Chemistry, applications, and future prospects of structured liquids

Structured liquids are emerging functional soft materials that combine liquid flowability with solid-like structural stability and spatial organization. Here, we delve into the chemistry and underlying principles of structured liquids, ranging from nanoparticle surfactants (NPSs) to supramolecular assemblies and interfacial jamming. We then highlight recent advancements related to the design of intricate all-liquid 3D structures and examine their reconfigurability. Additionally, we demonstrate the versatility of these soft functional materials through innovative applications, such as all-liquid microfluidic devices and liquid microreactors. We envision that in the future, the vast potential of the liquid-liquid interface combined with human creativity will pave the way for innovative platforms, exemplified by current developments like liquid batteries and circuits. Although still in its nascent stages, the field of structured liquids holds immense promise, with future applications across various sectors poised to harness their transformative capabilities.

Wimpled thin films via multiple motions of a bubble decorated with surface-active molecules

HYPOTHESIS

Thin liquid films play a crucial role in various systems and applications. Understanding the mechanisms that regulate their morphology is a scientific challenge with obvious implications for application optimization. Thin liquid films trapped between bubbles and air-liquid interface can show various configurations influenced by their deformation history and system characteristics.

EXPERIMENTS

The morphology of thin liquid films formed in the presence of surface-active molecules is here studied with interferometric techniques. Three different systems with varying interfacial properties are investigated to understand their influence on film morphology. Specific deformation histories are applied to the films to generate complex film structures.

FINDINGS

We achieve the creation of a rather stable wimple by implementing controlled bubble motions against the air-liquid interface. We provide a criterion for wimple formation based on lubrication theory. The long-term stability of the wimple is also investigated, and more complex multi-wimple structures are experimentally produced building upon the achieved wimple stability.

Strong Elastic Protein Nanosheets Enable the Culture and Differentiation of Induced Pluripotent Stem Cells on Microdroplets

Advances in stem cell technologies, revolutionizing regenerative therapies and advanced in vitro testing, require novel cell manufacturing pipelines able to cope with scale up and parallelization. Microdroplet technologies, which have transformed single cell sequencing and other cell-based assays, are attractive in this context, but the inherent soft mechanics of liquid-liquid interfaces is typically thought to be incompatible with the expansion of induced pluripotent stem cells (iPSCs), and their differentiation. In this work, the design of protein nanosheets stabilizing liquid-liquid interfaces and enabling the adhesion, expansion and retention of stemness by iPSCs is reported. Microdroplet microfluidic chips are used to control the formulation of droplets with defined dimensions and size distributions. The resulting emulsions sustain high expansion rates, with excellent retention of stem cell marker expression. iPSCs cultured in such conditions retain the capacity to differentiate into cardiomyocytes. This work provides clear evidence that local nanoscale mechanics, associated with interfacial viscoelasticity, provides strong cues able to regulate and maintain pluripotency, as well as to support commitment in defined differentiation conditions. Microdroplet technologies appear as attractive candidates to transform cell manufacturing pipelines, bypassing significant hurdles paused by solid substrates and microcarriers.

From a distance: Shuttleworth revisited

The Shuttleworth equation: a linear stress-strain relation ubiquitously used in modeling the behavior of soft surfaces. Its validity in the realm of materials subject to large deformation is a topic of current debate. Here, we allow for large deformation by deriving the constitutive behavior of the surface from the general framework of finite kinematics. We distinguish cases of finite and infinitesimal surface relaxation preceding an infinitesimal applied deformation. The Shuttleworth equation identifies as the Cauchy stress measure in the fully linearized setting. We show that both in finite and linearized cases, measured elastic constants depend on the utilized stress measure. In addition, we discuss the physical implications of our results and analyze the impact of surface relaxation on the estimation of surface elastic moduli in the light of two different test cases.

Fluid Ejections in Nature

From microscopic fungi to colossal whales, fluid ejections are universal and intricate phenomena in biology, serving vital functions such as animal excretion, venom spraying, prey hunting, spore dispersal, and plant guttation. This review delves into the complex fluid physics of ejections across various scales, exploring both muscle-powered active systems and passive mechanisms driven by gravity or osmosis. It introduces a framework using dimensionless numbers to delineate transitions from dripping to jetting and elucidate the governing forces. Highlighting the understudied area of complex fluid ejections, this review not only rationalizes the biophysics involved but also uncovers potential engineering applications in soft robotics, additive manufacturing, and drug delivery. By bridging biomechanics, the physics of living systems, and fluid dynamics, this review offers valuable insights into the diverse world of fluid ejections and paves the way for future bioinspired research across the spectrum of life.

Analytical description of elastocapillary membranes held by needles

Fluid objects bounded by elastocapillary membranes display intriguing physical properties due to the interplay of capillary and elastic stresses arising upon deformation. Increasingly exploited in foam or emulsion science, the mechanical properties of elastocapillary membranes are commonly characterised by the shape analysis of inflating/deflating bubbles or drops held by circular needles. These impose complex constraints on the membrane deformation, requiring the shape analysis to be done using elaborate numerical fitting procedures of the shape equations. While this approach has proven quite reliable, it obscures insight into the underlying physics of the problem. We therefore propose here the first fully theoretical approach to this problem using the elastic theory for a membrane with additive contributions of capillary and Hookean-type elastic stresses. We exploit this theory to discuss some of the key features of the predicted pressure-deformation relations. Interestingly, we highlight a breakdown of the quadratic approximation at a well-defined value of the elastocapillary parameter depending on the shape of the reference state, which is regularized by the non-quadratic terms. Additionally, we provide an analytical relationship which allows experimentalists to obtain the elastocapillary properties of a membrane by simple measurement of the height and the width of a deformed bubble (or a drop).

Interfacial mechanics of β-casein and albumin mixed protein assemblies at liquid-liquid interfaces

Protein emulsifiers play an important role in formulation science, from food product development to emerging applications in biotechnologies. The impact of mixed protein assemblies on surface composition and interfacial shear mechanics remains broadly unexplored, in comparison to the impact that formulation has on dilatational mechanics and surface tension or pressure. In this report, we use interfacial shear rheology to quantify the evolution of interfacial shear moduli as a function of composition in bovine serum albumin (BSA)/β-casein mixed assemblies. We present the pronounced difference in mechanics of these two protein, at oil interfaces, and observe the dominance of β-casein in regulating interfacial shear mechanics. This observation correlates well with the strong asymmetry of adsorption of these two proteins, characterised by fluorescence microscopy. Using neutron reflectometry and fluorescence recovery after photobleaching, we examine the architecture of corresponding protein assemblies and their surface diffusion, providing evidence for distinct morphologies, but surprisingly comparable diffusion profiles. Finally, we explore the impact of crosslinking and sequential protein adsorption on the interfacial shear mechanics of corresponding assemblies. Overall, this work indicates that, despite comparable surface densities, BSA and β-casein assemblies at liquid-liquid interfaces display almost 2 orders of magnitude difference in interfacial shear storage modulus and markedly different viscoelastic profiles. In addition, co-adsorption and sequential adsorption processes are found to further modulate interfacial shear mechanics. Beyond formulation science, the understanding of complex mixed protein assemblies and mechanics may have implications for the stability of emulsions and may underpin changes in the mechanical strength of corresponding interfaces, for example in tissue culture or in physiological conditions.

An Open-Source Membrane Stretcher for Simultaneous Mechanical and Structural Characterizations of Soft Materials and Biological Tissues

The ability to simultaneously measure material mechanics and structure is central for understanding their nonlinear relationship that underlies the mechanical properties of materials, such as hysteresis, strain-stiffening and -softening, and plasticity. This experimental capability is also critical in biomechanics and mechanobiology research, as it enables direct characterizations of the intricate interplay between cellular responses and tissue mechanics. Stretching devices developed over the past few decades, however, do not often allow simultaneous measurements of the structural and mechanical responses of the sample. In this work, we introduce an open-source stretching system that can apply uniaxial strain at a submicron resolution, report the tensile force response of the sample, and be mounted on an inverted microscope for real-time imaging. Our system consists of a pair of stepper-based linear motors that stretch the sample symmetrically, a force transducer that records the sample tensile force, and an optically clear sample holder that allows for high-magnification microscopy. Using polymer samples and cellular specimens, we characterized the motion control accuracy, force measurement robustness, and microscopy compatibility of our stretching system. We envision that this uniaxial stretching system will be a valuable tool for characterizing soft and living materials.

Viscoelasticity of a carbon nanotube-laden air-water interface

The viscoelasticity of a carbon nanotube (CNT)-laden air-water interface was characterized using two different experimental methods. The first experimental method used a Langmuir-Pockels (LP) trough coupled with a pair of oscillating barriers. The second method is termed the Bicone-Trough (BT) method, where a LP trough was custom-built and fit onto a rheometer equipped with a bicone fixture to standardize the preparation and conditioning of a particle-laden interface especially at high particle coverages. The performance of both methods was evaluated by performing Fast Fourier Transform (FFT) analysis to calculate the signal-to-noise ratios (SNR). Overall, the rheometer-based BT method offered better strain control and considerably higher SNRs compared to the Oscillatory Barriers (OB) method that oscillated barriers with relatively limited positional and speed control. For a CNT surface coverage of 165 mg/m2 and a frequency of 100 mHz, the interfacial shear modulus obtained from the OB method increased from 39 to 57 mN/m as the normal strain amplitude increased from 1 to 3%. No linear viscoelastic regime was experimentally observed for a normal strain as small as 0.5%. In the BT method, a linear regime was observed below a shear strain of 0.1%. The interfacial shear modulus decreased significantly from 96 to 2 mN/m as the shear strain amplitude increased from 0.025 to 10%.

Non-Stick Length of Polymer-Polymer Interfaces under Small-Amplitude Oscillatory Shear Measurement

Interfaces in soft materials often exhibit deviation from non-slip/stick response and play a determining role in the rheological response of the overall system. We discuss detection techniques for the excess interface rheology using small-amplitude oscillatory shear (SAOS) measurements. A stacked bilayer of different polymers is sheared parallel to the interface and the dynamic shear response is measured. Deviation of the bilayer shear modulus from the superposition of the shear moduli of the component layers is analysed. Furthermore, we introduce a frequency-dependent non-stick length based on the bilayer SAOS response to characterize the excess interface rheology. We observe an approximate stick response in the interface in bilayers composed of the chemically same monomer as well as an apparent slip in the interface between immiscible polymers. The results suggest that the proposed non-stick length in SAOS is capable of detecting the apparent interfacial slip. The non-stick length in SAOS is readily applicable to other complex interfaces of different soft materials and offers a convenient tool to characterize the excess interface rheology.

Engineering Nano/Microscale Chiral Self-Assembly in 3D Printed Constructs

Helical hierarchy found in biomolecules like cellulose, chitin, and collagen underpins the remarkable mechanical strength and vibrant colors observed in living organisms. This study advances the integration of helical/chiral assembly and 3D printing technology, providing precise spatial control over chiral nano/microstructures of rod-shaped colloidal nanoparticles in intricate geometries. We designed reactive chiral inks based on cellulose nanocrystal (CNC) suspensions and acrylamide monomers, enabling the chiral assembly at nano/microscale, beyond the resolution seen in printed materials. We employed a range of complementary techniques including Orthogonal Superposition rheometry and in situ rheo-optic measurements under steady shear rate conditions. These techniques help us to understand the nature of the nonlinear flow behavior of the chiral inks, and directly probe the flow-induced microstructural dynamics and phase transitions at constant shear rates, as well as their post-flow relaxation. Furthermore, we analyzed the photo-curing process to identify key parameters affecting gelation kinetics and structural integrity of the printed object within the supporting bath. These insights into the interplay between the chiral inks self-assembly dynamics, 3D printing flow kinematics and photo-polymerization kinetics provide a roadmap to direct the out-of-equilibrium arrangement of CNC particles in the 3D printed filaments, ranging from uniform nematic to 3D concentric chiral structures with controlled pitch length, as well as random orientation of chiral domains. Our biomimetic approach can pave the way for the creation of materials with superior mechanical properties or programable photonic responses that arise from 3D nano/microstructure and can be translated into larger scale 3D printed designs.

Model aggregated 2D suspensions in shear and compression: From a fluid layer to an auxetic interface?

HYPOTHESIS

Particle-laden interfaces play a crucial role in engineering stability of multiphase systems. However, a full understanding of the mechanical properties in shear and compression, especially in relation to the underlying microstructural changes, is as yet lacking. In this study, we investigate the interfacial rheological moduli in heterogeneous networks of aggregated 2D suspensions using different deformation modes and relate these moduli to changes in the microstructure.

EXPERIMENTS

Interfacial rheological experiments were conducted at different surface coverages and clean kinematic conditions, namely in (i) simple shear flow in a modified double wall-ring geometry and (ii) isotropic compression in a custom-built radial trough, while monitoring the evolution of the microstructure.

FINDINGS

The compressive moduli increase non-monotonically with decreasing void fraction, reflecting the combined effect of aggregate densification and reduction of void structures, with rotation of rigid clusters playing a significant role in closing voids. However, the shear moduli increase monotonically, which correlates with the increase in fractal dimension of the aggregates making up the backbone network. We also observe that these interfaces act as 2D auxetic materials at intermediate coverages, which is surprising given their amorphous structure. This finding has potential implications for the resilience of particle-coated bubbles or droplets subjected to time-varying compression-expansion deformations.

A new instrument for interfacial dilational rheology

We present a new design for an interfacial dilational rheometer that can generate oscillatory dilational strain on a planar air-liquid interface. The strain is generated by a pneumatic mechanism involving a deformable film, which forms a circular barrier that can contract or expand under different pressures. The interfacial stress is measured using a Wilhelmy rod. We carefully examine and demonstrate the effects of potential sources of measurement error, including inertia, drag, buoyancy, flow from the bulk phase, and surface waves. The design avoids mixed deformations present in other instruments and is currently capable of accurate measurements at frequencies up to ∼0.1 Hz and dilational strains below 0.001, with potential for higher frequencies after further theoretical development. We demonstrate the integration of the interfacial dilational rheometer with a Langmuir trough by measuring the compression isotherm of an insoluble surfactant, stearic acid. Furthermore, we verify the capability of the interfacial dilational rheometer to perform frequency and amplitude sweeps and present the storage and loss moduli for a water-soluble surfactant, sodium dodecylbenzenesulfonate, at different concentrations.

Segregation of fluids with polymer additives at domain interfaces: a dissipative particle dynamics study

This paper investigates the phase separation kinetics of ternary fluid mixtures composed of a polymeric component (C) and two simple fluids (A and B) using dissipative particle dynamics simulations with a system dimensionality of d = 3. We model the affinities between the components to enable the settling of the polymeric component at the interface of fluids A and B. Thus, the system evolves to form polymer coated morphologies, enabling alteration of the fluids' interfacial properties. This manipulation can be utilized across various disciplines, such as the stabilization of emulsions and foams, rheological control, biomimetic design, and surface modification. We probe the effects of various parameters, such as the polymeric concentration, chain stiffness, and length, on the phase separation kinetics of the system. The simulation results show that changes in the concentration of flexible polymers exhibit perfect dynamic scaling for coated morphologies. The growth rate decreases as the polymeric composition is increased due to reduced surface tension and restricted connectivity between A- and B-rich clusters. Variations in the polymer chain rigidity at fixed composition ratios and degrees of polymerization slow the evolution kinetics of AB fluids marginally, although the effect is more pronounced for perfectly rigid chains. Whereas flexible polymer chain lengths at fixed composition ratios slow down the segregation kinetics of AB fluids slightly, varying the chain lengths of perfectly rigid polymers leads to a significant deviation in the length scale and dynamic scaling for the evolved coated morphologies. The characteristic length scale follows a power-law growth with a growth exponent ϕ that shows a crossover from the viscous to the inertial hydrodynamic regime, where the values of ϕ depend on the constraints imposed on the system.

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.

Programmed Self-Assembly of DNA Nanosheets with Discrete Single-Molecule Thickness and Interfacial Mechanics: Design, Simulation, and Characterization

DNA is programmed to hierarchically self-assemble into superstructures spanning from nanometer to micrometer scales. Here, we demonstrate DNA nanosheets assembled out of a rationally designed flexible DNA unit (F-unit), whose shape resembles a Feynman diagram. F-units were designed to self-assemble in two dimensions and to display a high DNA density of hydrophobic moieties. oxDNA simulations confirmed the planarity of the F-unit. DNA nanosheets with a thickness of a single DNA duplex layer and with large coverage (at least 30 μm × 30 μm) were assembled from the liquid phase at the solid/liquid interface, as unambiguously evidenced by atomic force microscopy imaging. Interestingly, single-layer nanodiscs formed in solution at low DNA concentrations. DNA nanosheet superstructures were further assembled at liquid/liquid interfaces, as demonstrated by the fluorescence of a double-stranded DNA intercalator. Moreover, the interfacial mechanical properties of the nanosheet superstructures were measured as a response to temperature changes, demonstrating the control of interfacial shear mechanics based on DNA nanostructure engineering. The rational design of the F-unit, along with the presented results, provide an avenue toward the controlled assembly of reconfigurable/responsive nanosheets and membranes at liquid/liquid interfaces, to be potentially used in the characterization of biomechanical processes and materials transport.

Associative Liquid-In-Liquid 3D Printing Techniques for Freeform Fabrication of Soft Matter

Shaping soft materials into prescribed 3D complex designs has been challenging yet feasible using various 3D printing technologies. For a broader range of soft matters to be printable, liquid-in-liquid 3D printing techniques have emerged in which an ink phase is printed into 3D constructs within a bath. Most of the attention in this field has been focused on using a support bath with favorable rheology (i.e., shear-thinning behavior) which limits the selection of materials, impeding the broad application of such techniques. However, a growing body of work has begun to leverage the interaction or association of the two involved phases (specifically at the liquid-liquid interface) to fabricate complex constructs from a myriad of soft materials with practical structural, mechanical, optical, magnetic, and communicative properties. This review article has provided an overview of the studies on such associative liquid-in-liquid 3D printing techniques along with their fundamentals, underlying mechanisms, various characterization techniques used for ensuring the structural stability, and practical properties of prints. Also, the future paths with the potential applications 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.

Mesenchymal Stem Cells Sense the Toughness of Nanomaterials and Interfaces

Stem cells are known to sense and respond to the mechanical properties of biomaterials. In turn, cells exert forces on their environment that can lead to striking changes in shape, size and contraction of associated tissues, and may result in mechanical disruption and functional failure. However, no study has so far correlated stem cell phenotype and biomaterials toughness. Indeed, disentangling toughness-mediated cell response from other mechanosensing processes has remained elusive as it is particularly challenging to uncouple Youngs' or shear moduli from toughness, within a range relevant to cell-generated forces. In this report, it is shown how the design of the macromolecular architecture of polymer nanosheets regulates interfacial toughness, independently of interfacial shear storage modulus, and how this controls the expansion of mesenchymal stem cells at liquid interfaces. The viscoelasticity and toughness of poly(l-lysine) nanosheets assembled at liquid-liquid interfaces is characterised via interfacial shear rheology. The local (microscale) mechanics of nanosheets are characterised via magnetic tweezer-assisted interfacial microrheology and the thickness of these assemblies is determined from in situ ellipsometry. Finally, the response of mesenchymal stem cells to adhesion and culture at corresponding interfaces is investigated via immunostaining and confocal microscopy.

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.

Dilatational and shear rheology of soluble and insoluble monolayers with a Langmuir trough

HYPOTHESIS

The surface dilatational and shear moduli of surfactant and protein interfacial layers can be derived from surface pressures measured with a Wilhelmy plate parallel, ΔΠpar and perpendicular ΔΠperp to the barriers in a Langmuir trough.

EXPERIMENTAL

Applying area oscillations, A0+ ΔAeiωt, in a rectangular Langmuir trough induces changes in surface pressure, ΔΠpar and ΔΠperp for monolayers of soluble palmitoyl-lysophosphatidylcholine (LysoPC), insoluble dipalmitoylphosphatidylcholine (DPPC), and the protein β-lactoglobulin to evaluate Es∗+Gs∗=A0ΔΠparΔA and Es∗-Gs∗=A0ΔΠperpΔA. Gs∗ was independently measured with a double-wall ring apparatus (DWR) and Es∗ by area oscillations of hemispherical bubbles in a capillary pressure microtensiometer (CPM) and the results were compared to the trough measurements.

FINDINGS

For LysoPC and DPPC, A0ΔΠparΔA≅A0ΔΠperpΔA meaning Es∗≫Gs∗ and Es∗≅A0ΔΠparΔA≅A0ΔΠperpΔA. Trough values for Es∗ were quantitatively similar to CPM when corrected for interfacial curvature. DWR showed G∗ was 4 orders of magnitude smaller than Es∗ for both LysoPC and DPPC. For β-lactoglobulin films, A0ΔΠparΔA>A0ΔΠperpΔA and Es∗ and Gs∗ were in qualitative agreement with independent CPM and DWR measurements. For β-lactoglobulin, both Es∗ and Gs∗ varied with film age and history on the trough, suggesting the evolution of the protein structure.

Activation energy and force fields during topological transitions of fluid lipid vesicles

Topological transitions of fluid lipid membranes are fundamental processes for cell life. For example, they are required for endo- and exocytosis or to enable neurotransmitters to cross the neural synapses. Here, inspired by the idea that fusion and fission proteins could have evolved in Nature in order to carry out a minimal work expenditure, we evaluate the minimal free energy pathway for the transition between two spherical large unilamellar vesicles and a dumbbell-shaped one. To address the problem, we propose and successfully use a Ginzburg-Landau type of free energy, which allows us to uniquely describe without interruption the whole, full-scale topological change. We also compute the force fields needed to overcome the involved energy barriers. The obtained forces are in excellent agreement, in terms of intensity, scale, and spatial localization with experimental data on typical fission protein systems, whereas they suggest the presence of additional features in fusion proteins.

Adsorption of sterically-stabilized diblock copolymer nanoparticles at the oil-water interface: effect of charged end-groups on interfacial rheology

The RAFT aqueous emulsion polymerization of either methyl methacrylate (MMA) or benzyl methacrylate (BzMA) is conducted at 70 °C using poly(glycerol monomethacrylate) (PGMA) as a water-soluble precursor to produce sterically-stabilized diblock copolymer nanoparticles of approximately 30 nm diameter. Carboxylic acid- or morpholine-functional RAFT agents are employed to confer anionic or cationic functionality at the ends of the PGMA stabilizer chains, with a neutral RAFT agent being used as a control. Thus the electrophoretic footprint of such minimally-charged model nanoparticles can be adjusted simply by varying the solution pH. Giant (mm-sized) aqueous droplets containing such nanoparticles are then grown within a continuous phase of n-dodecane and a series of interfacial rheology measurements are conducted. The interfacial tension between the aqueous phase and n-dodecane is strongly dependent on the charge of the terminal group on the stabilizer chains. More specifically, neutral nanoparticles produce a significantly lower interfacial tension than either cationic or anionic nanoparticles. Moreover, adsorption of neutral nanoparticles at the n-dodecane-water interface produces higher interfacial elastic moduli than that observed for charged nanoparticles. This is because neutral nanoparticles can adsorb at much higher surface packing densities owing to the absence of electrostatic repulsive forces in this case.

Instrument for measurement of interfacial structure-property relationships with decoupled interfacial shear and dilatational flow: "Quadrotrough"

Understanding the interfacial structure-property relationship of complex fluid-fluid interfaces is increasingly important for guiding the formulation of systems with targeted interfacial properties, such as those found in multiphase complex fluids, biological systems, biopharmaceuticals formulations, and many consumer products. Mixed interfacial flow fields, typical of classical Langmuir trough experiments, introduce a complex interfacial flow history that complicates the study of interfacial properties of complex fluid interfaces. In this article, we describe the design, implementation, and validation of a new instrument capable of independent application of controlled interfacial dilation and shear kinematics on fluid interfaces. Combining the Quadrotrough with both in situ Brewster angle microscopy and neutron reflectometry provides detailed structural measurements of the interface at the mesoscale and nanoscale in relationship to interfacial material properties under controlled interfacial deformation histories.

One-Step Generation of Alginate-Based Hydrogel Foams Using CO2 for Simultaneous Foaming and Gelation

The reliable generation of hydrogel foams remains a challenge in a wide range of sectors, including food, cosmetic, agricultural, and medical applications. Using the example of calcium alginate foams, we introduce a novel foam generation method that uses CO2 for the simultaneous foaming and pH reduction of the alginate solution to trigger gelation. We show that gelled foams of different gas fractions can be generated in a simple one-step process. We macroscopically follow the acidification using a pH-responsive indicator and investigate the role of CO2 in foam ageing via foam stability measurements. Finally, we demonstrate the utility of interfacial rheology to provide evidence for the gelation process initiated by the dissolution of the CO2 from the dispersed phase. Both approaches, gas-initiated gelation and interfacial rheology for its characterization, can be readily transferred to other types of gases and formulations.

Reshaping sub-millimetre bubbles from spheres to tori

Shape-changing objects are prized for applications ranging from acoustics to robotics. We report sub-millimetre bubbles that reversibly and rapidly change not only their shape but also their topological class, from sphere to torus, when subjected to a simple pressure treatment. Stabilized by a solid-like film of nanoscopic protein "particles", the bubbles may persist in toroidal form for several days, most of them with the relative dimensions expected of Clifford tori. The ability to cross topological classes reversibly and quickly is enabled by the expulsion of protein from the strained surfaces in the form of submicron assemblies. Compared to structural modifications of liquid-filled vesicles, for example by slow changes in solution osmolality, the rapid inducement of shape changes in bubbles by application of pressure may hasten experimental investigations of surface mechanics, even as it suggests new routes to lightweight materials with high surface areas.

Reply to the 'Comment on "Surface elastic constants of a soft solid"' by E. Gutman, Soft Matter, 2022, 18, DOI: 10.1039/D1SM01412A

In response to Gutman's comment, we clarify the derivation of the Shuttleworth equation. In addition, we discuss the findings of our original paper in light of recent theoretical and experimental work on surface elasticity in soft solids.

Contamination in Sodium Dodecyl Sulfate Solutions: Insights from the Measurements of Surface Tension and Surface Rheology

The presence of contamination in sodium dodecyl sulfate (SDS) solutions in the form of dodecanol (LOH) is known to drastically affect the resulting interfacial properties such as surface tension (SFT) and rheology. Dodecanol molecules, which are the product of SDS hydrolysis and are inherently present in SDS solutions, have higher surface activity compared to SDS because they are less soluble in water. A characteristic dip in the SFT isotherm is an indicator of the dodecanol contamination in the sample. The presence of an electrolyte in the solution impacts the surface activity of SDS and its critical micelle concentration, and could yield SFT isotherms that closely match those obtained for pure SDS samples. The interpretation of the isotherms in such cases could thus lead to misinterpretation of the surface purity. In this work, we have examined the SFT isotherms for SDS solutions in both the absence and presence of electrolyte. We have fitted the isotherms to three different thermodynamic adsorption models to estimate the amount of dodecanol present in the sample. We have applied the estimated values for the LOH content in a two-component rheological model to predict the viscoelasticity of such surfactant-laden surfaces. We have compared these results with the experimentally measured interfacial rheological properties. Our findings demonstrate that the presence of impurities can be captured under dynamic expansion and contractions, even for solutions containing background electrolyte.

FM-AFM with a Hanging Fiber Probe for the Study of Liquid-Liquid Interfaces

This work describes how a frequency modulation atomic force microscope (AFM) using a hanging fiber force probe made from a quartz tuning fork provides local measurements on liquid-liquid interfaces. After detailing the manufacture and calibration of the force probe, we provide evidence that this AFM is suitable for quantitative measurements at the interface between two liquids. The repeatability of the measurements allows a poly-dimethylsiloxane-water moving interface to be monitored over several hours. The evaporation of a water droplet immersed in poly-dimethylsiloxane is observed, and its interfacial tension evolution over time is measured. Deformation of the interface is also observed. These capabilities, and preliminary results for the interface between two immiscible liquids, pave the way for interface manipulation and study of complex fluid-fluid interfaces.

Interfacial Rearrangements of Block Copolymer Micelles Toward Gelled Liquid-Liquid Interfaces with Adjustable Viscoelasticity

Though amphiphiles are ubiquitously used for altering interfaces, interfacial reorganization processes are in many cases obscure. For example, adsorption of micelles to liquid-liquid interfaces is often accompanied by rapid reorganizations toward monolayers. Then, the involved time scales are too short to be followed accurately. A block copolymer system, which comprises poly(ethylene oxide)₁₁₀ -b-poly{[2-(methacryloyloxy)ethyl]diisopropylmethylammonium chloride}₁₇₀ (i.e., PEO₁₁₀ -b-qPDPAEMA₁₇₀ with quaternized poly(diisopropylaminoethyl methacrylate)) is presented. Its reorganization kinetics at the water/n-decane interface is slowed down by electrostatic interactions with ferricyanide ([Fe(CN)₆ ]^3- ). This deceleration allows an observation of the restructuring of the adsorbed micelles not only by tracing the interfacial pressure, but also by analyzing the interfacial rheology and structure with help of atomic force microscopy. The observed micellar flattening and subsequent merging toward a physically interconnected monolayer lead to a viscoelastic interface well detectable by interfacial shear rheology (ISR). Furthermore, the "gelled" interface is redox-active, enabling a return to purely viscous interfaces and hence a manipulation of the rheological properties by redox reactions. Additionally, interfacial Prussian blue formation stiffens the interface. Such manipulation and in-depth knowledge of the rheology of complex interfaces can be beneficial for the development of emulsion formulations in industry or medicine, where colloidal stability or adapted permeability is crucial.

A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve.

Tuning the rheology and microstructure of particle-laden fluid interfaces with Janus particles

HYPOTHESIS

Particle-laden fluid interfaces are the central component of many natural and engineering systems. Understanding the mechanical properties and improving the stability of such interfaces are of great practical importance. Janus particles, a special class of heterogeneous colloids, might be used as an effective surface-active agent to control the assembly and interfacial rheology of particle-laden fluid interfaces.

EXPERIMENTS

Using a custom-built interfacial stress rheometer, we explore the effect of Janus particle additives on the interfacial rheology and microscopic structure of particle-laden fluid interfaces.

FINDINGS

We find that the addition of a small amount of platinum-polystyrene (Pt-PS) Janus particles within a monolayer of PS colloids (1:40 number ratio) can lead to more than an order-of-magnitude increase in surface moduli with enhanced elasticity, which improves the stability of the interface. This drastic change in interfacial rheology is associated with the formation of local particle clusters surrounding each Janus particle. We further explain the origin of local particle clusters by considering the interparticle interactions at the interface. Our experiments reveal the effect of local particle structures on the macroscopic rheological behaviors of particle monolayers and demonstrate a new way to tune the microstructure and mechanical properties of particle-laden fluid interfaces.

Emulsion characterization via microfluidic devices: A review on interfacial tension and stability to coalescence

Emulsions have gained significant importance in many industries including foods, pharmaceuticals, cosmetics, health care formulations, paints, polymer blends and oils. During emulsion generation, collisions can occur between newly-generated droplets, which may lead to coalescence between the droplets. The extent of coalescence is driven by the properties of the dispersed and continuous phases (e.g. density, viscosity, ion strength and pH), and system conditions (e.g. temperature, pressure or any external applied forces). In addition, the diffusion and adsorption behaviors of emulsifiers which govern the dynamic interfacial tension of the forming droplets, the surface potential, and the duration and frequency of the droplet collisions, contribute to the overall rate of coalescence. An understanding of these complex behaviors, particularly those of interfacial tension and droplet coalescence during emulsion generation, is critical for the design of an emulsion with desirable properties, and for the optimization of the processing conditions. However, in many cases, the time scales over which these phenomena occur are extremely short, typically a fraction of a second, which makes their accurate determination by conventional analytical methods extremely challenging. In the past few years, with advances in microfluidic technology, many attempts have demonstrated that microfluidic systems, characterized by micrometer-size channels, can be successfully employed to precisely characterize these properties of emulsions. In this review, current applications of microfluidic devices to determine the equilibrium and dynamic interfacial tension during droplet formation, and to investigate the coalescence stability of dispersed droplets applicable to the processing and storage of emulsions, are discussed.

Surface Tension and the Strain-Dependent Topography of Soft Solids

When stretched in one direction, most solids shrink in the transverse directions. In soft silicone gels, however, we observe that small-scale topographical features grow upon stretching. A quantitative analysis of the topography shows that this counterintuitive response is nearly linear, allowing us to tackle it through a small-strain analysis. We find that the surprising increase of small-scale topography with stretch is due to a delicate interplay of the bulk and surface responses to strain. Specifically, we find that surface tension changes as the material is deformed. This response is expected on general grounds for solid materials, but challenges the standard description of gel and elastomer surfaces.

Pressure-deformation relations of elasto-capillary drops (droploons) on capillaries

An increasing number of multi-phase systems exploit complex interfaces in which capillary stresses are coupled with solid-like elastic stresses. Despite growing efforts, simple and reliable experimental characterisation of these interfaces remains a challenge, especially of their dilational properties. Pendant drop techniques are convenient, but suffer from complex shape changes and associated fitting procedures with multiple parameters. Here we show that simple analytical relationships can be derived to describe reliably the pressure-deformation relations of nearly spherical elasto-capillary droplets ("droploons") attached to a capillary. We consider a model interface in which stresses arising from a constant interfacial tension are superimposed with mechanical extra-stresses arising from the deformation of a solid-like, incompressible interfacial layer of finite thickness described by a neo-Hookean material law. We compare some standard models of liquid-like (Gibbs) and solid-like (Hookean and neo-Hookean elasticity) elastic interfaces which may be used to describe the pressure-deformation relations when the presence of the capillary can be considered negligible. Combining Surface Evolver simulations and direct numerical integration of the drop shape equations, we analyse in depth the influence of the anisotropic deformation imposed by the capillary on the pressure-deformation relation and show that in many experimentally relevant circumstances either the analytical relations of the perfect sphere may be used or a slightly modified relation which takes into account the geometrical change imposed by the capillary. Using the analogy with the stress concentration around a rigid inclusion in an elastic membrane, we provide simple non-dimensional criteria to predict under which conditions the simple analytical expressions can be used to fit pressure-deformation relations to analyse the elastic properties of the interfaces via "Capillary Pressure Elastometry". We show that these criteria depend essentially on the drop geometry and deformation, but not on the interfacial elasticity. Moreover, this benchmark case shows for the first time that Surface Evolver is a reliable tool for predictive simulations of elastocapillary interfaces. This opens doors to the treatment of more complex geometries/conditions, where theory is not available for comparison. Our Surface Evolver code is available for download in the ESI.

Fabricating Robust Constructs with Internal Phase Nanostructures via Liquid-in-Liquid 3D Printing

The ability to print soft materials into predefined architectures with programmable nanostructures and mechanical properties is a necessary requirement for creating synthetic biomaterials that mimic living tissues. However, the low viscosity of common materials and lack of required mechanical properties in the final product present an obstacle to the use of traditional additive manufacturing approaches. Here, a new liquid-in-liquid 3D printing approach is used to successfully fabricate constructs with internal nanostructures using in situ self-assembly during the extrusion of an aqueous solution containing surfactant and photocurable polymer into a stabilizing polar oil bath. Subsequent photopolymerization preserves the nanostructures created due to surfactant self-assembly at the immiscible liquid-liquid interface, which is confirmed by small-angle X-ray scattering. Mechanical properties of the photopolymerized prints are shown to be tunable based on constituent components of the aqueous solution. The reported 3D printing approach expands the range of low-viscosity materials that can be used in 3D printing, and enables robust constructs production with internal nanostructures and spatially defined features. The reported approach has broad applications in regenerative medicine by providing a platform to print self-assembling biomaterials into complex tissue mimics where internal supramolecular structures and their functionality control biological processes, similar to natural extracellular matrices.

Foaming and rheological properties of aqueous solutions: an interfacial study

Although aqueous foam is composed of simple fluids, air and water, it shows a complex rheological behavior. It exhibits solid-like behavior at low shear and fluid-like behavior at high shear rate. Therefore, understanding such behavior is important for many industrial applications in foods, pharmaceuticals, and cosmetics. Additionally, air–water interface of bubble surface plays an important role in the stabilizing mechanism of foams. Therefore, the rheological properties associated with the aqueous foam highly depend on its interfacial properties. In this review, a systematic study of aqueous foam are presented primarily from rheology point of view. Firstly, foaming agents, surfactants and particles are described; then foam structure was explained, followed by change in structure under applied shear. Finally, foam rheology was linked to interfacial rheology for the interface containing particles whose surface properties were altered by surfactants.

Physiological fluid interfaces: Functional microenvironments, drug delivery targets, and first line of defense

Fluid interfaces, i.e. the boundary layer of two liquids or a liquid and a gas, play a vital role in physiological processes as diverse as visual perception, oral health and taste, lipid metabolism, and pulmonary breathing. These fluid interfaces exhibit a complex composition, structure, and rheology tailored to their individual physiological functions. Advances in interfacial thin film techniques have facilitated the analysis of such complex interfaces under physiologically relevant conditions. This allowed new insights on the origin of their physiological functionality, how deviations may cause disease, and has revealed new therapy strategies. Furthermore, the interactions of physiological fluid interfaces with exogenous substances is crucial for understanding certain disorders and exploiting drug delivery routes to or across fluid interfaces. Here, we provide an overview on fluid interfaces with physiological relevance, namely tear films, interfacial aspects of saliva, lipid droplet digestion and storage in the cell, and the functioning of lung surfactant. We elucidate their structure-function relationship, discuss diseases associated with interfacial composition, and describe therapies and drug delivery approaches targeted at fluid interfaces. STATEMENT OF SIGNIFICANCE: Fluid interfaces are inherent to all living organisms and play a vital role in various physiological processes. Examples are the eye tear film, saliva, lipid digestion & storage in cells, and pulmonary breathing. These fluid interfaces exhibit complex interfacial compositions and structures to meet their specific physiological function. We provide an overview on physiological fluid interfaces with a focus on interfacial phenomena. We elucidate their structure-function relationship, discuss diseases associated with interfacial composition, and describe novel therapies and drug delivery approaches targeted at fluid interfaces. This sets the scene for ocular, oral, or pulmonary surface engineering and drug delivery approaches.

Extreme reversal in mechanical anisotropy in liquid-liquid interfaces reinforced with self-assembled protein nanosheets

The structuring of liquid-liquid and liquid-air interfaces may play an important role in novel microfabrication platforms and biotechnologies, from the spontaneous formation of microfilaments from liquid droplets and the 3D printing of liquids, to the culture of stem cells on emulsions. Understanding the mechanical anisotropy of associated liquid interfaces is essential for the development of such systems. Models of AFM indentation at liquid interfaces, based on the Young-Laplace model, currently do not allow the quantification of interfacial mechanical properties of associated molecular films. This report presents such a model and compares its predictions to interfacial mechanical properties characterised via interfacial shear rheology. An extreme reversal of mechanical anisotropy of liquid-liquid interfaces is observed, upon self-assembly of protein nanosheets, by 5 orders of magnitude. Results indicate that, although interfacial rheology is more sensitive than AFM indentation to the mechanics of molecular films in the low range of interfacial mechanics, AFM indentation allows the quantification of mechanical properties of stiffer molecular films, and remains better adapted to the characterisation of small samples and enables the characterisation of local heterogeneity.