Droplet Control Based on Pinning and Substrate Wettability

Durotaxis and Antidurotaxis Droplet Motion onto Gradient Gel-Substrates

The self-sustained motion of fluids on gradient substrates is a spectacular phenomenon, which can be employed and controlled in applications by carefully engineering the substrate properties. Here, we report on a design of a gel substrate with stiffness gradient, which can cause the spontaneous motion of a droplet along (durotaxis) or to the opposite (antidurotaxis) direction of the gradient, depending on the droplet affinity to the substrate. By using extensive molecular dynamics simulations of a coarse-grained model, we find that the mechanisms of the durotaxis and antidurotaxis droplet motion are distinct, require the minimization of the interfacial energy between the droplet and the substrate, and share similarities with those mechanisms previously observed for brush substrates with stiffness gradient. Moreover, durotaxis motion takes place over a wider range of affinities and is generally more efficient (faster motion) than antidurotaxis. Thus, our study points to further possibilities and guidelines for realizing both antidurotaxis and durotaxis motion on the same gradient substrate for applications in microfluidics, energy conservation, and biology.

Evaporation Dynamics of Macro- and Nanodroplets on Heated Hydrophilic Rough Substrates: The Effect of Roughness and Scale

Droplet evaporation on rough substrates plays an essential role in cooling and micro/nanoparticle assembly. Currently, there are numerous macroscopic experiments and theoretical models to investigate the droplet evaporation behavior on rough substrates. However, due to the complexity of this phenomenon, understanding its mechanisms solely through macroscale studies is difficult. To this end, molecular dynamics simulations of the models with distinct roughness factors are performed, and the obtained results are compared with those of relevant experiments of droplet evaporation on three hydrophilic substrates with different roughness average of 0.1, 0.15, and 0.2 μm, respectively. In this way, we assess the evaporation on these rough systems and the effect of scale on macro- and nanodroplets, which allows us to explore deeper the mechanism of droplet evaporation on rough hydrophilic substrates. In particular, we find that in the case of macroscale droplets, the evaporation mode remains the same with increasing roughness, pointing to a combined mixed and constant-contact-radius (CCR) mode. In the case of nanoscale droplets, the evaporation model is the constant-contact-angle mode when the roughness factor r = 1, while the mixed and CCR modes are found for r = 1.5 and 2, respectively. The scale effect has significant influence on the evaporation pattern of droplets on rough hydrophilic substrates. Moreover, it is also found that increasing the roughness of substrates expands the substrate-droplet contact area on both the macro- and nanoscale, which in turn enhances the heat transfer from the substrate toward the droplet. We anticipate that this first systematic analysis of scale effects provides further insights into the evaporation dynamics of droplets on rough hydrophilic substrates and has significant implications for the advancement of nanotechnology.

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.

Multiscale simulation of fluids: coupling molecular and continuum

Computer simulation is an important tool for scientific progress, especially when lab experiments are either extremely costly and difficult or lack the required resolution. However, all of the simulation methods come with limitations. In molecular dynamics (MD) simulation, the length and time scales that can be captured are limited, while computational fluid dynamics (CFD) methods are built on a range of assumptions, from the continuum hypothesis itself, to a variety of closure assumptions. To address these issues, the coupling of different methodologies provides a way to retain the best of both methods. Here, we provide a perspective on multiscale simulation based on the coupling of MD and CFD with each a distinct part of the same simulation domain. This style of coupling allows molecular detail to be present only where it is needed, so CFD can model larger scales than possible with MD alone. We present a unified perspective of the literature, showing the links between the two main types of coupling, state and flux, and discuss the varying assumptions in their use. A unique challenge in such coupled simulation is obtaining averages and constraining local parts of a molecular simulation. We highlight that incorrect localisation has resulted in an error in the literature. We then finish with some applications, focused on the simulation of fluids. Thus, we hope to motivate further research in this exciting area with applications across the spectrum of scientific disciplines.

Antidurotaxis Droplet Motion onto Gradient Brush Substrates

Durotaxis motion is a spectacular phenomenon manifesting itself by the autonomous motion of a nano-object between parts of a substrate with different stiffness. This motion usually takes place along a stiffness gradient from softer to stiffer parts of the substrate. Here, we propose a new design of a polymer brush substrate that demonstrates antidurotaxis droplet motion, that is, droplet motion from stiffer to softer parts of the substrate. By carrying out extensive molecular dynamics simulation of a coarse-grained model, we find that antidurotaxis is solely controlled by the gradient in the grafting density of the brush and is favorable for fluids with a strong attraction to the substrate (low surface energy). The driving force of the antidurotaxial motion is the minimization of the droplet-substrate interfacial energy, which is attributed to the penetration of the droplet into the brush. Thus, we anticipate that the proposed substrate design offers a new understanding and possibilities in the area of autonomous motion of droplets for applications in microfluidics, energy conservation, and biology.

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.

Fabrication of Superhydrophobic Water-Pinning Surfaces through Integration of Silica Colloids into Cellulose Nanocrystals

The water-pinning effect is a phenomenon in which water droplets adhere to a surface and do not roll off, even when the surface is tilted or turned upside down. This effect holds great potential for applications in various areas, such as dew collection in arid regions, anti-drip function for a greenhouse, and liquid transport and control. However, creating surfaces that exhibit this effect poses challenges, necessitating materials with both hydrophobicity and high adhesive force along with a scalable, cost-effective method to produce the essential geometries that have not yet been established. To address these challenges, we propose a straightforward coating approach involving silica nanoparticles (SiO2) and cellulose nanocrystals (CNCs) to fabricate artificial water-pinning surfaces. We assessed the water-pinning ability of the coated surface through measurements of the contact angle, contact radius, and hysteresis. Remarkably, the coated surface exhibited a contact angle of approximately 153.87° and a contact radius of around 0.89 mm when a 10 μL water droplet was applied, demonstrating its resistance to rolling off, even at a tilting angle of 90°. The droplet only began to fall when its volume reached approximately 33 μL, requiring a substantial water pinning force of 323.4 μN. We also investigated the physicochemical characteristics of the SiO2@CNC coating surface, including morphology, chemical composition, and chemical structure, to unravel the underlying mechanism behind its water-pinning ability. Our proposed fabrication method offers a promising avenue for the development of functional biopolymer-based surfaces capable of precisely manipulating water droplets.

Looking for future biological control agents: the comparative function of the deutosternal groove in mesostigmatid mites

The physics of fluid laminar flow through an idealised deutosternum assembly is used for the first time to review predatory feeding designs over 72 different-sized example species from 16 mesostigmatid families in order to inform the finding of new biological control agents. Gnathosomal data are digitised from published sources. Relevant gnathosomal macro- and micro-features are compared and contrasted in detail which may subtly impact the control of channel- or 'pipe'-based transport of prey liquids around various gnathosomal locations. Relative deutosternal groove width on the mesostigmatid subcapitulum is important but appears unrelated to the closing velocity ratio of the moveable digit. Big mites are adapted for handling large and watery prey. The repeated regular distance between deutosternal transverse ridges ('Querleisten') supports the idea of them enabling a regular fluctuating bulging or pulsing droplet-based fluid wave 'sticking' and 'slipping' along the groove. Phytoseiids are an outlier functional group with a low deutosternal pipe flow per body size designed for slot-like microchannel transport in low volume fluid threads arising from daintily nibbling nearby prey klinorhynchidly. Deutosternal groove denticles are orientated topographically in order to synergise flow and possible mixing of coxal gland-derived droplets and circumcapitular reservoir fluids across the venter of the gnathosomal base back via the hypostome to the prey being masticated by the chelicerae. As well as working with the tritosternum to mechanically clean the deutosternum, denticles may suppress fluid drag. Shallow grooves may support edge-crawling viscous flow. Lateral features may facilitate handling unusual amounts of fluid arising from opportunistic feeding on atypical prey. Various conjectures for confirmatory follow-up are highlighted. Suggestions as to how to triage non-uropodoid species as candidate plant pest control agents are included.

Unidirectional Droplet Propulsion onto Gradient Brushes without External Energy Supply

Using extensive molecular dynamics simulation of a coarse-grained model, we demonstrate the possibility of sustained unidirectional motion (durotaxis) of droplets without external energy supply when placed on a polymer brush substrate with stiffness gradient in a certain direction. The governing key parameters for the specific substrate design studied, which determine the durotaxis efficiency, are found to be the grafting density of the brush and the droplet adhesion to the brush surface, whereas the strength of the stiffness gradient, the viscosity of the droplet, or the length of the polymer chains of the brush have only a minor effect on the process. It is shown that this durotaxial motion is driven by the steady increase of the interfacial energy between droplet and brush as the droplet moves from softer to stiffer parts of the substrate whereby the mean driving force gradually declines with decreasing roughness of the brush surface. We anticipate that our findings indicate further possibilities in the area of nanoscale motion without external energy supply.

Thermal capillary waves on bounded nanoscale thin films

The effect of confining walls on the fluctuation of a nanoscale thin film's free surface is studied using stochastic thin-film equations (STFEs). Two canonical boundary conditions are employed to reveal the influence of the confinement: (1) an imposed contact angle and (2) a pinned contact line. A linear stability analysis provides the wave eigenmodes, after which thermal-capillary-wave theory predicts the wave fluctuation amplitudes. Molecular dynamics (MD) simulations are performed to test the predictions, and a Langevin diffusion model is proposed to capture oscillations of the contact lines observed in MD simulations. Good agreement between the theoretical predictions and the MD simulation results is recovered, and it is discovered that confinement can influence the entire film. Notably, a constraint on the length scale of wave modes is found to affect fluctuation amplitudes from our theoretical model, especially for 3D films. This opens up challenges and future lines of inquiry.

A Study of the Critical Velocity of the Droplet Transition from the Cassie to Wenzel State on the Symmetric Pillared Surface

A droplet hitting a superhydrophobic surface will undergo the Cassie to Wenzel transition when the wetting force exceeds the anti-wetting force. The critical velocity of the droplet’s Cassie to Wenzel state transition can reflect the wettability of the surface. However, the critical velocity research is still at the microscale and has not been extended to the nanoscale mechanism. A cross-scale critical velocity prediction model for superhydrophobic surfaces with symmetric structures is proposed here based on a mechanical equilibrium system. The model’s applicability is verified by experimental data. It demonstrates that the mechanical equilibrium system of droplet impact with capillary pressure and Laplace pressure as anti-wetting forces is more comprehensive, and the model proposed in this study predicts the critical velocity more precisely with a maximum error of 12% compared to the simulation results. Furthermore, the correlation between the simulation at the nanoscale and the evaluation of the macroscopic symmetrical protrusion surface properties is established. Combined with the model and the correlation, the relationship between the microscopic mechanism and the macroscopic examination of droplet dynamics on the superhydrophobic surface be presented, and the wettability evaluation method of macroscopic surfaces based on the molecular simulation mechanism can be realized.