behaviour within each application and to tackle challenges within each field. The MFkMC modelling method was initially used to capture crystal dissolution for applications in pharmaceutical drug delivery. The developed model was designed to predict the dissolution of a wide variety of crystalline minerals, regardless of their composition and crystal structure. The MFkMC approach was compared against a standard kMC model of the same system to validate the MFkMC approach and highlight its advantages and limitations. The proposed framework was used to explore ways of enhancing crystal dissolution processes by assessing the variability from environmental uncertainties and by performing robust optimization to improve the dissolution performance. The approach was used to simulate calcium carbonate dissolution within the human gastrointestinal system. Polynomial chaos expansions (PCEs) were used to propagate the parametric uncertainty through the kMC model. Robust optimization was subsequently performed to determine the crystal design parameters that achieve target dissolution specifications using low-order PCE coefficient models (LPCMs). The results showcased the applicability of the kMC crystal dissolution model and the need to account for dissolution uncertainty within key biological applications. The MFkMC approach was additionally used to capture capillary rise in cavities of different shapes. The proposed model was adapted to capture the movement of a fluid-fluid interface, such as the moving interface present in capillary action studies, using kMC type approaches based on the forces acting locally upon the interface. The proposed force balance-based MFkMC (FB-MFkMC) expressions were subsequently coupled with capillary action force balance equations to capture capillary rise within any axisymmetric cavity. The developed model was validated against known analytical models that capture capillary rise dynamics in perfect cylinders. Furthermore, the resulting multiscale model was used to analyze capillary rise within axisymmetric cavities of irregular shape and in cylinders subject to surface roughness. These studies highlighted that the FB-MFkMC algorithm can capture the macroscale behaviour of a system subject to molecular-level irregularities such as surface roughness. Furthermore, they highlighted that phenomena such as roughness can significantly affect moving interface behaviour and highlight the need to accommodate for these phenomena. MFkMC was furthermore extended to capture sessile droplet spreading on a smooth surface. The developed approach adapted the capillary action FB-MFkMC model to capture the spreading behaviour of a droplet based on the force balance acting upon the droplet interface, which was developed using analytical inertial and capillary expressions from the literature. This study furthermore derived a new semi-empirical expression to depict the viscous damping force acting on the droplet. The developed viscous force term depends on a fitted parameter c, whose value was observed to vary solely depending on the droplet liquid as captured predominantly by the droplet Ohnesorge number. The proposed approach was subsequently validated using data obtained both from conducted experiments and from the literature to support the robustness of the framework. The predictive capabilities of the developed model were further inspected to provide insights on the sessile droplet system behaviour. The developed FB-MFkMC model was additionally modified to capture sessile droplet spreading on pillared superhydrophobic surfaces (SHSs). These adjustments included developing the Periodic Unit (PU) method of capturing periodic SHS pillar arrays and accommodating for the changes necessary to capture the droplet spreading behaviour across the gaps between the pillars (i.e., Cassie mode wetting). The proposed SHS-based FB-MFkMC (SHS-MFkMC) model was furthermore adapted to accommodate for spontaneous Cassie-to-Wenzel (C2W) droplet transitions on the solid surface. The capabilities of the full SHS-MFkMC model to capture both radial sessile droplet spread and spontaneous C2W transitions were compared to experimental results from within the literature. Furthermore, a sensitivity analysis was conducted to assess the effects of the various system parameters on the model performance and compare them with the expected system results.