Depinning Of Contact Line Research Articles

The effect of contact angle hysteresis on a droplet in a viscoelastic two-phase system

We investigate the dynamic behavior of a two-dimensional droplet adhering to a wall in Poiseuille flow at low Reynolds numbers, in a system where one of the phases is viscoelastic represented by a Giesekus model. The Cahn–Hilliard Phase-Field method is used to capture the interface between the two phases. The presence of polymeric molecules alters the viscoelastic drop's deformation over time, categorizing it into two stages before contact line depinning. In the first stage, the viscoelastic droplet deforms faster, while in the second stage, the Newtonian counterpart accelerates and its deformation outpaces the viscoelastic droplet. The deformation of viscoelastic drop is retarded significantly in the second stage with increasing Deborah number De. The viscous bending of viscoelastic drop is enhanced on the receding side for small De, but it is weakened by further increase in De. On the advancing side, the viscous bending is decreased monotonically for Ca < 0.25 with a non-monotonic behavior for Ca = 0.25. The non-monotonic behavior on the receding side is attributed to the emergence of outward pulling stresses in the vicinity of the receding contact line and the inception of strain-hardening at higher De, while the reduction in the viscous bending at the advancing side is the result of just strain-hardening. Finally, when the medium is viscoelastic, the viscoelasticity suppresses the droplet deformation on both receding and advancing sides, and this effect becomes more pronounced with increasing De. Increasing the Giesekus mobility parameter enhances the weakening effect of viscous bending on the advancing side.

Neutralizing coffee-ring effect using gradual structures for uniform particle distribution

The coffee-ring effect is a process that takes place when a tiny drop of liquid-containing particles disappears, resulting in a distinct deposit around the edge of the spill resembling a ring. One of the primary causes of this effect is the uneven distribution of particles due to dissimilar evaporation rates on the droplet surface and contact line pinning effects. In this research, a microwell with a gradual structure has been developed to regularize the slippery Wenzel wettability of the surface and control the particle distribution. The mobility and pinning of droplet contact lines during the evaporation process are greatly influenced by this structure. The uniform curvature of the sidewall structure is predisposed to contact line depinning and thus helps the sliding of droplets to further neutralize the coffee-ring effect. Contact line pinning is predominantly observed at the corners of the structure, which are encircled by the ends and bottoms of the microwell's sidewalls. The curvature changes at this point, enhancing van der Waals' forces and resulting in a uniform monolayer of sediment being deposited at the microwell's bottom. The restraining efficacy of microwells of gradual structure on coffee rings with polystyrene spheres was confirmed, and the impact of microwell diameter, particle diameter, and loading efficacy on particle deposition distribution was investigated. The results show that the gradient configuration permits a single layer and even distribution of particles, enabling the sediment's dimensions to be anticipated and evaluated.

On the dynamics of coalescence between droplets and partially filled microgrooves

When water vapor condenses on a hydrophobic surface equipped with microgrooves, a unique phenomenon of coalescence between droplets growing on the ridges and the microgrooves partially imbibed with a condensate is manifested. Such coalescence is distinctly different from droplet–droplet coalescence and can trigger rapid removal of the condensate from the surface, a critical requirement for high thermodynamic efficiency of condensation. In this work, we investigate the dynamics of this coalescence process. We develop an experimentally validated, three-dimensional, volume of fluid method-based numerical modeling framework that accounts for dynamic contact angle variation during contact line motion. The condensate wetting the microgroove forms a liquid column with a meniscus pinned to the microgroove edges. We show that ridge droplet coalescence with this pinned meniscus triggers capillary ripples that traverse the microgroove in transverse and longitudinal directions and can trigger the depinning of the contact line from the opposing edge depending on the size of the coalescing droplet. The contact line depins when the local contact angle at the opposing edge reaches ∼180° and, simultaneously, the kinetic energy converted from the excess surface energy available reaches a maximum. Additionally, we show that the overall coalescence process is significantly affected by the microgroove aspect ratio. For the same liquid volume, relatively shallower microgrooves cause the condensate to overflow, thus attaining a morphology akin to large droplets in the Wenzel state. As a result, the coalescence dynamics on such microgrooved surfaces are similar to that on a planar surface.

Role of Droplet Dynamics on Contact Line Depinning in Shearing Gas Flow.

Sessile droplets exposed to shearing gas flows resist depinning owing to surface tension and contact angle hysteresis. It is known that contact line depinning occurs when the shearing gas flow is large enough to deform the droplet beyond its contact angle hysteresis. This work explores the contact line depinning process by visualizing growing droplets on a porous layer in laminar shear gas flows. High-speed imaging of droplets revealed an oscillatory motion in droplets, which is speculated to originate from an interaction between the drag force and surface tension effects. This oscillatory motion creates an inertial force within the droplet which combines with the drag force when droplet acceleration is in the stream-wise direction. The combined effect competes against the droplet adhesion force, setting the depinning criteria. Analyzing droplet images revealed that droplet local velocity and acceleration (i.e., sessile droplet dynamics prior to detachment from the substrate) increase with the superficial gas velocity. At the same time, the contact line depinning occurs at a smaller droplet size for higher superficial gas velocities. This results in a "hill-like" variation of the inertial force as a function of the convective Weber number, Weconv, causing a local maximum in the inertial force data (Weconv scales the inertia effects of the shear flow to surface tension effects). For the experimental condition tested in the current study, the inertial force created in the droplet could reach up to half of the adhesion force, making the drag force only responsible for the other half to depin the droplet contact line. Even at low superficial gas velocities, which featured lower droplet oscillations, the inertial force created in the droplet was considerable with respect to the adhesion force, reaching around one-third of the adhesion force.

Coffee stain effect on a fibre from axisymmetric droplets

The so-called coffee stain effect has been intensively studied over the past decades, but most of the studies have focused on sessile droplets. In this paper, we analyse the origin of the difference between the deposition of suspended particles in a sessile drop and in an axisymmetric drop deposited on a fibre. First, we model the shape of a drop on a fibre and its evaporative flux with some approximations to derive analytical calculations. Then, for pinned contact lines, we solve the hydrodynamics equations in the liquid phase under the lubrication approximation to determine the flow velocity toward the contact lines. We comment on these results by comparison to a sessile drop of similar evaporating conditions, and we show that the substrate curvature plays a role on the contact line depinning, the local evaporative flux and the liquid flow field. The competition between the advection and the Brownian motion indicates that the transport of the particles toward the contact line occurs in a volume localised in the close vicinity of the contact lines for a drop on a fibre. Thus, the fibre geometry induces a weaker accumulation of particles at the contact line compared to a sessile drop, leading to the more homogeneous deposit observed experimentally.

Pinning and Depinning Dynamics of an Evaporating Sessile Droplet Containing Mono- and Bidispersed Colloidal Particles on a Nonheated/Heated Hydrophobic Substrate

The present study is primarily focused on the coupled effects of substrate heating, colloidal dispersion, and particle size variation on the contact line (CL) pinning-depinning dynamics of evaporating droplets containing mono- (3/4.5 μm) and bidispersed (3 and 4.5 μm) polystyrene colloidal particles on poly(dimethylsiloxane) (PDMS) substrates. Experimental techniques such as high-speed visualization, optical microscopy, infrared thermography, and scanning electron microscopy are implemented to discover the plausible causes dictating the underlying physics. In the case of the nonheated substrate, there exists a significant delay in the CL depinning for the evaporating droplets containing bidispersed particles, as opposed to the monodispersed cases. A first-order model is illustrated for the determination of the net horizontal force acting on the particles near the CL. Interestingly, the model's findings revealed that due to the difference of particle size in the case of the bidispersed suspension, the interparticle contact force gets modified, thus enhancing the CL pinning. For the heated substrate cases, droplets with monodispersed particles (3 μm) exhibit a substantial delay in the CL depinning, whereas a nearly complete pinning of the CL is witnessed for the case of bidispersed colloidal suspension droplets. It is mainly due to the augmentation of particle deposition near the CL because of the circulatory thermal Marangoni and outward capillary flows. Thus, the mobility of the CL is inhibited, which is further reinforced by the presence of different-sized particles. Eventually, a ring-like deposition is observed, as opposed to an inner deposit commonly observed from the evaporation of colloidal droplets on hydrophobic substrates.

Phenomenology and kinetics of sessile droplet evaporation on convex contours

In this article we probe experimentally and theoretically the evaporation phenomenology and kinetics of sessile droplets seated over convex hydrophilic and super-hydrophobic (SH) surfaces. To understand the role of convex contours, both cylinders (mono-curvature system) and spheres (two-curvature system) have been explored. The evolution of the droplet shape during evaporation was monitored by optical imaging. The observations reveal improved evaporation rates on convex substrates, and the same tends to increase with increasing curvature. The findings also show that the influence of a two-curvature system (sphere) on the evaporation rate is to a higher extent than that for a mono-curvature system (cylinder). These observations are attributed to the augmented liquid-vapor interfacial area and widened up vapor diffusion domain which renders the liquid-molecules more scope to diffuse in the surrounding environment. The dynamic behavior of the triple line (TL) on convex substrates shows higher receding velocity of the contact line especially on spherical substrates. To visualize the internal flow and understand the effect of substrate convexity on internal advection dynamics, particle image velocimetry (PIV) was carried out. These results show higher strength of circulation velocity inside a droplet evaporating over convex surfaces despite frequent de-pinning of contact line. This behavior can be explicated by the fact than on convex surfaces higher temperature gradient exists along the liquid-vapor interface of the droplet (due to more evaporative cooling, and mapped through infrared thermography), which induces stronger thermal-Marangoni convection, thereby scaling up the circulation velocity. The finding may hold implications towards the design and development of droplet-based thermofluidic devices.

A universal capillary-deflection based adhesion measurement technique.

Contact angle goniometry suffers from inherent optical challenges such as scattering and diffraction near the triple contact line (TCL) rendering erroneous results. Alternatively, the cantilever-based direct adhesion measurement was constrained to low-energy surfaces to date due to the inability of the probe droplet to retract (pull-off) from high-energy surfaces completely. The present study revisits the cantilever approach from a fundamental physical perspective and generalizes the approach to render it wettability invariant. The adhesive wetting interaction between a probe droplet (attached to a cantilever) with the test substrate is recorded with a high-speed camera. Image processing and subsequent motion analysis enable us to accurately calculate the adhesion force (in the sub-micron range) exhibited by the test substrate. We experimentally demonstrate the contact line depinning (and not the droplet pull-off) to be the only prerequisite for accurately quantifying the characteristic adhesion force. We alsoreveal that depinning precedes the onset of cantilever retraction due to the inertia effect. Further, we establish that the characteristic adhesion corresponds to zero acceleration of the cantilever and not to its maximum deflection. The inferences of the study will be beneficial in the rational design of direct wetting characterization methods for any substrate.

Pinning and depinning in imbibition beyond a sharp edge: A lattice Boltzmann study

The phenomenon of capillary rise or imbibition is governed by the inertia, the capillary force, the gravitational force and viscous force of fluids. Besides, the geometry also plays an important role on the imbibition dynamics since the motion of contact line could be affected by the sharp transition of geometry, and the oscillation of meniscus could be observed due to the confinement of contact line. The imbibition is a multiphase flow problem, which involves the movement of contact line and differences of fluid density and viscosity. In this paper, an axisymmetric lattice Boltzmann (LB) model based on the phase-field theory is proposed for investigating the oscillation phenomenon in the imbibition process. We also introduce a dimensionless Weber number to further analyze the pinning and depinning of contact line at the edge of capillary tube, and consider the effects of tube length and contact angle. The process of liquid spreading onto the top surface of capillary tube is presented, and several distinct phenomena are observed: depinning up and depinning down, pinning up and depinning down, pinning up and pinning down, pinning below the top edge. These transitions among different phenomena are dependent on the Weber number, which indicates the relative importance of inertial force compared to the surface tension force.

Evaporation kinetics of wettability-moderated capillary bridges and squeezed droplets

We experimentally and theoretically probe the evaporation kinetics of liquid capillary bridges and squeezed droplets for different heights and wettability conditions. Water droplets of uniform volume were squeezed between hydrophilic and superhydrophobic (SH) flat substrates, and the relative spacing between them is varied to understand the role of bridge height on its evaporation behavior. The transient evolution of bridge profile during the evaporation is monitored using optical imaging technique, with thermal imaging aid. Our observations reveal augmented evaporation rate for smaller relative spacing between the hydrophilic surfaces due to increased curvature of the liquid–vapor interface. For SH surfaces, the vapor entrapment phenomenon plays a significant role in addition to interfacial curvature, especially for small relative spacing. For mixed wettability bridge, the shape of the bridge exhibits a transition in curvature, which governs its temporal evaporation rate. We show that the bridge stability and contact line dynamics during evaporation is strongly dictated by the capillary pressure and the geometry of the liquid–vapor interface. For smaller relative spacing, the contact line de-pins at early stages and the liquid bridge remains stable for a longer duration. Whereas, bridges pinch off at early stages for higher spacing conditions via rapid evaporation of the neck. To model the evaporative mass loss rate, the transient bridge interfacial profile under influence of gravity is quantified using the principal of energy minimization, and the curvature driven evaporative flux is summed up over this interface to obtain the evaporation rate. The model predictions conform well to the experimental observations.

Effect of Macroscopic Surface Heterogeneities on an Advancing Contact Line.

The shape of a liquid-air interface advancing on a heterogeneous surface was studied experimentally, together with the force induced by the pinning of the contact line to surface defects. Different surfaces were considered with circular defects introduced as arrays of cocoa butter patches or small circular holes. These heterogeneous surfaces were submerged in aqueous ethanol solutions while measuring the additional force arising from the deformation of the advancing contact line and characterizing the interface shape and its pinning on the defects. Initially, the submersion force is linear with submerged depth, suggesting a constant defect-induced stiffness. This regime ends when the contact line depins from the defects. A simple scaling is proposed to describe the depinning force and the depinning energy. As the defect separation increases, the interface stiffness is found to increase too, with a weak dependency on the defect radius. This interaction between defects cannot be captured by simple scaling but can be well predicted by a theory considering the interface deformation in the presence of a periodic arrays of holes. Creating a four-phase contact line by including solid defects (cocoa butter) reduced pinning forces. The radius of the defect had a nonlinear effect on the depinning depth. The four-phase contact line resulted in depinning before the defects were fully submerged. These experimental results and the associated theory help to understand quantitatively the extent to which surface heterogeneities can slow down wetting. This in turn paves the way to tailoring the design of heterogeneous surfaces toward desired wetting performances.

Manipulating Trapped Nanobubbles Moving and Coalescing with Surface Nanobubbles.

Trapped nanobubbles are observed nucleating at nanopits on a pitted substrate, while surface nanobubbles are usually formed on the smooth solid surface in water. In this work, trapped nanobubbles and surface nanobubbles were captured by a tapping-mode atomic force microscope (AFM) on a nanopitted substrate based on the temperature difference method. A single trapped nanobubble was manipulated to change into a surface nanobubble, then to change into the trapped nanobubble again. At the same time, surface nanobubbles can be moved to merge into a trapped nanobubble. Our results show that the scan load and the size of the scan area were the main factors that significantly affect the mobility of surface/trapped nanobubbles. The coalescence and mutual transformation of the two kinds of nanobubbles indicate that trapped nanobubbles and surface nanobubbles have the same chemical nature, which also provides vital experimental proof of the existence of nanobubbles in the course of contact line depinning. Our results are of great significance for understanding nanobubble stability and providing guidelines in some industrial applications.

Contact Line Pinning and Depinning Can Modulate the Rod-Climbing Effect.

Our experiments on the rod-climbing effect with an oil-coated rod revealed two key differences in the rod-climbing phenomena compared to a bare rod. First, an enhancement in the magnitude of climbing height for any particular value of the rod rotational speed and second, a decrease in the threshold rod rotational speed required for the appearance of the rod-climbing effect were observed. Observed phenomena are explained by considering the contact line behavior at the rod-fluid interface. Transient evolution of the meniscus at the rod-fluid interface revealed that the three-phase contact line was pinned for a bare rod and depinned for an oil-coated rod. We modeled the subject fluid as a Giesekus fluid to predict the climbing height. The differences in the contact line behavior were incorporated via the contact angle at the rod-fluid interface as a boundary condition. Agreement was found between the observed and predicted climbing height, establishing that contact line behavior may modulate the rod-climbing effect.

Variety of Ordered Patterns in Donor-Acceptor Polymer Semiconductor Films Crystallized from Solution.

A huge challenge is to control the nucleation of crystallites/aggregates in the solution during polymer film formation to generate desired structures. In this work, we investigate crystallization of P(NDI2OD-T2), a donor–acceptor polymer semiconductor, with controlled solution flow along the contact line between the drying film and solution through a seesaw-like pivoting of samples during polymer drying. By controlling the pivoting frequency/amplitude, various types of line patterns can be observed: (I) an array of fishbone-like stripes oriented in the film-growth direction; (II) the pinning–depinning of contact line (PDCL)-mechanism-defined patterned wires along the contact line; and (III) periodic twined crystalline line pattern oriented in the direction of the contact line. The rich variety of pattern formation observed is attributed to the distinctiveness of the donor–acceptor conjugated polymer structure. The result measured from thin-film transistors made of the generated films/structures showed that the charge mobility of P(NDI2OD-T2) does not change much with the film morphology, which supports recent controversy over the charge-transportation mechanism of some donor–acceptor polymer semiconductors.

Universal spatio-topological control of crystallization in sessile droplets using non-intrusive vapor mediation

The present work showcases a mechanism of asymmetric solvent depletion using vapor-mediated interaction that can non-intrusively regulate the site of crystal precipitation. In general, the flow pattern inside a drying sessile saline droplet leads to circumferential deposition of salt crystals at the end of evaporation. Instead, we show that our proposed approach can manipulate the spatial location of crystal precipitation. The introduction of a pendant ethanol droplet near the sessile saline droplet’s vicinity creates an asymmetric ethanol vapor gradient around the sessile drop. The differential adsorption of ethanol vapor on the surface of the saline droplet gives rise to a spatial surface tension gradient. This, in turn, enhances the internal convection [∼O (102–103)] within the saline droplet. The vigorous and non-uniform flow promotes targeted contact line depinning, ensuring preferential segregation of the salt crystals. Using this methodology, we can inhibit crystal formation at selected locations and favorably control its deposition in definite regions. The interplay of flow hydrodynamics and the associated contact line motion governs this phenomenon marked by the inception and growth of crystals at a preferential site. The universal character of such a phenomenon is verified for a variety of salt solutions on the glass substrate. Tweaking of contact line motion using vapor mediation can be used as a strategic tool for controlling the salt crystallization sites for various potential applications starting from water purification to portable diagnostics, fouling, and scaling, particularly in cases that require the separation of unwarranted solutes from solvents.

Role of substrate softness in stabilizing surface nanobubbles

The contact line pinning and supersaturation theory for the nanobubble stability has attracted extensive concerns from experimental investigators, and some experimenters argue that the contact line pinning is unnecessary. To interpret the experimental observations, we have proposed previously through molecular dynamics simulations that the deformation of soft substrates caused by surface nanobubbles may play an important role in stabilizing surface nanobubbles, while yet no quantitative theory is available for explanation of this mechanism. Here, the detailed mechanism of self-pinning-induced stability of surface nanobubbles is investigated through theoretical analysis. By manipulating substrate softness, we find that the formation of surface nanobubbles may create a deformation ridge nearby their contact lines which leads to the self-pinning effect. Theoretical analysis shows that the formation of nanobubbles on sufficiently rigid substrates or on liquid–liquid interfaces corresponds to a local free energy maximum, while that on the substrates with intermediate softness corresponds to a local minimum. Thus, the substrate softness could regulate the surface nanobubble stability. The critical condition for the self-pinning effect is determined based on contact line depinning, and the effect of gas supersaturation is explored. Finally, the approximate stability range for the surface nanobubbles is also predicted.

Morphological Control of Linear Particle Deposits from the Drying of Inkjet-Printed Rivulets.

We studied the morphology of linear particle deposits obtained by inkjet printing of a silica nanoparticle suspension in drying conditions where contact line depinning occurs. We show that this evaporation mode can be obtained by adjusting the particle concentration in different solvents. For isolated drops, deposited manually or by inkjet printing, drying induces the formation of two concentric rings in which particles self-assemble into a monolayer. For fused drops, our main result is that stable rivulets could be formed by drop overlap leading, after drying, to the formation of three parallel lines composed of a self-assembled particle monolayer. The three lines are of homogeneous thickness with two very thin outer lines (∼1 μm width) and a wider central line (∼20 μm width). We reveal how the width of the resulting lines is influenced by drop spacing in a predictable manner for a large experimental window knowing the drop size.

Light-Guided Surface Plasmonic Bubble Movement via Contact Line De-Pinning by In-Situ Deposited Plasmonic Nanoparticle Heating.

Precise spatiotemporal control of surface bubble movement can benefit a wide range of applications like high-throughput drug screening, combinatorial material development, microfluidic logic, colloidal and molecular assembly, and so forth. In this work, we demonstrate that surface bubbles on a solid surface are directed by a laser to move at high speeds (>1.8 mm/s), and we elucidate the mechanism to be the depinning of the three-phase contact line (TPCL) by rapid plasmonic heating of nanoparticles (NPs) deposited in situ during bubble movement. On the basis of our observations, we deduce a stick-slip mechanism based on asymmetric fore-aft plasmonic heating: local evaporation at the front TPCL due to plasmonic heating depins and extends the front TPCL, followed by the advancement of the trailing TPCL to resume a spherical bubble shape to minimize surface energy. The continuous TPCL drying during bubble movement also enables well-defined contact line deposition of NP clusters along the moving path. Our finding is beneficial to various microfluidics and pattern writing applications.

Study of Microdroplet Growth on Homogeneous and Patterned Surfaces Using Lattice Boltzmann Modeling

We present droplet growth dynamics on homogeneous and patterned surfaces (surface with hydrophilic and hydrophobic region) using two-dimensional thermal lattice Boltzmann method (LBM). In the first part, we performed 2D simulations on homogeneous hydrophobic surfaces. The result shows that the droplet grows at higher rate on a surface with higher wettability which is attributed to low conduction resistance and high solid–liquid contact area. In the later part, we performed simulations on patterned surface and observed that droplet preferentially nucleates on the hydrophilic region due to lower energy barrier and grows in constant contact line (CCL) mode because of contact line pinning at the interface of hydrophilic–hydrophobic region. As the contact angle reaches the maximum value of hydrophobic surface, contact line depins and droplet shows constant contact angle (CCA) growth mode. We also discuss the effect of characteristic width of hydrophilic region on growth of droplet. We show that contact angle of the droplet increases rapidly and reaches the contact angle of hydrophobic region on a surface with a lower width of the hydrophilic surface.

Pinning-Free Evaporation of Sessile Droplets of Water from Solid Surfaces.

Contact-line pinning is a fundamental limitation to the motion of contact lines of liquids on solid surfaces. When a sessile droplet evaporates, contact-line pinning typically results in either a stick-slip evaporation mode, where the contact line pins and depins from the surface in an uncontrolled manner, or a constant contact-area mode with a pinned contact line. Pinning prevents the observation of the quasi-equilibrium constant contact-angle mode of evaporation, which has never been observed for sessile droplets of water directly resting on a smooth, nontextured, solid surface. Here, we report the evaporation of a sessile droplet from a flat glass substrate treated with a smooth, slippery, omni-phobic covalently attached liquid-like coating. Our characterization of the surfaces shows high contact line mobility with an extremely low contact-angle hysteresis of ∼1° and reveals a step change in the value of the contact angle from 101° to 105° between a relative humidity (RH) of 30 and 40%, in a manner reminiscent of the transition observed in a type V adsorption isotherm. We observe the evaporation of small sessile droplets in a chamber held at a constant temperature, T = (25.0 ± 0.1) °C and at constant RH across the range RH = 10-70%. In all cases, a constant contact-angle mode of evaporation is observed for most of the evaporation time. Furthermore, we analyze the evaporation sequences using the Picknett and Bexon ideal constant contact-angle mode for diffusion-limited evaporation. The resulting estimate for the diffusion coefficient, DE, of water vapor in air of DE = (2.44 ± 0.48) × 10-5 m2 s-1 is accurate to within 2% of the value reported in the literature, thus validating the constant contact-angle mode of the diffusion-limited evaporation model.