Thermal singularity and droplet motion in one-component fluids on solid substrates with thermal gradients

The static shape of droplets under electrowetting actuation is well understood. The steady-state shape of the droplet is obtained on the basis of the balance of surface tension and electrowetting forces, and the change in the apparent contact angle is well characterized by the Young-Lippmann equation. However, the transient droplet shape behavior when a voltage is suddenly applied across a droplet has received less attention. Additional dynamic frictional forces are at play during this transient process. We present a model to predict this transient behavior of the droplet shape under electrowetting actuation. The droplet shape is modeled using the volume of fluid method. The electrowetting and dynamic frictional forces are included as an effective dynamic contact angle through a force balance at the contact line. The model is used to predict the transient behavior of water droplets on smooth hydrophobic surfaces under electrowetting actuation. The predictions of the transient behavior of droplet shape and contact radius are in excellent agreement with our experimental measurements. The internal fluid motion is explained, and the droplet motion is shown to initiate from the contact line. An approximate mathematical model is also developed to understand the physics of the droplet motion and to describe the overall droplet motion and the contact line velocities.

In spite of the reported temperature dependent tunability in wettability of poly(N-isopropylacrylamide) (PNIPAAm) surfaces for below and above lower critical solution temperature (32 °C), the transport of water droplets is inhibited by the large contact angle hysteresis. Herein, for the first time, we report on-demand, fast, and reconfigurable droplet manipulation over a PNIPAAm grafted structured polymer surface using temperature-induced wettability gradient. Our study reveals that the PNIPAAm grafted on intrinsically superhydrophobic surfaces exhibit hydrophilic nature with high contact angle hysteresis below 30 °C and superhydrophobic nature with ultralow contact angle hysteresis above 36 °C. The transition region between 30 and 36 °C is characterized by a large change in water contact angle (∼100°) with a concomitant change in contact angle hysteresis. By utilizing this "transport zone" wherein driving forces overcome the frictional forces, we demonstrate macroscopic transport of water drops with a maximum transport velocity of approximately 40 cm/s. The theoretical calculations on the force measurements concur with dominating behavior of driving forces across the transport zone. The tunability in transport velocity by varying the temperature gradient along the surface or the inclination angle of the surface (maximum angle of 15° with a reduced velocity 0.4 mm/s) is also elucidated. In addition, as a practical application, coalescence of water droplets is demonstrated by using the temperature controlled wettability gradient. The presented results are expected to provide new insights on the design and fabrication of smart multifunctional surfaces for applications such as biochemical analysis, self-cleaning, and microfluidics.

The effect of sharp solid edges on the droplet wettability

Evaluation of unusual change in contact angle between MgO and molten magnesium

A study of the structure and surface properties of nanostructured biocompatible coatings on Ti alloys

Numerical study of the migration of a silicone plug inside a capillary tube subjected to an unsteady wall temperature gradient

<p style='text-indent:20px;'>We investigate numerically the advancing motion of 3D droplets spreading on physically flat chemically heterogeneous surfaces with periodic structures. We use the Navier-Stokes-Cahn-Hilliard equations with the generalized Navier boundary conditions to model the motion of droplets. Based on a convex splitting scheme, we have done numerical simulations and compared the results between different surface patterns quantitatively. We study the effect of pattern property on the advancing motion of three phase contact lines, the critical volume at the contact line jump and the effective advancing angles. By increasing the volume of droplet slowly on heterogeneous surfaces with different pattern property, we find that the advancing contact line approaches an equiangular octagon for the patterned surface with periodic squares separated by channels and approaches a regular hexagon for the patterned surface with periodic circles in regular hexagonal arrays. The shape of three-phase contact line is much more determined by the macro structure of the pattern than the micro structure of the pattern in each period.

Lattice Boltzmann Modeling (LBM) simulations were performed on the dynamic behavior of liquid droplets on chemically striped patterned surfaces, ultimately with the aim to develop a predictive tool enabling reliable design of future experiments. The simulations accurately mimic experimental results, which have shown that water droplets on such surfaces adopt an elongated shape due to anisotropic preferential spreading. Details of the contact line motion such as advancing of the contact line in the direction perpendicular to the stripes exhibit pronounced similarities in experiments and simulations. The opposite of spreading, i.e., evaporation of water droplets, leads to a characteristic receding motion first in the direction parallel to the stripes, while the contact line remains pinned perpendicular to the stripes. Only when the aspect ratio is close to unity, the contact line also starts to recede in the perpendicular direction. Very similar behavior was observed in the LBM simulations. Finally, droplet movement can be induced by a gradient in surface wettability. LBM simulations show good semiquantitative agreement with experimental results of decanol droplets on a well-defined striped gradient, which move from high- to low-contact angle surfaces. Similarities and differences for all systems are described and discussed in terms of the predictive capabilities of LBM simulations to model direction wetting.

In this paper, we have studied the droplet movements and continuous flows confined between two rough and hydrophobic surfaces. A recently proposed mean-field free-energy lattice Boltzmann model was employed. The movement of contact point over a well-patterned rough surface displays a periodic sticking-jumping-slipping behavior; while the dynamic contact angle changes accordingly from maximum to minimum values. These complex varying behaviors are totally different from those on flat surfaces and implies more carefulness is necessary in interpreting measured contact angles on rough surfaces. Two regimes were found of the droplet velocity changing with the surface roughness: first decreasing and then increasing; and qualitative analysis was given. We have also studied the continuous flow rates and two cases, with and without vapor trapped, were compared. Simulation results show the vapor trapped can indeed reduce the resistance to fluid motion from the channel surfaces, and such information could be useful for microfluidic applications.

Droplet motion induced by mechanical vibrations and superposed shear flows has not yet been investigated in detail, despite its major importance in many applications. The current study introduces a novel experimental setup for this purpose. Furthermore, droplet motion measurements on acrylic glass surfaces are presented. This study observes mechanical vibrations and shear flows separately as well as in combination. Measurements with sinusoidal vibrations show that the droplets overcome the force due to contact angle hysteresis, when vibrational acceleration is increased above a certain threshold. Consequently, droplets experience a lateral motion, particularly if the vibrational frequency matches their natural frequency. Separate experiments with shear flows indicate that droplet motions are initiated when a critical flow velocity is reached. The flow velocity required to initiate drop motions decreases when increasing droplet volume. Superposing vibration with the shear flow results in an inconvenient droplet contour and motion, the shaking slip motion. Additionally, the required flow velocity for droplet motion reduces noticeably. Furthermore, the influence of vibrations on the initial droplet motion increases with higher droplet volume. The study concludes that the mobility of water droplets on acrylic glass surfaces increases significantly when a superposition between vibrational forces and shear flows exists.

This work focuses on the numerical study of electrohydrodynamic multiphase fluid flow problems. Liquid bodies experience deformations caused by strong external electric fields. These deformations can be used in industrial applications to accurately control the motion of single droplets. In the limiting case, strong electric fields can force atomisation of fine microdroplets from much larger liquid bulks. Due to differences in the electrical properties of the different fluid phases, the flow affects in turn the electric field distribution. The analysis of such coupled flows requires numerical modelling of the interdependent hydrodynamic and electrodynamic problems. Since most liquids exhibit some conductivity due to intrinsic ionic species and dissolved impurities, the electrodynamic problem must be modelled by an electroquasistatic model taking into account capacitive, resistive and convective electrical currents. This electroquasistatic problem is coupled to an incompressible fluid flow problem described by the Navier-Stokes equations. Both problems are solved on the same computational grid, using the finite volume method. The fluid-fluid interface is modelled using the volume of fluid method. The resulting diffuse interface captures the motion of the phase boundaries while efficiently handling topology changes. The motion of contact lines is furthermore modelled using a dynamic contact angle model including hysteresis effects. Pinned contact lines and stick-slip contact line motion in transient problems can therefore be represented. The developed solver is readily applicable to a large range of electrohydrodynamic flow problems. This work investigates electrohydrodynamic flows occurring in three technical applications. First, the dynamics of sessile droplets subjected to an AC electric field on the surface of an insulator are considered. The dynamics of the oscillating droplets are compared with experimental data. Partial discharge inception fields are then estimated for similar configurations. Secondly, the detachment dynamics of two liquids in an on-demand droplet generator, where droplet detachment is enforced by electric fields, are considered and compared to experimental data. The different conductivities of the liquids are shown to lead to substantially different detachment dynamics. Relevant parameters in the detachment dynamics are extracted from the simulations. Finally, transient electrosprays in the cone-jet mode are characterised for a number of liquids with different electromechanical properties. The charge-radius correlations of the first ejections are found to obey the scaling laws reported in the literature. Moreover, additional scaling laws are found for the subsequent ejections.

Self-propelled motion of sessile droplets on gradient surfaces is key to the advancement of microfluidic, nanofluidic, and surface fluidic technologies. Precise control over droplet dynamics, which often involves liquid–vapor phase transitions, is crucial for a variety of applications, including thermal management, self-cleaning surfaces, biochemical assays, and microreactors. Understanding how specific phase changes like condensation and evaporation affect droplet motion is essential for enhancing droplet manipulation and improving transport efficiency. We use the thermal Navier–Stokes–Korteweg equations to investigate the effects of condensation and evaporation on the motion and internal dynamics of droplets migrating across a surface with a linear surface energy profile. The study focuses on the early dynamics of self-propelled motion of a phase changing droplet at sub-micron scale before viscous forces are comparable with the gradient forces. Our results demonstrate that phase change significantly affects the self-propelled motion of droplets by reshaping interfacial mass flux distributions and internal flow dynamics. Condensation increases droplet volume and promotes extensive spreading toward regions of higher wettability, while evaporation reduces both volume and spreading. These changes in droplet shape and size directly affect the driving forces of motion, augmenting self-propulsion through condensation and suppressing it during evaporation. Additionally, each phase change type generates distinct internal flow patterns within the droplet, with condensation and evaporation exhibiting unique circulatory movements driven by localized phase changes near the contact lines.

When a droplet interacts with a water-repellent surface, its triple-phase contact line typically exhibits varying contact angles, which can vary from point-to-point across the surface. Consequently, measuring the contact angles along the contact line would provide a better representation of the wetting properties of the surface than a single average contact angle. However, an effective method for estimating the local contact angle along the contact line on opaque hydrophobic surfaces is currently lacking. Here we present a method that combines through-drop imaging of the wetting interface during a sliding experiment with Finite Element Modeling of the droplet to estimate contact angle values along the contact line. Using this method, the mean advancing and receding contact angles were measured on four types of hydrophobic samples with contact angles between 99 and 178.9°. The method was further used to produce detailed advancing and receding contact angle maps of surfaces with wetting patterns with an unprecedented resolution of 3 μm.

The capillary-sealing efficiency of the caprock is one of the major factors that control the safety of geological CO2 storage. Possible changes in wettability due to geochemical processes could possibly decrease the capillary entry pressure and reduce the sealing integrity of the caprock. Changes in wettability have been measured by measuring the CO2 contact angle mineral substrates mica, quartz, calcite and feldspar in the presence of brine for pressures extending from atmospheric pressure up to 400 bars and for temperatures of 36 °C and 66 °C. The change in contact angle as function of pressure was non-significant for CO2 drop on the surface of quartz, feldspar and calcite. There was a significant change in contact angle on mica in which case the wettability changed from strongly water-wet to intermediate water-wet. The minimum in contact angle near the critical pressure was observed at 36 °C for three minerals (feldspar, calcite, quartz) and was maybe masked in the case of mica by the significant decrease in contact angle with increasing pressure. A relatively strong anomaly in CO2 compressibility is observed at 36 °C, less so at 66°C, indicating that the observed minimum may be related to the near-critical behavior of the CO2-phase.

High Reynolds number oscillating contact lines