Surfactant dynamics: hidden variables controlling fluid flows

Hydrodynamics of a disk in a thin film of weakly nematic fluid subject to linear friction

To make progress towards the development of a theory on the motion of inclusions in thin structured films and membranes, we here consider as an initial step a circular disk in a two-dimensional, uniaxially anisotropic fluid layer. We assume overdamped dynamics, incompressibility of the fluid, and global alignment of the axis of anisotropy. Motion within this layer is affected by additional linear friction with the environment, for instance, a supporting substrate. We investigate the induced flows in the fluid when the disk is translated parallel or perpendicular to the direction of anisotropy. Moreover, expressions for corresponding mobilities and resistance coefficients of the disk are derived. Our results are obtained within the framework of a perturbative expansion in the parameters that quantify the anisotropy of the fluid. Good agreement is found for moderate anisotropy when compared to associated results from finite-element simulations. At pronounced anisotropy, the induced flow fields are still predicted qualitatively correctly by the perturbative theory, although quantitative deviations arise. We hope to stimulate with our investigations corresponding experimental analyses, for example, concerning fluid flows in anisotropic thin films on uniaxially rubbed supporting substrates.

Dynamic duos: the building blocks of dimensional mechanics

Mechanics studies the relationships between space, time, and matter. These relationships can be expressed in terms of the dimensions of length , time , and mass . Each dimension broadens the scope of mechanics. Historically, mechanics emerged from geometry, which considers quantities like lengths or areas, with dimensions of the form . With the Renaissance, quantities combining space and time were considered, like speed, acceleration and later diffusivity, all of the form . Eventually, mechanics reached its full potential by including "mass-carrying" quantities such as mass, force, momentum, energy, action, power, viscosity, etc. These standard mechanical quantities have dimensions of the form where x and y are integers. In this contribution, we show that, thanks to this dimensional structure, these mass-carrying quantities can be readily arranged into a table such that x and y increase along the row and column, respectively. Ratios of quantities in the same rows provide characteristic lengths, while those in the same columns yield characteristic times, encompassing a great variety of physical phenomena from atomic to astronomical scales. Most generally, we show that selecting duos of mechanical quantities that are neither on the same row nor column of the table yields dynamics, where one mechanical quantity is understood as impelling motion, while the other impedes it. The force and the mass are the prototypes of impelling and impeding factors, but many other duos are possible. We present examples from the physical and biological realms, including planetary motion, sedimentation, explosions, fluid flows, turbulence, diffusion, cell mechanics, capillary and gravity waves, and spreading, pinching, and coalescence of drops and bubbles. This review provides a novel synthesis revealing the power of scaling or dimensional analysis, to understand processes governed by the interplay of two mechanical quantities. This elementary decomposition of space, time and motion into pairs of mechanical factors is the foundation of "dimensional mechanics", a method that this review wishes to promote and advance. Pairs are the fundamental building blocks, but they are only a starting point. Beyond this simple world of mechanical duos, we envision a richer universe that beckons with an interplay of three, four, or more quantities, yielding multiple characteristic lengths, times, and kinematics. This review is complemented by online video lectures, which initiate a discussion on the elaborate interplay of two or more mechanical quantities.

Effect of surface viscoelasticity on top jet drops produced by bursting bubbles

Jet drops resulting from bubble bursting at a liquid surface play a key role in various mass transfer processes across the interface, including sea spray aerosol generation and pathogen transmission. However, the impact of structurally compound interfaces, characterized by complex surface rheology introduced by surface-active contaminants, on the jet drop ejection still remains unclear. Here, we experimentally investigate the influence of surface viscoelasticity on the size and velocity of the top jet drops from surface bubble bursting, examining both pure protein and mixed protein-surfactant solutions. We document that for bubble bursting at a pure-protein-laden surface where surface elasticity dominates, the increase in Ec, i.e. the interfacial elastocapillary number as the ratio between the effects of interfacial elasticity and capillarity, efficiently increases the radius and decreases the velocity of the top jet drop, ultimately inhibiting the jet drop ejection. On the other hand, considering the mixed protein-surfactant solution, we show that the top jet drop radius and velocity exhibit a different variation trend with Ec, which is attributed to the additional dissipation on the capillary waves as well as the retardation and resistance on the converging flow for jet formation from surface viscoelasticity. Our work may advance the understanding of bubble bursting dynamics at contaminated liquid surfaces and shed light on the potential influence of surface viscoelasticity on the generation of bubble bursting aerosols.

Magnetic field effects on the surfactant concentration over ferrofluid droplet surfaces in shear flows

We investigate the impact of a magnetic field on surfactant concentration and interfacial forces across droplet surfaces within shear flows. Our analysis centers on a single two-dimensional ferrofluid droplet covered with surfactants, suspended in an immiscible, non-magnetizable liquid. The model combines incompressible Navier-Stokes equations and Maxwell's equations in the superparamagnetic limit in the single-fluid formulation, augmented by terms accounting for Marangoni, capillary, and magnetic forces at the droplet interface. We solve the surfactant convection-diffusion equation at the surface, while a non-linear Langmuir equation of state relates surfactant concentration to surface tension. The model is numerically solved using finite differences, a level-set method for multiphase flow computation, and the closest-point method for concentration equation. Our findings reveal that even though the surfactant is magnetically neutral, the presence of a magnetic field significantly modifies its distribution at the interface. A magnetic field perpendicular to the primary flow direction shifts the maximum concentration zone from the droplet tips toward the flow vorticity direction, while a parallel field produces the opposite effect. Alterations in surfactant distribution directly impact the surface tension field, offering a potential wireless means of controlling droplet dynamics.

Air invasion into three-dimensional foam induces viscous fingering instabilities

We conducted an experimental investigation to examine the immiscible radial displacement flows of air invading three-dimensional foam in a Hele-Shaw cell. Our study successfully identified three distinct flow regimes. In the initial regime, characterized by relatively low fingertip velocities, the foam underwent a slow displacement through plug flow. During this process, the three-phase contact lines slipped at the cell walls. Notably, we discovered that the air injection pressure exhibited a proportional relationship with the power of the fingertip velocity. This relationship demonstrated excellent agreement with a power law, where the exponent was determined to be 2/3. Transitioning to the second regime, we observed relatively high velocities, resulting in the displacement of the foam as a plug within single layers of foam bubbles. The movement of these bubbles near the cell walls was notably slower. Similar to the first regime, the behavior in this regime also adhered to a power law. In the third regime, which manifested at higher air injection pressures, the development of air fingers occurred through narrow channels. These channels had the potential to isolate the air fingers as they underwent a process of "healing." Furthermore, our results unveiled a significant finding that the width of the air fingers exhibited a continuous scaling with the air injection pressure, irrespective of the flow regimes being observed.

Stability and thinning of liquid jets in the presence of soluble surfactants

The dynamics of many multiphase fluid systems involve the thinning and eventual break up of a slender fluid filament or a liquid jet. The interfacial instability that controls the rate of jet thinning depends on the relative magnitudes of capillary, viscous, and inertial stresses. Surfactants add an additional layer of physicochemical dynamics by reducing the surface tension of the interface and introducing reverse Marangoni flows in response to surface concentration gradients. Surfactants may also introduce an intrinsic surface rheology that affects jet thinning. Quantifying these effects has been a significant problem in chemical physics and a topic of key research interest. Recent studies have shown that insoluble surfactants delay thread thinning and suppress instabilities in Newtonian jets. However, the role of surfactant solubility in liquid jet stability is still unknown. In this work, we use linear stability analysis to quantitatively show the stabilizing effects of Marangoni stresses, surfactant adsorption and desorption time, and intermolecular forces upon adsorption. We highlight the seemingly indistinguishable way in which various surfactant properties result in the same outcome. We also identify a surface dissipative contribution that arises from the interplay of Marangoni flows with finite adsorption and desorption, which acts as an "apparent" surface viscosity. We verify predictions of our linear stability results against numerical simulations and conclude by noting that tuning surface activity and kinetics of adsorbed surfactants or particles can potentially suppress droplet formation, which is of significant impact in the printing industry and in the control of the spread of aerosols.

Interplay of bulk soluble surfactants and interfacial kinetics governs the stability of two-layer channel flows

The linear stability of two-layer channel flows in the presence of bulk-soluble surfactants is investigated here, taking into account the rheological properties of the interface. The interfacial stresses are quantified using the Boussinesq-Scriven model, while the surfactant kinetics is assumed to follow the Frumkin isotherm, which accounts for their non-ideal behavior. Our results show that in general, the bulk solubility of surfactants has a stabilizing effect on the interface, both with and without the presence of inertia. On the other hand, the interfacial viscosities play a more complex role, depending on the viscosity ratios of the two fluids, the thickness of the fluid layers, the strength of the surface tension gradients, and the extent of inertia. We show that depending on the strength of inertia and the variability in the surface tension, the interfacial rheology may either stabilize or destabilize the base flow. However, for sufficiently small Reynolds numbers, the surface viscosity always has a stabilizing influence. Our results may be used to better design stable co-flow systems with applications in various processes such as surface coating, preparation of fluid lenses, as well as in a host of multi-purpose microfluidic devices.

Shell viscosity estimation of lipid-coated microbubbles

Understanding the shell rheology of ultrasound contrast agent microbubbles is vital for anticipating their bioeffects in clinical practice. Past studies using sophisticated acoustic and optical techniques have made enormous progress in this direction, enabling the development of shell models that adequately reproduce the nonlinear behaviour of the coated microbubble under acoustic excitation. However, there have also been puzzling discrepancies and missing physical explanations for the dependency of shell viscosity on the equilibrium bubble radius, which demands further experimental investigations. In this study, we aim to unravel the cause of such behaviour by performing a refined characterisation of the shell viscosity. We use ultra-high-speed microscopy imaging, optical trapping and wide-field fluorescence to accurately record the individual microbubble response upon ultrasound driving across a range of bubble sizes. An advanced model of bubble dynamics is validated and employed to infer the shell viscosity of single bubbles from their radial time evolution. The resulting values reveal a prominent variability of the shell viscosity of about an order of magnitude and no dependency on the bubble size, which is contrary to previous studies. We find that the method called bubble spectroscopy, which has been used extensively in the past to determine the shell viscosity, is highly sensitive to methodology inaccuracies, and we demonstrate through analytical arguments that the previously reported unphysical trends are an artifact of these biases. We also show the importance of correct bubble sizing, as errors in this aspect can also lead to unphysical trends in shell viscosity, when estimated through a nonlinear fitting from the time response of the bubble.

Role of interfacial rheology on fingering instabilities in lifting Hele-Shaw flows

The lifting Hele-Shaw cell setup is a popular modification of the classic, fixed-gap, radial viscous fingering problem. In the lifting cell configuration, the upper cell plate is lifted such that a more viscous inner fluid is invaded by an inward-moving outer fluid. As the fluid-fluid interface contracts, one observes the rising of distinctive patterns in which penetrating fingers having rounded tips compete among themselves, reaching different lengths. Despite the scholarly and practical relevance of this confined lifting flow problem, the impact of interfacial rheology effects on its pattern-forming dynamics has been overlooked. Authors of recent studies on the traditional injection-induced radial Hele-Shaw flow and its centrifugally driven variant have shown that, if the fluid-fluid interface is structured (i.e., laden with surfactants, particles, proteins, or other surface-active entities), surface rheological stresses start to act, influencing the development of the viscous fingering patterns. In this paper, we investigate how interfacial rheology affects the stability as well as the shape of the emerging fingered structures in lifting Hele-Shaw flows, at linear and early nonlinear dynamic stages. We tackle the problem by utilizing the Boussinesq-Scriven model to describe the interface and by employing a perturbative mode-coupling scheme. Our linear stability results show that interfacial rheology effects destabilize the interface. Furthermore, our second-order findings indicate that interfacial rheology significantly alters intrinsically nonlinear morphological features of the shrinking interface, inducing the formation of narrow sharp-tip penetrating fingers and favoring enhanced competition among them.

Curvature and shape relaxation in surface-viscous domains

The mechanics of curved, heterogeneous, surfactant-laden surfaces and interfaces are important to a variety of engineering and biological applications. To date, most models of rheologically complex interfaces have focused on homogeneous systems of planar or fixed curvature. In this study, we investigate a simple, dynamical model of a two-phase surface fluid on a curved interface: a condensed, surface-viscous domain embedded within a surface-inviscid, spherical interface of time-varying radius of curvature. Our aim is to understand how changes in surface curvature generate two-dimensional Stokes flows inside the domain, thereby resisting curvature deformation and distorting the domain shape. We model the surface stress within the domain using the classical Boussinesq-Scriven constitutive equation, simplified for a near-spherical cap undergoing a small-amplitude curvature deformation. We then analyze the frequency-dependent dynamics of the surface stress and curvature within the domain when the pressure difference across the surface is sinusoidally oscillated. We find that the curvature relaxes diffusively, and thus define a Peclet number (Pe) relating the rate of diffusion to the oscillation frequency. At small enough Pe, the surface deforms quasi-statically, whereas at high Pe, the curvature varies sharply within a thin boundary layer adjacent to the domain border. Consequently, the curvature of the domain appears discontinuous from the rest of the surface under rapid oscillation. We then examine the linear stability of the domain shape to small, non-axisymmetric perturbations when the surface is steadily compressed (i.e., the pressure difference across it is increased). While the line tension at the domain border tends to maintain circular symmetry, surface-viscous stresses generated by surface compression tend to destabilize the perimeter. A shape instability arises above a critical surface capillary number (Ca) relating surface-viscous stresses to line tension. Moreover, we show that the mechanism of instability is distinct from that of the famous Saffman-Taylor fingering instability. Various extensions of our model are discussed, including materials with finite dilatational surface viscosity, linear and nonlinear (visco)elasticity, and large-amplitude deformations.

Non-equilibrium ordering of liquid crystalline (LC) films driven by external gradients in surfactant concentration

HYPOTHESIS

Gradients in the concentration of amphiphiles play an important role in many non-equilibrium processes involving complex fluids. Here we explore if non-equilibrium interfacial behaviors of thermotropic (oily) liquid crystals (LCs) can amplify microscopic gradients in surfactant concentration into macroscopic optical signals.

EXPERIMENTS

We use a milli-fluidic system to generate gradients in aqueous sodium dodecyl sulfate (SDS) concentration and optically quantify the dynamic ordering of micrometer-thick nematic LC films that contact the gradients.

FINDINGS

We find that the reordering of the LCs is dominated by interfacial shearing by Marangoni flows, thus providing simple methods for rapid mapping of interfacial velocities from a single optical image and investigating the effects of confinement of surfactant-driven interfacial flows. Additionally, we establish that surface advection and surfactant desorption are the two key processes that regulate the interfacial flows, revealing that the dynamic response of the LC can provide rapid and potentially high throughput approaches to measurement of non-equilibrium interfacial properties of amphiphiles. We also observe flow-induced assemblies of microparticles to form at the LC interface, hinting at new non-equilibrium approaches to microparticle assembly. We conclude that dynamic states adopted by LCs in the presence of surfactant concentration gradients provide new opportunities for engineering complex fluids beyond equilibrium.

Hydrodynamic considerations for spring-driven autoinjector design

In recent years, significant progress has been made in the studies of the spring-driven autoinjector, leading to an improved understanding of this device and its interactions with tissue and therapeutic proteins. The development of simulation tools that have been validated against experiments has also enhanced the prediction of the performance of spring-driven autoinjectors. This paper aims to address critical hydrodynamic considerations that impact the design of spring-driven autoinjectors, with a specific emphasis on sloshing and cavitation. Additionally, we present a framework that integrates simulation tools to predict the performance of spring-driven autoinjectors and optimize their design. This work is valuable to the pharmaceutic industry, as it provides crucial insights into the development of spring-driven autoinjectors and therapeutic proteins. This work can also enhance the efficacy and safety of the delivery of therapeutic proteins, ultimately improving patient outcomes.

Non-equilibrium molecular simulations of thin film rupture

The retraction of thin films, as described by the Taylor-Culick (TC) theory, is subject to widespread debate, particularly for films at the nanoscale. We use non-equilibrium molecular dynamics simulations to explore the validity of the assumptions used in continuum models by tracking the evolution of holes in a film. By deriving a new mathematical form for the surface shape and considering a locally varying surface tension at the front of the retracting film, we reconcile the original theory with our simulation to recover a corrected TC speed valid at the nanoscale.

Pair dynamics of active force dipoles in an odd-viscous fluid

We discuss the lateral dynamics of two active force dipoles, which interact with each other via hydrodynamic interactions in a thin fluid layer that is active and chiral. The fluid layer is modeled as a two-dimensional (2D) compressible fluid with an odd viscosity, while the force dipole (representing an active protein or enzyme) induces a dipolar flow. Taking into account the momentum decay in the 2D fluid, we obtain analytically the mobility tensor that depends on the odd viscosity and includes nonreciprocal hydrodynamic interactions. We find that the particle pair shows spiral behavior due to the transverse flow induced by the odd viscosity. When the magnitude of the odd viscosity is large as compared with the shear viscosity, two types of oscillatory behaviors are seen. One of them can be understood as arising from closed orbits in dynamical systems, and its circular trajectories are determined by the ratio between the magnitude of the odd viscosity and the force dipole. In addition, the phase diagrams of the particle dipolar angles are obtained numerically. Our findings reveal that the nonreciprocal response leads to complex dynamics of active particles embedded in an active fluid with odd viscosity.

Air/Water Interface Rheology Probed by Thermal Capillary Waves

Atomic force microscopy (AFM) was used to study the interfacial rheology of air/water interfaces by investigating the thermal capillary fluctuations of surfactant-loaded interfaces. These interfaces are formed by depositing an air bubble on a solid substrate immersed in a surfactant (Triton X-100) solution. An AFM cantilever, in contact with the north pole of the bubble, probes its thermal fluctuations (amplitude of the vibration versus the frequency). The measured power spectral density of the nanoscale thermal fluctuations presents several resonance peaks corresponding to the different vibration modes of the bubble. The measured damping versus the surfactant concentration of each mode presents a maximum and then decreases to a saturation value. The measurements are in good agreement with the model developed by Levich for the damping of capillary waves in the presence of surfactants. Our results show that the AFM cantilever in contact with a bubble is a powerful tool to probe the rheological properties of air/water interfaces.

Optical Fingerprinting of Dynamic Interfacial Reaction Pathways Using Liquid Crystals

Reactions at interfaces between fluid phases are widely used to synthesize small molecules, polymers, and nanoparticles. In situ monitoring of the underlying dynamic reaction pathways remains challenging. Liquid crystals (LCs) have been used to detect simple chemical transformations at interfaces in situations where interface-bound reactants and products trigger distinct equilibrium orientations of LCs. However, whether or not LCs can be used to report complex reaction pathways via nonequilibrium states generated by reactions has not been explored. Here we explore this question using S_N2' nucleophilic substitution reactions that involve a synthetic amphiphile and a series of amine-based nucleophiles with one to four reaction sites. Although all reactants and products generate the same equilibrium LC orientation, we find that each nucleophile defines a distinct set of possible reaction pathways with a characteristic spatial and temporal LC optical response unique to the nucleophile. Additional experiments reveal that the nonequilibrium orientational states of the LCs arise from a combination of dynamic interfacial processes that include adsorption/desorption of reactants, the presence of reaction intermediates on the LC interface, and the generation of interfacial tension gradients (Marangoni stresses). Overall, our results reveal that the spatiotemporal optical outputs of LCs ("optical fingerprints") can be a rich source of information regarding interfacial reactions.

Effects of microplastics and surfactants on surface roughness of water waves

We study the flow physics underlying the recently developed remote sensing capability of detecting oceanic microplastics, which is based on the measurable surface roughness reduction induced by the presence of microplastics on the ocean surface. In particular, we are interested in whether this roughness reduction is caused by the microplastics as floating particles, or by surfactants which follow similar transport paths as microplastics. For this purpose, we experimentally test the effects of floating particles and surfactants on surface roughness, quantified by the mean square slope (MSS), with waves generated by a mechanical wave maker or by wind. For microplastics, we find that their effect on MSS critically depends on the surface area fraction of coverage. The damping by particles is observed only for fractions above O (5-10%), much higher than the realistic ocean condition. For surfactants, their damping effects on both mechanically generated waves and wind waves are quantified, which are shown to be much more significant than that by microplastics. Several new mechanisms/relations for roughness damping by surfactants are also identified. The implications of these experimental results to remote sensing are discussed.

Effect of interfacial rheology on fingering patterns in rotating Hele-Shaw cells

In rotating Hele-Shaw flows, centrifugal force acts, and the interface separating two viscous fluids becomes unstable, driven by the density difference between them. Complex interfacial structures develop where fingers of various shapes and sizes grow, and compete. These patterns have been well studied over the last few decades, analytically, numerically, and experimentally. However, one feature of the pattern-forming dynamics of much current interest has been underappreciated: the role of surface rheological stresses in the deformation, and time evolution of the fluid-fluid interface. In this paper, we employ a perturbative, second-order mode-coupling analysis to investigate how interfacial rheology effects influence centrifugally driven fingering phenomena, beyond the scope of linear stability theory. Describing the viscous Newtonian interface by using a Boussinesq-Scriven model, we derive a nonlinear differential equation that governs the early linear, and nonlinear time evolution of the system. In this framing, the most prevalent dynamical features of the patterns are described in terms of two dimensionless parameters: the viscosity contrast A (dimensionless viscosity difference between the fluids), and the Boussinesq number Bq which involves a ratio between interfacial and bulk viscosities. At the linear level, our results show that for a given A, surface rheological stresses dictated by Bq have a stabilizing role. Nevertheless, our weakly nonlinear findings reveal a more elaborate scenario in which the shape of the fingers, and their finger competition behavior result from the coupled influence of A and Bq. It is found that, although finger competition phenomena depend on the specific values of A and Bq, the fingers tend to widen as Bq is increased, regardless of the value of A.

A single parameter can predict surfactant impairment of superhydrophobic drag reduction

Recent experimental and computational investigations have shown that trace amounts of surfactants, unavoidable in practice, can critically impair the drag reduction of superhydrophobic surfaces (SHSs), by inducing Marangoni stresses at the air-liquid interface. However, predictive models for realistic SHS geometries do not yet exist, which has limited the understanding and mitigation of these adverse surfactant effects. To address this issue, we derive a model for laminar, three-dimensional flow over SHS gratings as a function of geometry and soluble surfactant properties, which together encompass 10 dimensionless groups. We establish that the grating length g is the key geometric parameter and predict that the ratio between actual and surfactant-free slip increases with g². Guided by our model, we perform synergistic numerical simulations and microfluidic experiments, finding good agreement with the theory as we vary surfactant type and SHS geometry. Our model also enables the estimation, based on velocity measurements, of a priori unknown properties of surfactants inherently present in microfluidic systems. For SHSs, we show that surfactant effects can be predicted by a single parameter, representing the ratio between the grating length and the interface length scale beyond which the flow mobilizes the air-water interface. This mobilization length is more sensitive to the surfactant chemistry than to its concentration, such that even trace-level contaminants may significantly increase drag if they are highly surface active. These findings advance the fundamental understanding of realistic interfacial flows and provide practical strategies to maximize superhydrophobic drag reduction.

Impact of interfacial rheology on finger tip splitting

Fluid-fluid interfaces, laden with polymers, surfactants, lipid bilayers, proteins, solid particles, or other surface-active agents, often exhibit a rheologically complex response to deformations. Despite its academic and practical relevance to fluid dynamics and various other fields of research, the role of interfacial rheology in viscous fingering remains fairly underexplored. A noteworthy exception is the work by Li and Manikantan [Phys. Rev. Fluids 6, 074001 (2021)2469-990X10.1103/PhysRevFluids.6.074001], who used linear stability analysis to show that surface rheological stresses act to stabilize the development of radial viscous fingering at the linear regime. In this paper, we perform a perturbative, second-order mode-coupling analysis of the system and investigate the influence of interfacial rheology on the morphology of the fingering structures at early nonlinear stages of the dynamics. In particular, we focus on understanding how interfacial rheology impacts the emblematic finger tip-widening and finger tip-splitting phenomena that take place in radial viscous fingering in Hele-Shaw cells. We describe the viscous Newtonian fluid-fluid interface by using a Boussinesq-Scriven model, and derive a generalized Young-Laplace pressure jump condition at the fluid-fluid interface. In this framing, we go beyond the purely linear description and use Darcy's law to obtain a perturbative mode-coupling differential equation which describes the time evolution of the perturbation amplitudes, accurate to second order. Our early nonlinear mode-coupling results indicate that regardless of their stabilizing action at the linear regime, interfacial rheology effects favor finger tip widening, leading to the occurrence of enhanced finger tip-splitting events.

Evaporation-driven liquid flow in sessile droplets

The evaporation of a sessile droplet spontaneously induces an internal capillary liquid flow. The surface-tension driven minimisation of surface area and/or surface-tension differences at the liquid-gas interface caused by evaporation-induced temperature or chemical gradients set the liquid into motion. This flow drags along suspended material and is one of the keys to control the material deposition in the stain that is left behind by a drying droplet. Applications of this principle range from the control of stain formation in the printing and coating industry, to the analysis of DNA, to forensic and medical research on blood stains, and to the use of evaporation-driven self-assembly for nanotechnology. Therefore, the evaporation of sessile droplets attracts an enormous interest from not only the fluid dynamics, but also the soft matter, chemistry, biology, engineering, nanotechnology and mathematics communities. As a consequence of this broad interest, knowledge on evaporation-driven flows in drying droplets has remained scattered among the different fields, leading to various misconceptions and misinterpretations. In this review we aim to unify these views, and reflect on the current understanding of evaporation-driven liquid flows in sessile droplets in the light of the most recent experimental and theoretical advances. In addition, we outline open questions and indicate promising directions for future research.

Evaporation of a Sessile Colloidal Water-Glycerol Droplet: Marangoni Ring Formation

The transport and aggregation of particles in suspensions is an important process in many physicochemical and industrial processes. In this work, we study the transport of particles in an evaporating binary droplet. Surprisingly, the accumulation of particles occurs not only at the contact line (due to the coffee-stain effect) or at the solid substrate (due to sedimentation) but also at a particular radial position near the liquid-air interface, forming a "ring", which we term as the Marangoni ring. The formation of this ring is primarily attributed to the solutal Marangoni flow triggered by the evaporation dynamics of the water-glycerol droplet. Experiments and simulations show fair agreement in the volume evolution and the general structure of the solutal Marangoni flow, that is, the Marangoni vortex. Experiments show that the location of the Marangoni ring is strongly correlated with the Marangoni vortex. However, finite element numerical simulations fail to describe the particle distribution seen in the experiments. Interestingly, the particles not only accumulate to form the Marangoni ring but also assemble as colloidal crystals close to the liquid-air interface, yielding iridescence. The formation of the colloidal crystals in the experiments is strong evidence that non-hydrodynamic interactions, which are not represented in the simulations, also play a significant role in our system.

Exact solutions for viscous Marangoni spreading

When surface-active molecules are released at a liquid interface, their spreading dynamics is controlled by Marangoni flows. Though such Marangoni spreading was investigated in different limits, exact solutions remain very few. Here we consider the spreading of an insoluble surfactant along the interface of a deep fluid layer. For two-dimensional Stokes flows, it was recently shown that the nonlinear transport problem can be exactly mapped to a complex Burgers equation [D. Crowdy, SIAM J. Appl. Math. 81, 2526 (2021)]SMJMAP0036-139910.1137/21M1400316. We first present a very simple derivation of this equation. We then provide fully explicit solutions and find that varying the initial surfactant distribution-pulse, hole, or periodic-results in distinct spreading behaviors. By obtaining the fundamental solution, we also discuss the influence of surface diffusion. We identify situations where spreading can be described as an effective diffusion process but observe that this approximation is not generally valid. Finally, the case of a three-dimensional flow with axial symmetry is briefly considered. Our findings should provide reference solutions for Marangoni spreading that may be tested experimentally with fluorescent or photoswitchable surfactants.

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces

Adsorption of surface-active molecules to fluid-fluid interfaces is ubiquitous in nature. Characterizing these interfaces requires measuring surfactant adsorption rates, evaluating equilibrium surface tensions as a function of bulk surfactant concentration, and relating how surface tension changes with changes in the interfacial area following equilibration. Simultaneous visualization of the interface using fluorescence imaging with a high-speed confocal microscope allows the direct evaluation of structure-function relationships. In the capillary pressure microtensiometer (CPM), a hemispherical air bubble is pinned at the end of the capillary in a 1 mL volume liquid reservoir. The capillary pressure across the bubble interface is controlled via a commercial microfluidic flow controller that allows for model-based pressure, bubble curvature, or bubble area control based on the Laplace equation. Compared to previous techniques such as the Langmuir trough and pendant drop, the measurement and control precision and response time are greatly enhanced; capillary pressure variations can be applied and controlled in milliseconds. The dynamic response of the bubble interface is visualized via a second optical lens as the bubble expands and contracts. The bubble contour is fit to a circular profile to determine the bubble curvature radius, R, as well as any deviations from circularity that would invalidate the results. The Laplace equation is used to determine the dynamic surface tension of the interface. Following equilibration, small pressure oscillations can be imposed by the computer-controlled microfluidic pump to oscillate the bubble radius (frequencies of 0.001-100 cycles/min) to determine the dilatational modulus The overall dimensions of the system are sufficiently small that the microtensiometer fits under the lens of a high-speed confocal microscope allowing fluorescently tagged chemical species to be quantitatively tracked with submicron lateral resolution.

Advances in antibubble formation and potential applications

Antibubbles are unusual physical objects consisting of a liquid core(s) surrounded by a thin air film/shell while in a bulk liquid. Antibubbles carry two air-liquid interfaces, i.e., one with the inner liquid and the other with the outer liquid. The distinct structure of antibubbles makes them quite attractive for drug and therapeutic delivery, although their potential applications have not been realized so far. The major challenge in this regard is a short-lived span of antibubbles, which is usually in the order of a few minutes to a few hours based on the stabilization mechanism used. We present a critical overview of different techniques that can be used to generate antibubbles. This includes a more commonly applied conventional approach in which the air-film is created through surface entrapment when a liquid jet/drop falls on a bulk liquid. The other available options rely on entirely different mechanisms for antibubble formation, for instance, through drop encapsulation by a submerged air bubble, or through evaporation/sublimation of volatile oil from a W/O/W double emulsion. Furthermore, the mechanisms of antibubble formation and collapse, and the factors affecting their stability have been discussed explicitly; and wherever required, the concept is correlated to other allied physical objects such as bubbles, liquid marbles, etc. Finally, the potential applications, research gaps in the existing knowledge, and some directions for future research are provided towards the end of this article.

Wall-Confined Spreading Dynamics on the Surface of Surfactant Solution

A liquid spreading over another is a universal physical process in the nature, which was investigated by the scaling law to reveal the underlying mechanical mechanism over the decades. However, scaling laws are restricted to piecewise physical stages, respectively. It is a challenge to present a full physical picture for a dynamic spreading process covering a wide-spectrum speed. We propose a general wall-confined spreading dynamics (WCSD) model originating from molecular kinetic theory (MKT). It creatively illustrates the order and domination between driving energy and energy dissipation (or transfer) using a phase diagram according to theory and experiments. This work reveals the deep mechanical mechanism of WCSD which provides an indirect guidance on the solution processing methods of two-dimensional molecular crystals (2DMCs) growth.

Particle Separation from Liquid Marbles by the Viscous Folding of Liquid Films

Particle separation from fluid interfaces is one of the major challenges due to the large capillary energy associated with particle adsorption. Previous approaches rely on physicochemical modification or tuning the electrostatic action. Here, we show experimentally that particle separation can be achieved by fast dynamics of drop impact on soap films. When a droplet wrapped with particles (liquid marble) collides with a soap film, it undergoes bouncing and coalescence, stripping and viscous separation, or tunneling through the film. Despite the violence of splashing events, the process robustly yields the stripping in a tunable range. This viscous separation is supported by the transfer front of dynamic contact among the film, particle crust, and drop and can be well controlled in a deterministic manner by selectable impact parameters. By extensive experiments, together with thermodynamic analysis, we disclose that the separation thresholds depend on the energy competition between the kinetic energy, the increased surface energy, and the viscous dissipation. The mechanical cracking of the particle crust arises from the complex coupling between interfacial stress and viscous forces. This study is of potential benefit in soft matter research and also permits the study of a drop with colloid and surface chemistry.

Spectral Properties of Foams and Emulsions

The optical and spectral properties of foams and emulsions provide information about their micro-/nanostructures, chemical and time stability and molecular data of their components. Foams and emulsions are collections of different kinds of bubbles or drops with particular properties. A summary of various surfactant and emulsifier types is performed here, as well as an overview of methods for producing foams and emulsions. Absorption, reflectance, and vibrational spectroscopy (Fourier Transform Infrared spectroscopy-FTIR, Raman spectroscopy) studies are detailed in connection with the spectral characterization techniques of colloidal systems. Diffusing Wave Spectroscopy (DWS) data for foams and emulsions are likewise introduced. The utility of spectroscopic approaches has grown as processing power and analysis capabilities have improved. In addition, lasers offer advantages due to the specific properties of the emitted beams which allow focusing on very small volumes and enable accurate, fast, and high spatial resolution sample characterization. Emulsions and foams provide exceptional sensitive bases for measuring low concentrations of molecules down to the level of traces using spectroscopy techniques, thus opening new horizons in microfluidics.

Flow profiles near receding three-phase contact lines: influence of surfactants

The dynamics of wetting and dewetting is largely determined by the velocity field near the contact lines. For water drops it has been observed that adding surfactant decreases the dynamic receding contact angle even at a concentration much lower than the critical micelle concentration (CMC). To better understand why surfactants have such a drastic effect on drop dynamics, we constructed a dedicated setup on an inverted microscope, in which an aqueous drop is held stationary while the transparent substrate is moved horizontally. Using astigmatism particle tracking velocimetry, we track the 3D displacement of the tracer particles in the flow. We study how surfactants alter the flow dynamics near the receding contact line of a moving drop for capillary numbers in the order of 10^-6. Even for surfactant concentrations c far below the critical micelle concentration (c ≪ CMC) Marangoni stresses change the flow drastically. We discuss our results first in a 2D model that considers advective and diffusive surfactant transport and deduce estimates of the magnitude and scaling of the Marangoni stress from this. Modeling and experiment agree that a tiny gradient in surface tension of a few μN m^-1 is enough to alter the flow profile significantly. The variation of the Marangoni stress with the distance from the contact line suggests that the 2D advection-diffusion model has to be extended to a full 3D model. The effect is ubiquitous, since surfactant is present in many technical and natural dewetting processes either deliberately or as contamination.

A two-step strategy for delivering particles to targets hidden within microfabricated porous media

The delivery of small particles into porous environments remains highly challenging because of the low permeability to the fluids that carry these colloids. Even more challenging is that the specific location of targets in the porous environment usually is not known and cannot be determined from the outside. Here, we demonstrate a two-step strategy to deliver suspended colloids to targets that are "hidden" within closed porous media. The first step serves to automatically convert any hidden targets into soluto-inertial "beacons," capable of sustaining long-lived solute outfluxes. The second step introduces the deliverable objects, which are designed to autonomously migrate against the solute fluxes emitted by the targets, thereby following chemical trails that lead to the target. Experimental and theoretical demonstrations of the strategy lay out the design elements required for the solute and the deliverable objects, suggesting routes to delivering colloidal objects to hidden targets in various environments and technologies.

Gas cell stabilization by aqueous-phase constituents during bread production from wheat and rye dough and oat batter: Dough or batter liquor as model system

Proper gas cell stability during fermentation and baking is essential to obtain high-quality bread. Gas cells in wheat dough are stabilized by the gluten network formed during kneading and, from the moment this network locally ruptures, by liquid films containing nonstarch polysaccharides (NSPs) and surface-active proteins and lipids. Dough liquor (DL), the supernatant after ultracentrifugation of dough, is a model system for these liquid films and has been extensively studied mostly in the context of wheat bread making. Nonwheat breads are often of lower quality (loaf volume and crumb structure) than wheat breads because their doughs/batters lack a viscoelastic wheat gluten network. Therefore, gas cell stabilization by liquid film constituents may be more important in nonwheat than in wheat bread making. This manuscript aims to review the knowledge on DL/batter liquor (BL) and its relevance for studying gas cell stabilization in wheat and nonwheat (rye and oat) bread making. To this end, the unit operations in wheat, rye, and oat bread making are described with emphasis on gas incorporation and gas cell (de)stabilization. A discussion of the knowledge on the recoveries and chemical structures of proteins, lipids, and NSPs in DLs/BLs is provided and key findings of studies dealing with foaming and air-water interfacial properties of DL/BL are discussed. Next, the extent to which DL/BL functionality can be related to bread properties is addressed. Finally, the extent to which DL/BL is a representative model system for the aqueous phase of dough/batter is discussed and related to knowledge gaps and further research opportunities.

Coupling Vortical Bulk Flows to the Air–Water Interface: From Putting Oil on Troubled Waters to Surfactants on Protein Solutions

The air–water interface in flowing systems remains a challenge to model, even in cases where the interface is essentially flat. This is because even though each side is governed by the Navier–Stokes equations, the stress balance which provides the boundary conditions for the equations involves properties associated with surfactants that are inevitably present at the air–water interface. Aside from challenges in measuring interfacial properties, either intrinsic or flow-dependent, the two-way coupling of bulk and interfacial flows is non-trivial, even for very simple flow geometries. Here, we present an overview of the physics associated with surfactant monolayers of flowing liquid and describe how the monolayer affects the bulk flow and how the monolayer is transported and deformed by the bulk flow. The emphasis is primarily on cylindrical flow geometries, and both Newtonian and non-Newtonian interfacial responses are considered. We consider interfacial flows that are solenoidal as well as those where the surface velocity is not divergence free.

Using Liquid Crystals for In Situ Optical Mapping of Interfacial Mobility and Surfactant Concentrations at Flowing Aqueous-Oil Interfaces

Flow-induced states of fluid interfaces decorated with amphiphiles underlie phenomena such as emulsification, foaming, and spreading. While past studies have shown that interfacial mass transfer, the kinetics of surfactant adsorption and desorption, interfacial mobility, and surfactant reorganization regulate the dynamic properties of surfactant-laden interfaces, few simple methods permit simultaneous monitoring of this interplay. Here, we explore the optical responses of micrometer-thick films of oils (4-cyano-4'-pentylbiphenyl, 5CB) with a liquid crystalline order in contact with flowing aqueous phases of soluble [e.g., sodium dodecyl sulfate (SDS)] or insoluble (e.g., 1,2-dilauroyl-sn-glycero-3-phosphocholine) amphiphiles. We observe the onset of flow of 0.5 mM SDS solutions within a millifluidic channel (area-average velocity of 200 mm/s) to transform a liquid crystal (LC) film with an alignment along the interface normal into a bright birefringent state (average LC tilt angle of 30°), consistent with an initially mobile interface that shears and thus tilts the LC along the flow direction. Subsequently, we observed the LC film to evolve to a steady state (over ∼10 s) with position-dependent optical retardance controlled by gradients in surfactant concentration and thus Marangoni stresses. For 0.5 mM SDS solutions, by using particle tracking and a simple hydrodynamic model, we reveal that the dominant role of the flow-induced interfacial surfactant concentration gradient is to change the mobility of the interface (and thus shear rate of LC) and not to change the easy axis (equilibrium orientation) or anchoring energy (orientation-dependent interfacial energy) of the LC. At lower surfactant concentrations (0.015 mM SDS), however, we show that the LC directly maps flow-induced interfacial surfactant concentration gradients via a change in the local easy axis of the LC. When combined with additional measurements obtained with simple salts and insoluble amphiphiles, these results hint that LC oils may offer the basis of general and facile methods that permit mapping of both interfacial mobilities and surfactant distributions at flowing interfaces.

Dilatational rheology of water-in-diesel fuel interfaces: effect of surfactant concentration and bulk-to-interface exchange

Micrometer-sized water droplets dispersed in diesel fuel are stabilized by the fuel's surface-active additives, such as mono-olein and poly(isobutylene)succinimide (PIBSI), making the droplets challenging for coalescing filters to separate. Dynamic material properties found from interfacial rheology are known to influence the behavior of microscale droplets in coalescing filters. In this work, we study the interfacial dilatational properties of water-in-fuel interfaces laden with mono-olein and PIBSI, with a fuel phase of clay-treated ultra-low sulphur diesel (CT ULSD). First, the dynamic interfacial tension (IFT) is measured using pendant drop tensiometry, and a curvature-dependent form of the Ward and Tordai diffusion equation is applied for extracting the diffusivity of the surfactants. Additionally, Langmuir kinetics are applied to the dynamic IFT results to obtain the maximum surface concentration (Γ∞) and ratio of adsorption to desorption rate constants (κ). We then use a capillary pressure microtensiometer to measure the interfacial dilatational modulus, and further extract the characteristic frequency of surfactant exchange (ω0) by fitting a model assuming diffusive exchange between the interface and bulk. In this measurement, 50-100 μm diameter water droplets are pinned at the tip of a glass capillary in contact with the surfactant-containing fuel phase, and small amplitude capillary pressure oscillations over a range of frequencies from 0.45-20 rad s-1 are applied to the interface, inducing changes in interfacial tension and area to yield the dilatational modulus, E*(ω). Over the range of concentrations studied, the dilatational modulus of CT ULSD with either mono-olein or PIBSI increases with a decrease in bulk concentration and plateaus at the lowest concentrations of mono-olein. Characteristic frequency (ω0) values extracted from the fit are compared with those calculated using equilibrium surfactant parameters (κ and Γ∞) derived from pendant drop tensiometry, and good agreement is found between these values. Importantly, the results imply that diffusive exchange models based on the equilibrium relationships between surfactant concentration and interfacial tension can be used to infer the dynamic dilatational behavior of complex surfactant systems, such as the water-in-diesel fuel interfaces in this study.

Nonreciprocal response of a two-dimensional fluid with odd viscosity

We discuss the linear hydrodynamic response of a two-dimensional active chiral compressible fluid with odd viscosity. The viscosity coefficient represents broken time-reversal and parity symmetries in the 2D fluid and characterizes the deviation of the system from a passive fluid. Taking into account the hydrodynamic coupling to the underlying bulk fluid, we obtain the odd viscosity-dependent mobility tensor, which is responsible for the nonreciprocal hydrodynamic response to a point force. Furthermore, we consider a finite-size disk moving laterally in the 2D fluid and demonstrate that the disk experiences a nondissipative lift force in addition to the dissipative drag one.

Motion of Particles in a Monolayer Induced by Coalescing of a Bubble with a Planar Air-Water Interface

The motion of particles in a monolayer induced by the coalescing of a bare bubble with a planar air-water interface was investigated in a modified Langmuir trough. Experiments were performed to understand the effect of particle hydrophobicity, subphase pH, packing density, the presence of a weak surfactant, and particle size distribution on the behavior of particle movement in the monolayer during the coalescence process. Video tracking software was used to track the particles and extract data based on the video footage. Visual inspection indicated that the coalescence of the bubble with the monolayer was a chaotic process which led the interface to oscillate to an extent that the particles underwent complete rearrangement. A simple analysis was carried out on the main forces involved in particle motion and rearrangement at the oscillating air-water interface. The motion characteristic of particles was evaluated by speed and mean-square displacement (MSD). The results showed that the butanol-treated particles had higher speed and MSD than the particles with a stronger affinity to the air-water interface. Similar results were also found at high subphase pH and low packing factor.

Tunable Collective Dynamics of Active Inclusions in Viscous Membranes

We study hydrodynamic interactions and clustering mechanisms of active membrane inclusions within lipid bilayers. Pairs of inclusions display unique oscillatory dynamics that disappear when the 3D fluid adjacent to the membrane is confined. We reduce the governing equations to a coupled dynamical system whose phase behavior reveals the striking role of bulk confinement in enhancing cluster formation within the membrane. Using numerical simulations, we then extend this finding to demonstrate the role of confinement in controlling large-scale aggregation of membrane inclusions.

Phase-Dependent Surfactant Transport on the Microscale: Interfacial Tension and Droplet Coalescence

Liquid-liquid emulsion systems are usually stabilized by additives, known as surfactants, which can be observed in various environments and applications such as oily bilgewater, water-entrained diesel fuel, oil production, food processing, cosmetics, and pharmaceuticals. One important factor that stabilizes emulsions is the lowered interfacial tension (IFT) between the fluid phases due to surfactants, inhibiting the coalescence. Many studies have investigated the surfactant transport behavior that leads to corresponding time-dependent lowering of the IFT. For example, the rate of IFT decay depends on the phase in which the surfactant is added (dispersed vs continuous) due in part to differences in the near-surface depletion depth. Other key factors, such as the viscosity ratio between the dispersed and continuous phases and Marangoni stress, will also have an impact on surfactant transport and therefore the coalescence and emulsion stability. In this feature article, the measurement techniques for dynamic IFT are first reviewed due to their importance in characterizing surfactant transport, with a specific focus on macroscale versus microscale techniques. Next, equilibrium isotherm models as well as dynamic diffusion and kinetic equations are discussed to characterize the surfactant and the time scale of the surfactant transport. Furthermore, recent studies are highlighted showing the different IFT decay rates and its long-time equilibrium value depending on the phase into which the surfactant is added, particularly on the microscale. Finally, recent experiments using a hydrodynamic Stokes trap to investigate the impact of interfacial surfactant transport, or "mobility", and the phase containing the surfactant on film drainage and droplet coalescence will be presented.

Evaporation-Induced Crystallization of Surfactants in Sessile Multicomponent Droplets

Surfactants have been widely studied and used in controlling droplet evaporation. In this work, we observe and study the crystallization of sodium dodecyl sulfate (SDS) within an evaporating glycerol-water mixture droplet. The crystallization is induced by the preferential evaporation of water, which decreases the solubility of SDS in the mixture. As a consequence, the crystals shield the droplet surface and cease the evaporation. The universality of the evaporation characteristics for a range of droplet sizes is revealed by applying a diffusion model, extended by Raoult's law. To describe the nucleation and growth of the crystals, we employ the 2-dimensional crystallization model of Weinberg [J. Non-Cryst. Solids 1991, 134, 116]. The results of this model compare favorably to our experimental results. Our findings may inspire the community to reconsider the role of high concentration of surfactants in a multicomponent evaporation system.