Dynamics of spreading on a liquid substrate

Spreading of aqueous surfactant solutions on oil substrates: Superspreaders vs non-superspreaders

HYPOTHESIS

The question of why aqueous solutions of some surfactants demonstrate a rapid spreading (superspreading) over hydrophobic solid substrates, while solutions of other similar surfactants do not, has no definitive explanation despite numerous previous studies. The suggested hypothesis for this study assumes that once the spreading coefficient of surfactant is positive, there is a concentration range for solutions of any surfactant which demonstrates rapid spreading. As it is impossible to calculate spreading coefficients for solid substrates, we compare the spreading performance of known superspreaders and non-superspreaders on liquid (oil) substrate.

EXPERIMENTS

The kinetics of spreading of aqueous solutions of a series of branched ionic surfactants and non-ionic trisiloxane surfactants on two liquid substrates was studied and compared with the spreading of a surfactant-free liquid, silicone oil. Both dynamic and equilibrium spreading coefficients were calculated using measured surface and interfacial tensions.

FINDINGS

There is no difference in spreading rate on liquid substrate between solutions of surfactants proven as superspreaders (while spreading on solid substrate) or non-superspreaders. A rapid spreading (superspreading) with the characteristic rate of spreading O(102-103) mm2/s occurs if the dynamic spreading coefficients exceeds the positive threshold value. If the dynamic spreading coefficient is negative or slightly positive, complete wetting still occurs, but the spreading is slow with the spreading rate is O(1) mm2/s. Spreading exponents for surfactant solutions in the rapid spreading regime are considerably larger than for the surfactant-free liquid. A number of spreading and dewetting patterns were observed depending on the surfactant type, its concentration and substrate.

Dynamics of spreading of an asymmetrically placed droplet near a fluid-fluid interface

Two-dimensional numerical simulations are carried out to study the spreading dynamics of a droplet placed in the vicinity of a fluid-fluid interface. Simulations are performed using the hybrid lattice-Boltzmann technique and the diffuse-interface model by considering three immiscible fluids of the same density and viscosity. In contrast to the well-studied spreading of drops placed symmetrically across fluid-fluid interfaces, this work considers the simultaneous migration, spreading and eventual adsorption of an asymmetrically placed drop. These processes, which are solely driven by interfacial forces, are characterised by monitoring the temporal evolution of geometric parameters, such as the centre of mass, radius and height of the drop, the surface energy of the three interfaces and the associated flow fields inside and outside the droplet. The rate of spreading and rate of adsorption are also calculated to determine the dominant processes that drive the dynamics of the system.

Marangoni-driven spreading of a droplet on a miscible thin liquid layer

HYPOTHESIS

The coalescence of droplets with liquid-gas interfaces of different surface tensions is common in nature and industrial applications, where the Marangoni-driven film spreading is an essential process. Unlike immiscible fluids governed by triple contact line dynamics, the mixing between two miscible fluids strongly couples with the film spreading process, which are expected to manifest distinct power-law relations for the temporal increase in the film radius.

EXPERIMENTS

We experimentally investigate the Marangoni-driven film spreading phenomenon for a droplet with lower surface tension dropping onto a miscible, thin liquid layer. The temporal growth of the film radius was detected by using a novel deep convolutional neural network, the U2-net method. Scaling analysis was performed to interpret the spreading dynamics of the film.

FINDINGS

We find that the film radius exhibits a three-stage power-law relation over time, with the exponent varying from 1/2 to 1/8, and back to 1/2. The diffusion-affected Marangoni stresses in these three stages were derived, and two estimations of viscous stress were considered. Through estimating and balancing the viscous stress with the Marangoni stress, the three-stage power-law relation was derived and validated.

Migration and Spreading of Droplets across a Fluid-Fluid Interface in Microfluidic Coflow

Interfacial migration of droplets in microfluidic confinements has significant relevance in cell biology and biochemical assays. So far, studies on passive interfacial migration of droplets are limited to co-flow interfaces having small interfacial tension (IFT ∼ 1 mN/m). Here, we elucidate the migration and spreading of droplets (SiO-1000, SiO-100, FC40, and castor oil as phase 3, P3) across the interface between a pair of coflowing streams (PEG as P1, SiO-100, SiO-20, FC40, and olive oil as P2) having large IFT (∼10 mN/m), with the three different phases immiscible. Interfacial migration involving interfaces of large IFT is facilitated by confining droplets between the channel wall and coflow interface. We find that contact between droplets and the coflow interface is governed by the confinement ratio (i.e., the ratio of drop size to stream width) and the ratio of the capillary numbers of the coflowing streams. Depending on the sign of the spreading parameter (S) of the co-flowing phases, droplet migration or spreading at the interface is observed. While interfacial migration is observed for S₁ < 0 and S₂ > 0, droplet spreading is observed for S₁ < 0 and S₂ < 0, where S₁ and S₂ are P1 and P2 side spreading parameters, respectively. We investigate the droplet migration dynamics and time evolution of the contact line and the interface. Our results show that the speed of interfacial migration increases with increasing spreading parameter contrast between the coflowing phases. In the droplet spreading case, we experimentally study the variation in the spreading length with time, revealing three distinct regimes in good agreement with predictions from analytical scaling. Our study explores the interfacial transport of droplets involving high IFT interfaces, advancing the fundamental understanding of the topic that may find relevance in droplet microfluidics.

Interfacial instabilities in Marangoni-driven spreading of polymer solutions on soap films

HYPOTHESIS

Tuning and controlling the flow behavior of multi-component liquids has been a long-lasting struggle in various technological applications. Here, we studied Marangoni spreading of a polymer-surfactant ternary solution when deposited on a soap film with higher surface tension. The spreading front becomes unstable into a fingering pattern above the entanglement concentration of the polymer solution, indicating that the interplay between the elastic and interfacial properties drives the instability. Balancing these terms results in a critical length scale for the onset of the instability.

EXPERIMENTS

To investigate the connection between the rheological characteristics of the samples and the origins of the instabilities, various rheological tests were performed. Elastic and loss modulus of the samples were measured within the linear viscoelastic regime. The spreading behavior of the solutions was studied using high-speed imaging techniques.

FINDINGS

At low concentrations of polymers, spreading dynamics are governed by surface tension gradient and viscous dissipation leading to a stable front growing linearly in time. However, above the entanglement concentration of polymers spreading front destabilizes into a daisy shape pattern suggesting the elastic forces dominating the spreading dynamics. We introduced a length scale that precisely predicts the onset of the instability.

Buoyancy-Marangoni Fingering of a Miscible Spreading Drop

We experimentally investigate the interfacial instability that emerges when a water droplet is deposited on a bath of glycerol-water solution. Despite the absence of surface tension to stabilize short-wavelength undulations, we observe finite-size fingers that grow and pinch off from the drop. We show that the fingering patterns formed in the experiments resultes from a balance between the outward buoyancy effect and inward Marangoni flow. This induced Marangoni flow inhibits small perturbations and acts as an effective surface tension on the miscible interface of the spreading drop. To characterize the final size and shape of the drop, we perform systematic experiments by varying the drop volume and the glycerol-water volume fraction. In addition, we have developed scaling arguments for the drop’s final radius using key physical forces, and show that the final wavelength is inversely proportional to the Bond number.

Coupled Dynamics of Colloidal Nanoparticle Spreading and Self-Assembly at a Fluid-Fluid Interface

We investigated the physicochemical and transport phenomena governing the self-assembly of colloidal nanoparticles at the interface of two immiscible fluids. By combining in situ grazing-incidence small-angle X-ray scattering (GISAXS) with a temporal resolution of 200 ms and electron microscopy measurements, we gained new insights into the coupled effects of solvent spreading, nanoparticle assembly, and recession of the vapor-liquid interface on the morphology of the self-assembled thin films. We focus on oleate-passivated PbSe nanoparticles dispersed across an ethylene glycol subphase as a model system and demonstrate how solvent parameters such as surface tension, nanoparticle solubility, aromaticity, and polarity influence the mesoscale morphology of the nanoparticle superlattice. We discovered that a nanoparticle precursor monolayer film spreads in front of the bulk solution and influences the fluid spreading across the subphase. Improved understanding of the impact of kinetic phenomena (i.e., solvent spreading and evaporation) on the superlattice morphology is important to describe the formation mechanism and ultimately enable the assembly of high-quality superlattices with long-range order.

Rapid Spreading of a Droplet on a Thin Soap Film

We study the spreading of a droplet of surfactant solution on a thin suspended soap film as a function of dynamic surface tension and volume of the droplet. Radial growth of the leading edge (R) shows power-law dependence on time with exponents ranging roughly from 0.1 to 1 for different surface tension differences (Δσ) between the film and the droplet. When the surface tension of the droplet is lower than the surface tension of the film (Δσ > 0), we observe rapid spreading of the droplet with R ≈ t^α, where α (0.4 < α < 1) is highly dependent on Δσ. Balance arguments assuming the spreading process is driven by Marangoni stresses versus inertial stresses yield α = 2/3. When the surface tension difference does not favor spreading (Δσ < 0), spreading still occurs but is slow with 0.1 < α < 0.2. This phenomenon could be used for stretching droplets in 2D and modifying thin suspended films.

Dynamic contact angle of water-based titanium oxide nanofluid

This paper presents an investigation into spreading dynamics and dynamic contact angle of TiO2-deionized water nanofluids. Two mechanisms of energy dissipation, (1) contact line friction and (2) wedge film viscosity, govern the dynamics of contact line motion. The primary stage of spreading has the contact line friction as the dominant dissipative mechanism. At the secondary stage of spreading, the wedge film viscosity is the dominant dissipative mechanism. A theoretical model based on combination of molecular kinetic theory and hydrodynamic theory which incorporates non-Newtonian viscosity of solutions is used. The model agreement with experimental data is reasonable. Complex interparticle interactions, local pinning of the contact line, and variations in solid-liquid interfacial tension are attributed to errors.

Autophobing on liquid subphases driven by the interfacial transport of amphiphilic molecules

We investigated the phenomenon of incomplete wetting of a high-energy liquid subphase by drops of pure amphiphilic molecules as well as drops of amphiphile solutions that are immiscible with the subphase. We show that amphiphiles escape across the contact line of the drop, move on the subphase/vapor interface, and form a submonolayer or full monolayer external to the drop. If this monolayer is sufficiently dense, then it can reduce the surface tension of the subphase, raise the contact angle of the drop, and prevent the drop from fully wetting the subphase. This phenomenon is called autophobing and has been extensively studied on solid substrates. For the liquid subphase studied here, we measure the surface tensions of the three relevant interfaces before and after the drop is deposited. The measured surface tension external to the drop shows that amphiphiles can move across the contact line and form a monolayer outside of the drop. In some cases, at equilibrium, the monolayer is in a sufficiently packed state to create the nonwetting condition. In other cases, at equilibrium the monolayer density is insufficient to lower the surface tension enough to achieve the nonwetting condition. Unlike on solid substrates where the formation of the monolayer external to the drop is kinetically hindered, the amphiphiles can move rapidly across the liquid subphase by Marangoni-driven surface transport, and local equilibrium is achieved. However, because the amphiphile inventory and subphase area are limited, the achievement of autophobing on a liquid subphase depends not only on the instrinsic subphase/amphiphile interaction but also on the total amphiphile inventory and area of the liquid subphase.

Beyond Tanner's law: crossover between spreading regimes of a viscous droplet on an identical film

We present results on the leveling of polymer microdroplets on thin films prepared from the same material. In particular, we explore the crossover from a droplet spreading on an infinitesimally thin film (Tanner's law regime) to that of a droplet leveling on a film thicker than the droplet itself. In both regimes, the droplet's excess surface area decreases towards the equilibrium configuration of a flat liquid film, but with a different power law in time. Additionally, the characteristic leveling time depends on molecular properties, the size of the droplet, and the thickness of the underlying film. Flow within the film makes this system fundamentally different from a droplet spreading on a solid surface. We thus develop a theoretical model based on thin film hydrodynamics that quantitatively describes the observed crossover between the two leveling regimes.

On the dynamics of liquid lenses

The spreading of a lens of one liquid on the surface of another liquid is examined. Lubrication theory is used to derive a coupled system of equations for the air-liquid and liquid-liquid interfaces. In the case of highly viscous lenses, extensional stresses are promoted and an additional equation for the lens velocity is derived. The potential singularity at the three-phase line is relieved by a microscopic precursor layer of the spreading fluid assumed to be present ahead of the macroscopic lens. This layer is stabilised via the inclusion of disjoining pressure effects in the lens. The results of our full parametric study show that, for weak gravitational forces, the shape of the lens at equilibrium depends solely on the surface tension ratio for sufficiently deep substrate thicknesses. For thin substrates, the underlying liquid film deforms severely near the point of deposition exhibiting flattening and dimpling.

Spontaneous spreading of nematic liquid crystals

The spontaneous spreading of macroscopic drops of nematic liquid crystals on hydrophilic substrates has been investigated by interferometric techniques. There is a complex interplay between the elastic energy, due to antagonist anchoring at the interfaces, and the radial flow in the spreading drop. A relevant parameter appears to be the relative humidity of the atmosphere, because it controls the amount of water molecules adsorbed on the substrate and, therefore, the strength of anchoring defects. The spreading laws differ from the ones of simple wetting liquids, and contact line instabilities coupled to short- (anchoring) or large-scale (disclinations) defects of the nematic film are observed.

Non-aqueous phase liquid spreading during soil vapor extraction

Many non-aqueous phase liquids (NAPLs) are expected to spread at the air-water interface, particularly under non-equilibrium conditions. In the vadose zone, this spreading should increase the surface area for mass transfer and the efficiency of volatile NAPL recovery by soil vapor extraction (SVE). Observations of spreading on water wet surfaces led to a conceptual model of oil spreading vertically above a NAPL pool in the vadose zone. Analysis of this model predicts that spreading can enhance the SVE contaminant recovery compared to conditions where the liquid does not spread. Experiments were conducted with spreading volatile oils hexane and heptane in wet porous media and capillary tubes, where spreading was observed at the scale of centimeters. Within porous medium columns up to a meter in height containing stagnant gas, spreading was less than ten centimeters and did not contribute significantly to hexane volatilization. Water film thinning and oil film pinning may have prevented significant oil film spreading, and thus did not enhance SVE at the scale of a meter. The experiments performed indicate that volatile oil spreading at the field scale is unlikely to contribute significantly to the efficiency of SVE.

On the Spreading of Partially Miscible Liquids

As time proceeds, partially miscible liquids spread as a cap surrounded by a primary film according to power laws, t(n), for both the leading edge (front) and the central cap. The corresponding exponents depend on the thickness, H, of the liquid aqueous substrate and the deviation of concentration from its saturation value, DeltaC=C-C(sat). As long as H is thick enough, here H>/=5 mm, the exponents are n=1/2 and n=1/3 for the front and the central cap, respectively. For thinner layers, H approximately 2 mm, and moderate DeltaC, the spreading is drastically hindered and the measured values can go down to n=0.1, due to the additional friction imposed by the confinement of the convective cells generated by dissolution below the primary film which anchor on the solid surface beneath the liquid substrate. Copyright 2001 Academic Press.

A Mathematical Model for Crater Defect Formation in a Drying Paint Layer

Certain deep indentations observed in dry coatings are referred to as "craters". They are believed to arise from gradients in the coating surface tension. A mathematical model of surface-tension-gradient-driven flow, using the lubrication approximation for thin layers, is developed to study the formation of craters. The paint is modeled as consisting of an evaporating "solvent" part and a nonvolatile "resin" part. Surface tension gradients on the coating surface arise due to a nonuniform distribution of surfactant. Axisymmetric numerical simulations using the model are performed to explore two candidate crater production mechanisms: an initial release of concentrated surfactant and a steady surfactant source. The effects of changes in various properties, such as the paint drying rate, the surfactant diffusivity, and the viscosity increase during drying, are examined. The model produces craters with large diameters, pronounced rims, and central peaks, similar to those seen in practice. Drying rate has a large influence on crater diameter and depth, by limiting flow due to surface tension gradients within a given time. Reduction of the paint viscosity increase during drying causes increased flow rates, leading to larger craters. A preexisting layer of surfactant on the paint surface sharply reduces the extent of cratering. Surfactant diffusion also tends to reduce the severity of cratering by alleviating surface tension gradients. In some cases, a simplified form of the drying model may be used to quickly approximate the results of the full model. The model provides useful insights into the craters seen in industrial coating applications. Copyright 2000 Academic Press.

A Sorption-Kinetic Model for Surfactant-Driven Spreading of Aqueous Drops on Insoluble Liquid Substrates

Spreading of aqueous drops on hydrocarbon liquids occurs only when particular surfactants are added to the droplets above a critical concentration. For surfactant solutions of didodecyl ammonium bromide (DDAB) in water spreading over mineral oil, rates of droplet expansion are much slower than those corresponding to pure liquids spreading over immiscible liquid substrates with the same initial spreading coefficients. We present a sorption-kinetic model to explain quantitatively the spreading histories for aqueous DDAB droplets on mineral oil. Due to surfactant transport limitations, spreading occurs only when enough surfactant arrives at the dilating lens surfaces to establish a slightly positive, but near-zero spreading coefficient. We solve the convective diffusion equation for a cylindrical disk-like lens under the integral constraint of a constant surfactant adsorption density corresponding to a near-zero spreading coefficient. All observed spreading behavior is correctly portrayed by the proposed sorption-kinetic model including final equilibrium lens formation and spreading rates that are sensibly independent of drop volume, but are strongly dependent on drop surfactant concentration. Quantitative agreement is found with the experimental spreading data for a surfactant diffusion coefficient of 6x10(-12) m(2)/s and an effective adsorption rate constant of 6.5x10(-7) m/s. Both values prove physically reasonable. The sorption-kinetic model provides a new mechanism for understanding slow surfactant-driven spreading. Copyright 2000 Academic Press.

Spreading Dynamics Modeled by Lattice-Boltzmann Techniques

Utilizing a recently developed numerical technique, known as the lattice-Boltzmann method, we study 2D immiscible three-phase flow at the microscopic scale. In this paper, the spreading of a droplet on a fluid-fluid interface has been investigated. Different spreading regimes, depending on the governing forces, are identified. It has been found that the spreading rates derived from simulations agree with analytically obtained spreading rates for both capillary- and gravity-driven flow. In the gravity driven case, a formula can be derived for the drop shape. The numerical results regarding the drop shape turn out to resemble the predicted shape. Copyright 1998 Academic Press.