Tuning Drop Motion by Chemical Chessboard-Patterned Surfaces: A Many-Body Dissipative Particle Dynamics Study

A model for micro-front dynamics using a ϕ4 equation

In this article, we propose a numerical model based on the ϕ4 equation to simulate the dynamics of a front inside a microchannel that features an imperfection at a sidewall to different flow rates. The micro-front displays pinning-depinning phenomena without damped oscillations in the aftermath. To model this behavior, we propose a ϕ4 model with a localized external force and a damping coefficient. Numerical simulations with a constant damping coefficient show that the front displays pinning-depinning phenomena showing damped oscillations once the imperfection is overcome. Replacing the constant damping coefficient with a parabolic spatial function, we reproduce accurately the experimental front-defect interaction.

Sliding Behavior of Droplets on a Tilted Substrate with a Chemical Step

Controlling and predicting the motion of droplets on a heterogeneous substrate have received widespread attention. In this paper, we numerically simulate the droplet sliding through a "chemical step", that is, different wetting properties at two sides of the step, on a tilted substrate by the multiphase lattice Boltzmann method (LBM). Three kinds of equilibrium statuses are reproduced by observing the deformation of the droplet and the velocities of the front contact line. This study shows the droplet obtains a driving force to break through the step by deformation in the initial stage that the droplet is blocked. The droplet spreads to two sides along the step when the front end is blocked and is stretched after the front end is passed over the step. The lengths of the lateral spreading and the longitudinal stretching and the time required to pass over the step depend on the strength of the step. In the sliding process, the kinetic energy is converted into surface energy as the droplet is blocked, and the gravitational potential energy is converted into surface and kinetic energy following the droplet passes over the step. If the droplet can slide through the step, the more strength in the step, the more the gravitational potential energy is converted, and the more the surface energy increases. When the strength of the step is small, unbalanced Young's force hinders the contact line moving forward after the central part of the front end of the droplet breaks through the step. While the velocity of droplet sliding slows down with the increasing strength of the step, the unbalanced Young's force pushes the contact line forward against the resistance. These observations throw insight into the dynamics of the droplets sliding on a heterogeneous surface, which may facilitate potential applications like microfluidics and liquid transportation.

Molecular View of the Distortion and Pinning Force of a Receding Contact Line: Impact of the Nanocavity Geometry

We present a molecular view using many-body dissipative particle dynamics simulations to unravel the pinning phenomenon of a liquid film receding over a solid substrate with a nanocavity. We find that the pinning force and distortion of the pinned contact line vary across different nanocavity shapes. We show that the mechanism of a caterpillar motion, which has previously been proposed for advancing precursor films, persists in a partially pinned receding contact line. Our results also demonstrate a localized clamping effect, which is originated from the variation of the dynamic contact angle along the pinned contact line. The simulation results suggest that the clamping effect can be controlled by the geometry of the nanocavity and hydrophilicity of the underlying substrate.

Operator learning for predicting multiscale bubble growth dynamics

Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming "hand-shaking" interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh-Plesset (R-P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R-P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

Droplet Sliding: The Numerical Observation of Multiple Contact Angle Hysteresis

Droplets sliding on surfaces always exhibit an advancing and a receding contact angle. When exerting different driving forces on the droplet to force it to slide at different velocities, the droplet would alter its shape to adapt to the new motion. Hence, different advancing/receding contact angles are likely to be observed, leading to the multiple contact angle hysteresis on a given surface. To verify this hypothesis, many-body dissipative particle dynamics is employed to perform the sliding simulation on both chemically homogeneous and heterogeneous surfaces. By ensuring the droplet sliding in uniform motions under different driving forces, the advancing/receding contact angles are recorded for analysis. Simulation results show that, for homogeneous surfaces, a larger driving force can result in both larger advancing contact angle and smaller receding contact angle, while for heterogeneous surfaces, increasing the driving force only results in smaller receding contact angles. For both cases, multiple contact angle hysteresis can be observed. These observations are contrary to the currently prevailing opinion, which believes that the contact angle hysteresis should be unique on given surfaces. Our findings would advance the understanding of wetting phenomena and possibly inspire new guidance for the design of functional interfaces.

Anisotropic Wetting of Droplets on Stripe-Patterned Chemically Heterogeneous Surfaces: Effect of Length Ratio and Deposition Position

The equilibrium state of a droplet deposited on chemically heterogeneous surfaces is studied by using many-body dissipative particle dynamics. The length ratio covers 2 orders from 0.01 to 1 and allows a systematical inspection of the changes of the droplet shape, contact angle, and aspect ratio with this parameter. Moreover, a new parameter, global aspect ratio, is introduced to better characterize the distortion of the droplet. It is found that the droplet shape at the equilibrium stage strongly lies on the deposition position when the length ratio is beyond 0.1. Additionally, the lateral displacement is observed when depositing the droplet on the border of two stripes at large length ratios (over 0.1). On the other hand, the Cassie area fraction also has a significant effect on the wetting behaviors. When the droplet is driven by a body force with a 45° inclined angle to the stripes, the moving direction could be strictly in line with the force direction, deviating from the force direction, or totally in line with the stripes, depending on the length ratio.

Self-Cleaning of Hydrophobic Rough Surfaces by Coalescence-Induced Wetting Transition

The superhydrophobic leaves of a lotus plant and other natural surfaces with self-cleaning function have been studied intensively for the development of artificial biomimetic surfaces. The surface roughness generated by hierarchical structures is a crucial property required for superhydrophobicity and self-cleaning. Here, we demonstrate a novel self-cleaning mechanism of textured surfaces attributed to a spontaneous coalescence-induced wetting transition. We focus on the wetting transition as it represents a new mechanism, which can explain why droplets on rough surfaces are able to change from the highly adhesive Wenzel state to the low adhesion Cassie-Baxter state and achieve self-cleaning. In particular, we perform many-body dissipative particle dynamics simulations of liquid droplets (with a diameter of 89 μm) sitting on mechanically textured substrates. We quantitatively investigate the wetting behavior of an isolated droplet as well as coalescence of droplets for both Cassie-Baxter and Wenzel states. Our simulation results reveal that droplets in the Cassie-Baxter state have much lower contact angle hysteresis and smaller hydrodynamic resistance than droplets in the Wenzel state. When small neighboring droplets coalesce into bigger ones on textured hydrophobic substrates, we observe a spontaneous wetting transition from the Wenzel state to the Cassie-Baxter state, which is powered by the surface energy released upon coalescence of the droplets. For superhydrophobic surfaces, the released surface energy may be sufficient to cause a jumping motion of droplets off the surface, in which case adding one more droplet to the coalescence may increase the jumping velocity by one order of magnitude. When multiple droplets are involved, we found that the spatial distribution of liquid components in the coalesced droplet can be controlled by properly designing the overall arrangement of droplets and the distance between them. These findings offer new insights for designing effective biomimetic self-cleaning surfaces by enhancing spontaneous Wenzel-to-Cassie wetting transitions, and additionally, for developing new noncontact methods to manipulate liquids inside the small droplets via multiple-droplet coalescence.