An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and the receding side -- to respective solutions of the problem on the microscale. On the microscale the velocity of movement is used as the small parameter of an asymptotic expansion. Matching gives the droplet shape, velocity of movement as a function of the imposed wettability gradient and droplet volume.
Droplets move on substrates with a spatio-temporal wettability pattern as generated, for example, on light-switchable surfaces. To study such cases, we implement the boundary-element method to solve the governing Stokes equations for the fluid flow field inside and on the surface of a droplet and supplement it by the Cox-Voinov law for the dynamics of the contact line. Our approach reproduces the relaxation of an axisymmetric droplet in experiments, which we initiate by instantaneously switching the uniform wettability of a substrate quantified by the equilibrium contact angle. In a step profi…
The directional movement and rebound behaviours of two droplets simultaneously impacting a designed flat surface with wettability difference is investigated based on the three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann model. The effects of several factors, such as wettability difference, Weber number and droplet spacing on the directional movement and rebound behaviours are investigated in detail. The numerical results show that the unbalanced Young 's force caused by the wetting difference will cause the droplets to rebound or migrate laterally toward to the side wit…
Droplet motion over a surface with wettability gradient has been simulated using molecular dynamics (MD) simulation to highlight the underlying physics. GROMACS and Visual Molecular Dynamics (VMD) were used for simulation and intermittent visualization of the droplet configuration respectively. The simulations mimic experiments in a comprehensive manner wherein micro-sized droplets are propelled by surface wettability gradient against a number of retarding forces. The liquid-wall Lennard-Jones interaction parameter and the substrate temperature were varied to explore their effects on the three…
We demonstrate \textit{bendotaxis}, a novel mechanism for droplet self-transport at small scales. A combination of bending and capillarity in a thin channel causes a pressure gradient that, in turn, results in the spontaneous movement of a liquid droplet. Surprisingly, the direction of this motion is always the same, regardless of the wettability of the channel. We use a combination of experiments at a macroscopic scale and a simple mathematical model to study this motion, focussing in particular on the time scale associated with the motion. We suggest that \emph{bendotaxis} may be a useful me…
In recent decades novel solid substrates have been designed which change their wettability in response to light or an electrostatic field. Here, we investigate a droplet on substrates with oscillating uniform wettability by varying minimium and maximum contact angles and frequency. To simulate this situation, we use our previous work [Grawitter and Stark, Soft Matter 17, 2454 (2021)], where we implemented the boundary element method in combination with the Cox-Voinov law for the contact-line velocity, to determine the fluid flow inside a droplet. After a transient regime the droplet performs s…
The influence of miscibility and liquid wettability during droplet impact onto thin wall films is investigated experimentally. Despite similar liquid properties and impact conditions, differences in the splashing limit, the crown extension and the duration of the ascending phase are observed. These differences are related to the interfacial tension of the droplet/wall-film liquid pairs, which is linked to their miscibility and wettability. More precisely, by calculating the crown surface energy, we show that the energy stored in the interface between droplet and wall-film (if any) is not negli…
Experimental investigations were carried out to elucidate the role of surface wettability and inclination on the post impact dynamics of droplets. Maximum spreading diameter and spreading time were found to decrease with increasing inclination angle and normal Weber number for superhydrophobic surfaces. The experiments on SH surfaces were found to be in excellent agreement with an existing analytical model, incorporated with the modifications for the oblique impact conditions. Energy ratios and elongation factor were also measured for different inclination angles. On inclined SH surfaces, diff…
This study has numerically investigated the effect of surface wettability on two-phase immiscible flow and dynamics of droplet pinch-off in a T-junction microchannel using finite element method. A conservative level set method (CLSM) has been adopted to capture the interface topology in squeezing regime ($Ca_c <10^{-2}$) for wide flow rate ratio ($1/10 \leq Q_r \leq 10$) and contact angle ($120^{\circ} \leq θ\leq 180^{\circ}$). Based on the instantaneous phase profiles, droplet formation stages are classified as initial, filling, squeezing, pinch-off and stable droplet. Wettability effects are…
Post impingement morphology and dynamics of water droplets on convex cylindrical surfaces has been explored experimentally. Droplet impact and post-impact feature studies have been conducted on hydrophillic and superhydrophobic cylindrical surfaces. Effects of the impact Weber number and target-to-drop diameter ratio have been studied. The post-impact hydrodynamics have been quantified using the wetting fraction, the spreading factor and nondimensional film thickness at the north pole of the target. The observations reveal that the wetting fraction and spread factor increases with an increase …
Droplets confined in a microfluidic channel often exhibit intriguing shapes, primarily attributable to complex hydrodynamic interactions over small scales. We show that effect of varied substrate wettability conditions may further complicate these interactions remarkably, and often non-trivially. Our studies reveal that the combined influence of substrate wettability and fluidic confinement eventually culminates towards influencing the droplet transients, distortion of the local shear flow field, as well as drop stabilization against breakup or detachment, allowing one to develop different reg…
Effects of substrate temperature, substrate wettability and particles concentration are experimentally investigated for evaporation of a sessile water droplet containing colloidal particles. Time-varying droplet shapes and temperature of the liquid-gas interface are measured using high-speed visualization and infrared thermography, respectively. The motion of the particles inside the evaporating droplet is qualitatively visualized by an optical microscope and profile of final particle deposit is measured by an optical profilometer. On a non-heated hydrophilic substrate, a ring-like deposit for…
This paper reports the dynamic wetting behavior and heat transfer characteristics for impinging droplets on heated bi-phobic surfaces (superhydrophobic matrix with hydrophobic spots). A non-patterned superhydrophobic and a sticky hydrophobic surface acted as control wettability surfaces. As expected, differences in wetting and heat transfer dynamics were noticeable for all surfaces, with the most pronounced variation during the receding phase. During spreading, inertia from the impact dominated the droplet dynamics and heat transfer was dominated by convection at the contact line and internal …
Making liquid droplets move spontaneously on solid surfaces is a key challenge in lab-on-chip and heat exchanger technologies. The best-known mechanism, a wettability gradient, does not generally move droplets rapidly enough and cannot drive droplets smaller than a critical size. Here we report how a curvature gradient is particularly effective at accelerating small droplets, and works for both hydrophilic and hydrophobic surfaces. Experiments for water droplets on tapered surfaces with curvature radii in the sub-millimeter range show a maximum speed of 0.28 m/s, two orders of magnitude higher…
Droplet Impact on Microparticle Raft: Wettability, density and size govern splashing and microplastic ejection from rafts under raindrop impact
University College London（伦敦大学学院）；University of Oxford（牛津大学）；Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México（墨西哥国立自治大学材料研究所）
On Free Moving Micron-Sized Droplet-Particle Collisions
School of Chemical and Process Engineering, University of Leeds（利兹大学化学与工艺工程学院）；School of Natural Sciences, Department of Mathematics, University of Manchester（曼彻斯特大学自然科学学院数学系）；School of Mathematics, Statistics, Chemistry and Physics, Murdoch University（默多克大学数学、统计、化学和物理学院）
Dynamic Wettability Modulation of Textured, Soft and LIS Interfaces Using Electrowetting
School of Mechanical Sciences, Indian Institute of Technology (IIT) Goa（印度理工学院果阿分校机械科学学院）；Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur（印度理工学院卡拉格普尔分校机械工程系）
Surface wettability has a huge influence on its functional properties. For example, to minimize smudging, surfaces should be able to repel oil droplets. To quantify surface wettability, the most common approach is to measure the contact angles of a liquid droplet on the surface. While well-established and relatively easy to perform, contact angle measurements are crude and imprecise; moreover, they cannot spatially resolve surface heterogeneities that can contribute to surface fouling. To address these shortcomings, we report on using an Atomic Force Microscopy (AFM) technique to quantitativel…
Would a raindrop impacting on a coarse beach behave differently from that impacting on a desert of fine sand? We study this question by a series of model experiments, where the packing density of the granular target, the wettability of individual grains, the grain size, the impacting liquid, and the impact speed are varied. We find that by increasing the grain size and/or the wettability of individual grains the maximum droplet spreading undergoes a transition from a capillary regime towards a viscous regime, and splashing is suppressed. The liquid-grain mixing is discovered to be the underlyi…
How to make small liquid droplets move spontaneously and directionally on solid surfaces is a challenge in lab-on-chip technologies, DNA analysis, and heat exchangers. The best-known mechanism, a wettability gradient, does not move droplets rapidly enough for most purposes and cannot move droplets smaller than a critical size defined by the contact angle hysteresis. Here we report on a mechanism using curvature gradients, which we show is particularly effective at accelerating small droplets, and works for both hydrophilic and hydrophobic surfaces. Experiments for water droplets on glass cones…
The classical wetting models, such as the Wenzel and Cassie-Baxter have been extensively used to quantify the wettability of laser-textured surfaces. However, these models do not provide any description of the corresponding droplet dynamics. In this work, we propose a detailed continuum-level modelling to study the wetting dynamics of a water droplet on Ti-6Al-4V alloy. The calculations are performed for flat surfaces and surfaces with various reliefs. The calculated evolutions of the droplet spreading parameter for flat surfaces, surfaces with triangular reliefs and one with two different per…
We investigate velocity variations inside of and surrounding a gravity driven drop impacting on and moving through a confining orifice, wherein the effects of edge geometry (round- vs. sharp-edged) and surface wettability (hydrophobic vs. hydrophilic) of the orifice are considered. Using refractive index matching and time-resolved PIV, we quantify the redistribution of energy in the drop and the surrounding fluid during the drop's impact and motion through a round-edged orifice. The measurements show the importance of a) drop kinetic energy transferred to and dissipated within the surrounding …
A numerical method for simulating three-phase flows with moving contact lines on arbitrarily complex surfaces is developed in the framework of lattice Boltzmann method. In this method, the immiscible three-phase flow is modeled through a multiple-relaxation-time color-gradient model, which not only allows for a full range of interfacial tensions but also produces stable outcomes for a wide range of viscosity ratios. A characteristic line model is introduced to implement the wetting boundary condition, which is not only easy to implement but also able to handle arbitrarily complex boundaries wi…
The article demonstrates that the internal circulation velocity and patterns in sessile droplets on superhydrophobic surfaces is governed by the surface curvature. Particle Image Velocimetry reveals that increasing convexity deteriorates the advection velocity whereas concavity augments it. A scaling model based on the effective curvature modulated change in wettability can predict the phenomenon, but weakly. Potential flow theory is appealed to and the curvatures are approximated as wedges with the rested droplet engulfing them partly. The spatially averaged experimental velocities are found …
Bumps are omnipresent from human skin to the geological structures on planets, which offer distinct advantages in numerous phenomena including structural color, drag reduction, and extreme wettability. Although the topographical parameters of bumps such as radius of curvature of convex regions significantly influence various phenomena including anti-reflective structures and contact time of impacting droplets, the effect of the detailed bump topography on growth and transport of condensates have not been clearly understood. Inspired by the millimetric bumps of the Namib Desert beetle, here we …
The dynamics of drop(s) has been simulated by the finite volume/moving mesh interface tracking method (MMIT) with adaptive mesh refining and coarsening. In MMIT, the interface is of zero thickness and moves in a Lagrangian fashion. A number of mesh refining and mesh coarsening schemes have been developed to distribute the mesh in an optimized way to achieve computing efficiency and accuracy. Three cases are displayed in this video, which include a droplet pair in tandem impulsively accelerated by a gaseous flow, a droplet moving through a convergent-divergent liquid-filled tube, and a droplet …
Droplet(s) breakup and coalescence have been simulated by the finite volume/moving mesh interface tracking method (MMIT) with adaptive mesh refining and coarsening. In this method, the interface is zero-thickness and moves in a Lagrangian fashion. The breakup and the coalescence of the interfaces are simulated by the mesh separation and mesh combination schemes. Three cases are displayed in this video, which include the relaxation and breakup of an initially extended droplet, two identical droplets off-center collision, and a droplet pair in a shear flow. The mesh adaptation is capable of capt…
Compound droplets can be used in substance encapsulation and material compartmentalization to achieve a precise control over the relevant processes in many applications, such as bioanalysis, pharmaceutical manufacturing, and material synthesis. The flow fields in compound droplets directly affect the performance of these applications, but it is challenging to measure them experimentally. In this study, the flow in compound droplets in axisymmetric microchannels is simulated using the Finite Volume Method, and the interface is captured using the Level Set Method with surface tension accounted f…
Lubricated surfaces have shown promise in numerous applications where impinging foreign droplets must be removed easily; however, before they can be widely adopted, the problem of lubricant depletion, which eventually leads to decreased performance, must be solved. Despite recent progress, a quantitative mechanistic explanation for lubricant depletion is still lacking. Here, we first explained the shape of a droplet on a lubricated surface by balancing the Laplace pressures across interfaces. We then showed that the lubricant film thicknesses beneath, behind, and wrapping around a moving dropl…
We recently put in evidence (\cite{noblin2}) that combined vertical and horizontal vibrations can induced a controlled motion of a sessile supported drop. In this video we generalize this finding and demonstrate that a remote 2d controlled motion is possible. This video was submitted as part of the Gallery of Fluid Motion 2010 which is showcase of fluid dynamics videos.
Various microfluidic systems, such as chemical and biological lab-on-a-chip devices, involve motion of multiple droplets within an immersing fluid in shallow micro-channels. Modeling the dynamics of such systems requires calculation of the forces of interaction between the moving droplets. These forces are commonly approximated by superposition of dipoles solutions, which requires an assumption of sufficiently large distance between the droplets. In this work we obtain exact solutions (in the Hele-Shaw limit) for two moving droplets, and a droplet within a droplet, located within a moving imme…
The Feynman path integral approach for solving the motion of a droplet along a silicon oil surface is developed by replacing the Planck constant by a surrogate parameter. The latter is proportional to the surface tension of the silicon oil multiplied by the area of the thin air film, separating the droplet from the oil, and by the half-period of the Faraday oscillations. It is shown that the Navier-Stokes equation together with the mass conservation equation can be reduced to the Schrödinger equation when the surrogate parameter replaces the Planck constant. The Feynman path integral underlyin…
Evaporation-Driven Nanowire Self-Assembly in an Elongated Droplet
Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IET-2), Forschungszentrum Jülich（于利希研究中心埃尔朗根-纽伦堡亥姆霍兹可再生能源研究所）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）
We propose a generic model for thin films and shallow drops of a polar active liquid that have a free surface and are in contact with a solid substrate. The model couples evolution equations for the film height and the local polarization profile in the form of a gradient dynamics supplemented with active stresses and fluxes. A wetting energy for a partially wetting liquid is incorporated allowing for motion of the liquid-solid-gas contact line. This gives a consistent basis for the description of drops of dense bacterial suspensions or compact aggregates of living cells on solid substrates. As…
We simulate gravity driven dynamics of partially wetting droplets moving along a fibre using the lattice Boltzmann method. For the so-called clamshell morphology, we find three possible dynamic regimes upon varying the droplet Bond number and the fibre radius: compact droplet, droplet breakup and droplet oscillation. For small Bond numbers, in the compact droplet regime, the droplet reaches a steady state and its velocity scales linearly with the driving body force. A similar scaling law can also be observed for the barrel morphology. For higher Bond numbers, in the droplet breakup regime, sat…
We study spreading of a droplet, with insoluble surfactant covering its capillary surface, on a textured substrate. In this process, the surfactant-dependent surface tension dominates the behaviors of the whole dynamics, particularly the moving contact lines. This allows us to derive the full dynamics of the droplets laid by the insoluble surfactant: (i) the moving contact lines, (ii) the evolution of the capillary surface, (iii) the surfactant dynamics on this moving surface with a boundary condition at the contact lines and (iv) the incompressible viscous fluids inside the droplet. Our deriv…
We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting long-wave evolution equation for the droplet thickness is treated analytically via the method of matched asymptotic expansions in the limit of slow mass transfer rates, quasi-static dynamics and vanishingly small slip lengths to deduce a lower-dimensional system of integrodifferential equations for the two moving fronts. We demonstrate that the predictions of the deduced system agree excellently with simul…
