Thermocapillary Migration of Liquid Droplets Induced by a Unidirectional Thermal Gradient

Thermocapillary migration of a drop with a thermally conducting stagnant cap

Hypothesis The thermocapillary migration of a spherical drop with a stagnant cap in the presence of a constant applied temperature gradient can be strongly affected by the finite thermal conductivity of the stagnant cap. Numerics The heat conduction of the stagnant cap is analytically modeled. The effects of the additional interfacial stresses generated by the disturbances to the local temperature field due to the presence of the cap at the fluid-fluid interface and the corresponding velocity of migration of the drop are evaluated by solving for the temperature and hydrodynamic field equations in and around the drop. An asymptotic model is derived to predict the terminal velocity in the presence of an infinitely conducting stagnant cap. Findings The effects of the surface conductivity and size of the stagnation region alongside the bulk thermal conductivities and viscosities of the drop and surrounding media are evaluated. The terminal velocity of the drop is shown to have a monotonic dependence on the conductivity of the stagnant cap. The bounds to the terminal velocity increment due to the stagnant cap are derived. These bounds can be of significance to multiphysics problems involving particle laden drops, Pickering emulsions and other multi-phase technologies where the conductivity of the surface adsorbents is non-negligible.

Droplet Transportation on Liquid-Infused Asymmetrically Structured Surfaces by Mechanical Oscillation and Viscosity Control

The transportation of droplets on solid surfaces has received significant attention owing to its importance in biochemical analysis and microfluidics. In this study, we propose a novel strategy for controlling droplet motion by combining an asymmetric structure and infused lubricating oil on a vibrating substrate. The transportation of droplets with volumes ranging from 10 to 90 μL was realized, and the movement speed could be adjusted from 1.45 to 10.87 mm/s. Typical droplet manipulations, including droplet transportation along a long trajectory and selective movement of multiple droplets, were successfully demonstrated. Through experimental exploration and theoretical analysis, we showed that the adjustment of droplet transport velocity involves an intricate interaction among the Ohnesorge number, droplet volume, and input amplitude. It can potentially be used for the more complex manipulation of liquid droplets in microfluidic and biochemical analysis systems.

Dynamics of Thermocapillary-Driven Motion of Liquid Drops

The thermocapillary migration of a drop placed on a solid plate is examined. The Brochard model using the lubrication approximation provides both Marangoni and Poiseuille flow components. The present 2D model extends Brochard analysis and provides a solution for the dynamics of drop migration using extended boundary conditions at the advancing and receding contact lines to account for both Marangoni and Poiseuille flow components, derived approximate drop profiles, and conservation of mass. The model is analytical, and the results are presented in a dimensionless form. The effects of the temperature gradient, surface tension coefficient to surface tension ratio, liquid viscosity, and static advancing and receding contact angles on migration dynamics are analyzed.

Light-manipulated binary droplet transport on a high-energy surface

Flexible and precise manipulation of droplet transport is of significance for scientific and engineering applications, but real-time and on-demand droplet manipulation remains a challenge. Herein, we report a strategy using light for the outstanding manipulation of binary droplet motion on a high-energy surface and reveal the underlying mechanism. Upon irradiation to a substrate by a focused light beam, the substrate can provide a localized heating source via photothermal conversion, and a binary droplet can be flexibly transported on a high-energy surface with free contact-line pinning, exhibiting light-propelled droplet transport. We theoretically showed that the surface tension gradient across the droplet interface resulting from the localized photothermal effect is responsible for actuating droplet transport. Remarkably, the high reconfigurability and flexibility of light allowed for binary droplet transport with dynamically tunable velocity and direction as well as arbitrary trajectory assisted by 2D channels on a high-energy surface. Complex droplet transportation, controllable droplet coalescence, and anti-gravity motion were realized. The promising applicability of this light-fueled droplet platform was also demonstrated by directional transport of biosample droplets containing DNA molecules and cells, as well as successional microreactions.

Electric field and viscous fluid polarity effects on capillary-driven flow dynamics between parallel plates

-Micropumps have attracted considerable interest in micro-electro-mechanical systems (MEMS), microfluidic devices, and biomedical engineering to transfer fluids through capillaries. However, improving the sluggish capillary-driven flow of highly viscous fluids is critical for commercializing MEMS devices, particularly in underfill applications. This study investigated the behavior of different viscous fluid flows under the influence of capillary and electric potential effects. We observed that upon increasing the electric potential to 500 V, the underfill flow length of viscous fluids increased by 45% compared to their capillary flow length. To explore the dynamics of underfill flow under the influence of an electric potential, the polarity of highly viscous fluids was altered by adding NaCl. The results indicated an increase of 20-41% in the underfill flow length of highly viscous conductive fluids (0.5-4% NaCl additives in glycerol) at 500 V compared to that at 0 V. The underfill viscous fluid flow length improved under the electric potential effect owing to the polarity across the substance and increased permittivity of the fluid. A time-dependent simulation, which included a quasi-electrostatic module, level set module, and laminar two-phase flow, was executed using the COMSOL Multiphysics software to analyze the effect of the external electric field on the capillary-driven flow. The numerical simulation results agreed well with the experimental data, with an average deviation of 4-7% at various time steps for different viscous fluids. Our findings demonstrate the potential of utilizing electric fields to control the capillary-driven flow of highly viscous fluids in underfill applications.

Creating lifting force in liquids via thermal gradients

In this paper, we explore a concept and present the first experimental evidence to show that it is possible to form a stable liquid film and create lifting force at the interface via thermal gradient to minimize interfacial rubbing of surfaces and the associated wear. The approach is based on manipulating the flow behavior via thermocapillary, which describes how a liquid can be made to flow from warm to cold regions purely by inducing a thermal gradient. We show that liquid bridges between two parallel plates can be manipulated and stabilized under a combined effect of the thermocapillary flow and the Couette flow, which describes the motion of a viscous fluid between two parallel plates in a relative sliding motion. The equilibrium stage is confirmed under different experimental conditions of a thermal gradient, interfacial gap, liquid viscosity, and liquid bridge volume. A strategy is proposed to control liquid motion and create lifting force between two plates. A theoretical model is also presented to illustrate the principle of the equilibrium stage. Creating lifting forces at the interface offers a new thermo-hydrodynamic tool for manipulating liquids behavior. This approach has the potential for controlling liquid motion in mechanical components and nature.

Bioinspired Functional Structures for Lubricant Control at Surfaces and Interfaces: Wedged-Groove with Oriented Capillary Patterns

In this work, a design concept of bioinspired functional surfaces is proposed for lubricant control at surfaces and interfaces subjected to external thermal gradients. Inspired by the conical structures of cactus and the motion configuration of Centipedes, a bioinspired surface of wedged-groove with an oriented capillary pattern is constructed. The effect of geometrical parameters on the directional lubricant manipulation capacity and sliding anisotropy is discussed. It is found that by regulating the orientation of the capillary pattern, a controllable lubricant self-transport capacity can be achieved for varying conditions from surfaces to interfaces, with or without thermal gradients. The lubricant self-transport process is captured, and the mechanism is revealed. The design philosophy of the proposed bioinspired functional surface is believed to have potential applications for lubricant control in modern machinery and complex liquid control in lab-on-a-chip and microfluidics devices.

Thermophobic Leidenfrost

We report that a volatile liquid deposited on a hot substrate with a gradient of temperature does not only levitate (Leidenfrost effect), but also spontaneously accelerates to the cold. This thermophobic effect is also observed with sublimating solids, and we attribute it to the ability of temperature differences to tilt (slightly) the base of the "object", which induces a horizontal component to the levitating force. This scenario is tested by varying the drop size (with which the acceleration increases) and the substrate temperature (with which the acceleration decreases), showing that the effect can be used to control, guide and possibly trap the elusive Leidenfrost drops.

Migration of Liquid Bridges at the Interface of Spheres and Plates with an Imposed Thermal Gradient

In this paper, we experimentally investigate the migration of liquid bridges at the interface of spheres and plates with an imposed thermal gradient. The key influencing factors of interface gap, sphere material and diameter, liquid viscosity, and thermal gradient on the migration behaviors are highlighted. Furthermore, the physical mechanism of this intriguing interfacial phenomenon is numerically unraveled. The originality of this work lies in the fact that when thermal gradients were encountered, liquid bridges could migrate at the interface of spheres and plates, and a general design philosophy of related parameters for enhancing or weakening this thermal flow is proposed.

Manipulating thermocapillary migration via superoleophobic surfaces with wedge shaped superoleophilic grooves

HYPOTHESIS

Thermocapillary migration is a phenomenon that liquid droplets can move from warm to cold regions on a nonuniformly heated surface. We expect to construct functional surfaces to manipulate the migration of liquid lubricants on rubbing surfaces.

EXPERIMENTS

Superoleophobic surfaces with wedge shaped superoleophilic grooves of varying geometrical parameters are fabricated, and migration experiments of typical liquid lubricants are performed on the designed surfaces.

FINDINGS

Manipulation capacity of the designed surfaces on the migration of liquid lubricants is confirmed, and the mechanism is revealed. An effective method using superoleophobic surfaces with wedge shaped superoleophilic grooves to reconcentrate the migrated lubricants is highlighted. Moreover, a general design philosophy for patterns of wedge shaped groove is proposed.

Electron Beam Patterning of Polymerizable Ionic Liquid Films for Application in Photonics

Planar photonic components can be fabricated with high resolution by electron beam patterning of polymer thin films on solid substrates such as silicon and glass. However, polymer films are normally formed by spin-coating lithographic resists containing not only polymers but also volatile solvents, which is a serious environmental and health issue. Therefore, we investigate a new type of material for planar structure fabrication (i.e., room-temperature ionic liquids (RTILs) with a polymerizable allyl group) that is electron-beam-curable, solvent-free, and thus potentially interesting for processing materials with weak resistance to solvents. We fabricate planar polymer microstructures by electron beam patterning of RTIL thin films in vacuum, which is possible because of the negligible volatility of ionic liquids. Three different polymerizable ionic liquids {i.e., [Allmim][Cl] (1-allyl-3-methylimidazolium chloride), [Allmim][NTf₂] (1-allyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide), and [Allmmim][NTf₂] (1-allyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide)} are compared in terms of the quality of the fabricated microstructures. We demonstrate that the shape of the more viscous RTIL with the Cl^- anion is less distorted during electron-beam-activated polymerization than the shape of the less viscous RTILs with a large NTf₂^- anion. Furthermore, the surface tension of the NTf₂-based ionic liquid decreases significantly with temperature as compared to that of the Cl-based ionic liquid. Thus, we suggest that the thermocapillary effect, that is, the Marangoni flow caused by a temperature gradient, might be responsible for the differences in the shape of the RTIL-derived microstructures. Also, we analyze the chemistry of the electron-beam-activated polymerization of RTIL by the use of Fourier-transform infrared spectroscopy (FTIR) and conclude that because of the disappearance of C═C bonds the free radical polymerization is a probable reaction mechanism. Finally, we show that polymerized microstructures are potentially attractive as planar photonic components because of good optical properties such as a high refractive index.

On the Thermocapillary Migration on Radially Microgrooved Surfaces

Thermocapillary migration describes the phenomenon in which a droplet placed on a nonuniformly heated surface can migrate from warm to cold regions. Herein, we report an experimental investigation of the migration of silicone oil droplets on radially microgrooved surfaces subjected to a thermal gradient; the effects of the initial divergence angle and divergent direction on the migration behavior are highlighted. A theoretical model is established to predict the migration velocity considering the thermocapillary, viscous resistance, and radial structure-induced forces; furthermore, the proposed theoretical derivation is validated. This study advances the understanding of this interfacial phenomenon, which has great potential for regulating and controlling liquid motion in lubrication systems, condensation and heat-transfer devices, and open microfluidics.

Ladderlike Tapered Pillars Enabling Spontaneous and Consecutive Liquid Transport

Directional liquid transport has significant domestic and industrial applications. Tapered objects have theoretically and experimentally been demonstrated to have the ability to spontaneously transport liquids. However, the transporting distance is limited, and consecutively and spontaneously transporting liquids has always been a challenge. In this work we proposed to exploit ladderlike tapered pillars, which are inspired by relay races, to increase the transport distance. These pillars were designed using a developed numerical model and fabricated by a novel alternating etching and coating method followed by wettability enhancement. We demonstrated through experiments that the resulting pillars could consecutively and spontaneously transport a liquid droplet at an average velocity of 0.139 m/s with a maximum acceleration of 5 g. The optimum window of the tilt angle range (0°-25°), contact angle (50°), and the chemical modification time (5 min) were obtained. Such ladderlike tapered pillars are able to improve the water-collection efficiency. These results may provide a new and systematic way to design and fabricate materials and structures for directional liquid transport.

Directional Passive Transport of Microdroplets in Oil-Infused Diverging Channels for Effective Condensate Removal

Condensation widely exists in nature and industry, and its performance heavily relies on the efficiency of condensate removal. Recent advances in micro-/nanoscale surface engineering enable condensing droplet removal from solid surfaces without extra energy cost, but it is still challenging to achieve passive transport of microdroplets over long distances along horizontal surfaces. The mobility of these condensate droplets can be enhanced by lubricant oil infusion on flat surfaces and frequent coalescence, which lead to fast growth but random motion of droplets. In this work, we propose a novel design of diverging microchannels with oil-infused surfaces to achieve controllable, long-distance, and directional transport of condensing droplets on horizontal surfaces. This idea is experimentally demonstrated with diverging copper and silicon microchannels with nanoengineered surfaces. Along these hierarchical surface structures, microdroplets condense on the top channel wall and submerge into microchannels owing to the capillary pressure gradient in infusing oil. Confined by the microchannel walls, the submerged droplets deform and maintain the back-front curvature difference, which enables the motion of droplets along the channel diverging direction. Subsequent droplet coalescences inside the channel further enhance this directional transport. Moreover, fast-moving deformed droplets transfer their momentum to downstream spherical droplets through the infusing oil. As a result, simultaneous passive transport of multiple droplets (20-400 μm) is achieved over long distances (beyond 7 mm). On these oil-infused surfaces, satellite microdroplets can further nucleate and grow on an oil-cloaked droplet, demonstrating an enlarged surface area for condensation. Our findings on passive condensate removal offer great opportunities in condensation enhancement, self-cleaning, and other applications requiring directional droplet transport along horizontal surfaces.

Mimicking wettability alterations using temperature gradients for water nanodroplets

A sessile droplet or a film usually moves from hotter regions to colder regions, due to variations in interfacial tension. This, known as the so-called Marangoni effect, is true for most pure liquids like water for which the surface tension decreases with an increase in temperature. In stark contrast to this existing understanding, we bring forth the coupled effect of wettability and temperature gradients on the dynamics of the three-phase contact line. By simultaneously tracking the dynamic evolution of the three-phase contact line due to the evaporation and diffusion of molecules through molecular dynamics simulations, we explore the coterminous effects of the change of surface tension coefficients and wetting parameters with temperature on sessile droplets residing on surfaces with different wettabilities. We demonstrate, for the very first time, that the inverse Marangoni effect, which is believed to be exclusively observed in mixtures and self-rewetting fluids, is feasible in pure water at scales where inertial effects are negligible. The results of the study find application in electronic chip cooling where by the combined tuning of surface characteristics and Marangoni forces, droplets can be passively transported to warmer regions for efficient thermal management.

On the migration of a droplet on an incline

A liquid droplet placed on a nonuniformly heated solid surface will migrate from a high temperature region to a low temperature region. The present study reports the results of an experimental investigation on the migration behavior of mineral oil droplets subjected to a thermal gradient on an inclined plane. A particular attention is paid to the relationship between the critical inclination angle and thermal gradients. It is shown that there exists a critical inclination angle at which the droplet migration is halted. This critical inclination angle can be readily predicted using analytical expressions derived in this paper. This study puts forward the understanding of the interface phenomenon of thermocapillary migration on an incline. The knowledge of the critical inclination is important in applications where the migration on an incline must be obstructed to retain adequate lubrication in the desired location.