Droplet Self-Propulsion on Slippery Liquid-Infused Surfaces with Dual-Lubricant Wedge-Shaped Wettability Patterns.

Young's equation is fundamental to the concept of the wettability of a solid surface. It defines the contact angle for a droplet on a solid surface through a local equilibrium at the three-phase contact line. Recently, the concept of a liquid Young's law contact angle has been developed to describe the wettability of slippery liquid-infused porous surfaces (SLIPS) by droplets of an immiscible liquid. In this work, we present a new method to fabricate biphilic SLIP surfaces and show how the wettability of the composite SLIPS can be exploited with a macroscopic wedge-shaped pattern of two distinct lubricant liquids. In particular, we report the development of composite liquid surfaces on silicon substrates based on lithographically patterning a Teflon AF1600 coating and a superhydrophobic coating (Glaco Mirror Coat Zero), where the latter selectively dewets from the former. This creates a patterned base surface with preferential wetting to matched liquids: the fluoropolymer PTFE with a perfluorinated oil Krytox and the hydrophobic silica-based GLACO with olive oil (or other mineral oils or silicone oil). This allows us to successively imbibe our patterned solid substrates with two distinct oils and produce a composite liquid lubricant surface with the oils segregated as thin films into separate domains defined by the patterning. We illustrate that macroscopic wedge-shaped patterned SLIP surfaces enable low-friction droplet self-propulsion. Finally, we formulate an analytical model that captures the dependence of the droplet motion as a function of the wettability of the two liquid lubricant domains and the opening angle of the wedge. This allows us to derive scaling relationships between various physical and geometrical parameters. This work introduces a new approach to creating patterned liquid lubricant surfaces, demonstrates long-distance droplet self-propulsion on such surfaces, and sheds light on the interactions between liquid droplets and liquid surfaces.

A bending rigidity parameter for stress granule condensates.

Interfacial tension plays an important role in governing the dynamics of droplet coalescence and determining how condensates interact with and deform lipid membranes and biological filaments. We demonstrate that an interfacial tension-only model is inadequate for describing stress granules in live cells. Harnessing a high-throughput flicker spectroscopy pipeline to analyze the shape fluctuations of tens of thousands of stress granules, we find that the measured fluctuation spectra require an additional contribution, which we attribute to elastic bending deformation. We also show that stress granules have an irregular, nonspherical base shape. These results suggest that stress granules are viscoelastic droplets with a structured interface, rather than simple Newtonian liquids. Furthermore, we observe that the measured interfacial tensions and bending rigidities span a range of several orders of magnitude. Hence, different types of stress granules (and more generally, other biomolecular condensates) can only be differentiated via large-scale surveys.

Phase field simulation of liquid filling on grooved surfaces for complete, partial, and pseudo-partial wetting cases.

We develop and harness a phase field simulation method to study liquid filling on grooved surfaces. We consider both short-range and long-range liquid-solid interactions, with the latter including purely attractive and repulsive interactions as well as those with short-range attraction and long-range repulsion. This allows us to capture complete, partial, and pseudo-partial wetting states, demonstrating complex disjoining pressure profiles over the full range of possible contact angles as previously proposed in the literature. Applying the simulation method to study liquid filling on grooved surfaces, we compare the filling transition for the three different classes of wetting states as we vary the pressure difference between the liquid and gas phases. The filling and emptying transitions are reversible for the complete wetting case, while significant hysteresis is observed for the partial and pseudo-partial cases. In agreement with previous studies, we also show that the critical pressure for the filling transition follows the Kelvin equation for the complete and partial wetting scenarios. Finally, we find the filling transition can display a number of distinct morphological pathways for the pseudo-partial wetting cases, as we demonstrate here for varying groove dimensions.

A robust and memory-efficient transition state search method for complex energy landscapes.

Locating transition states is crucial for investigating transition mechanisms in wide-ranging phenomena, from atomistic to macroscale systems. Existing methods, however, can struggle in problems with a large number of degrees of freedom, on-the-fly adaptive remeshing and coarse-graining, and energy landscapes that are locally flat or discontinuous. To resolve these challenges, we introduce a new double-ended method, the Binary-Image Transition State Search (BITSS). It uses just two states that converge to the transition state, resulting in a fast, flexible, and memory-efficient method. We also show that it is more robust compared to existing bracketing methods that use only two states. We demonstrate its versatility by applying BITSS to three very different classes of problems: Lennard-Jones clusters, shell buckling, and multiphase phase-field models.

A minimal model of elastic instabilities in biological filament bundles.

We present a model of a system of elastic fibres which exhibits complex, coupled, nonlinear deformations via a connecting elastic spring network. This model can capture physically observed deformations such as global buckling, pinching and internal collapse. We explore the transitions between these deformation modes numerically, using an energy minimization approach, highlighting how supported environments, or stiff outer sheath structures, favour internal structural collapse over global deformation. We then derive a novel analytic buckling criterion for the internal collapse of the system, a mode of structural collapse pertinent in many biological filament bundles such as the optic nerve bundle and microtubule bundles involved in cell abscission.

Spontaneous phase separation of ternary fluid mixtures.

We computationally study the spontaneous phase separation of ternary fluid mixtures using the lattice Boltzmann method both when all the surface tensions are equal and when they have different values. To rationalise the phase diagram of possible phase separation mechanisms, previous theoretical works typically rely on analysing the sign of the eigenvalues resulting from a simple linear stability analysis, but we find this does not explain the observed simulation results. Here, we classify the possible separation pathways into four basic mechanisms, and develop a phenomenological model that captures the composition regimes where each mechanism is prevalent. We further highlight that the dominant mechanism in ternary phase separation involves enrichment and instability of the minor component at the fluid-fluid interface, which is absent in the case of binary fluid mixtures.

Systematic characterization of effect of flow rates and buffer compositions on double emulsion droplet volumes and stability.

Double emulsion droplets (DEs) are water/oil/water droplets that can be sorted via fluorescence-activated cell sorting (FACS), allowing for new opportunities in high-throughput cellular analysis, enzymatic screening, and synthetic biology. These applications require stable, uniform droplets with predictable microreactor volumes. However, predicting DE droplet size, shell thickness, and stability as a function of flow rate has remained challenging for monodisperse single core droplets and those containing biologically-relevant buffers, which influence bulk and interfacial properties. As a result, developing novel DE-based bioassays has typically required extensive initial optimization of flow rates to find conditions that produce stable droplets of the desired size and shell thickness. To address this challenge, we conducted systematic size parameterization quantifying how differences in flow rates and buffer properties (viscosity and interfacial tension at water/oil interfaces) alter droplet size and stability, across 6 inner aqueous buffers used across applications such as cellular lysis, microbial growth, and drug delivery, quantifying the size and shell thickness of >22 000 droplets overall. We restricted our study to stable single core droplets generated in a 2-step dripping-dripping formation regime in a straightforward PDMS device. Using data from 138 unique conditions (flow rates and buffer composition), we also demonstrated that a recent physically-derived size law of Wang et al. can accurately predict double emulsion shell thickness for >95% of observations. Finally, we validated the utility of this size law by using it to accurately predict droplet sizes for a novel bioassay that requires encapsulating growth media for bacteria in droplets. This work has the potential to enable new screening-based biological applications by simplifying novel DE bioassay development.

Apparent contact angle of drops on liquid infused surfaces: geometric interpretation.

We theoretically investigate the apparent contact angle of drops on liquid infused surfaces as a function of the relative size of the wetting ridge and the deposited drop. We provide an intuitive geometrical interpretation whereby the variation in the apparent contact angle is due to the rotation of the Neumann triangle at the lubricant-drop-gas contact line. We also derive linear and quadratic corrections to the apparent contact angle as power series expansion in terms of pressure differences between the lubricant, drop and gas phases. These expressions are much simpler and more compact compared to those previously derived by Semprebon et al. [Soft Matter, 2017, 13, 101-110].

Wetting of phase-separated droplets on plant vacuole membranes leads to a competition between tonoplast budding and nanotube formation.

Seeds of dicotyledonous plants store proteins in dedicated membrane-bounded organelles called protein storage vacuoles (PSVs). Formed during seed development through morphological and functional reconfiguration of lytic vacuoles in embryos [M. Feeney et al., Plant Physiol. 177, 241-254 (2018)], PSVs undergo division during the later stages of seed maturation. Here, we study the biophysical mechanism of PSV morphogenesis in vivo, discovering that micrometer-sized liquid droplets containing storage proteins form within the vacuolar lumen through phase separation and wet the tonoplast (vacuolar membrane). We identify distinct tonoplast shapes that arise in response to membrane wetting by droplets and derive a simple theoretical model that conceptualizes these geometries. Conditions of low membrane spontaneous curvature and moderate contact angle (i.e., wettability) favor droplet-induced membrane budding, thereby likely serving to generate multiple, physically separated PSVs in seeds. In contrast, high membrane spontaneous curvature and strong wettability promote an intricate and previously unreported membrane nanotube network that forms at the droplet interface, allowing molecule exchange between droplets and the vacuolar interior. Furthermore, our model predicts that with decreasing wettability, this nanotube structure transitions to a regime with bud and nanotube coexistence, which we confirmed in vitro. As such, we identify intracellular wetting [J. Agudo-Canalejo et al., Nature 591, 142-146 (2021)] as the mechanism underlying PSV morphogenesis and provide evidence suggesting that interconvertible membrane wetting morphologies play a role in the organization of liquid phases in cells.

Tailoring the multistability of origami-inspired, buckled magnetic structures via compression and creasing.

Origami-inspired multistable structures are gaining increasing interest because of their potential applications in fields ranging from deployable structures to reconfigurable microelectronics. The multistability of such structures is critical for their applications but is challenging to manipulate due to the highly nonlinear deformations and complex configurations of the structures. Here, a comprehensive experimental and computational study is reported to tailor the multistable states of origami-inspired, buckled ferromagnetic structures and their reconfiguration paths. Using ribbon structures as an example, a design phase diagram is constructed as a function of the crease number and compressive strain. As the crease number increases from 0 to 7, the number of distinct stable states first increases and then decreases. The multistability is also shown to be actively tuned by varying the strain from 0% to 40%. Furthermore, analyzing energy barriers for reconfiguration among the stable states reveals dynamic changes in reconfiguration paths with increasing strains. Guided by studies above, diverse examples are designed and demonstrated, from programmable structure arrays to a soft robot. These studies lay out the foundation for the rational design of functional, multistable structures.

Intracellular wetting mediates contacts between liquid compartments and membrane-bound organelles.

Protein-rich droplets, such as stress granules, P-bodies, and the nucleolus, perform diverse and specialized cellular functions. Recent evidence has shown the droplets, which are also known as biomolecular condensates or membrane-less compartments, form by phase separation. Many droplets also contact membrane-bound organelles, thereby functioning in development, intracellular degradation, and organization. These underappreciated interactions have major implications for our fundamental understanding of cells. Starting with a brief introduction to wetting phenomena, we summarize recent progress in the emerging field of droplet-membrane contact. We describe the physical mechanism of droplet-membrane interactions, discuss how these interactions remodel droplets and membranes, and introduce "membrane scaffolding" by liquids as a novel reshaping mechanism, thereby demonstrating that droplet-membrane interactions are elastic wetting phenomena. "Membrane-less" and "membrane-bound" condensates likely represent distinct wetting states that together link phase separation with mechanosensitivity and explain key structures observed during embryogenesis, during autophagy, and at synapses. We therefore contend that droplet wetting on membranes provides a robust and intricate means of intracellular organization.

Capillary Bridges on Liquid-Infused Surfaces.

We numerically study two-component capillary bridges formed when a liquid droplet is placed in between two liquid-infused surfaces (LIS). In contrast to commonly studied one-component capillary bridges on noninfused solid surfaces, two-component liquid bridges can exhibit a range of different morphologies where the liquid droplet is directly in contact with two, one, or none of the LIS substrates. In addition, the capillary bridges may lose stability when compressed due to the envelopment of the droplet by the lubricant. We also characterize the capillary force, maximum separation, and effective spring force and find that they are influenced by the shape and size of the lubricant ridge. Importantly, these can be tuned to increase the effective capillary adhesion strength by manipulating the lubricant pressure, Neumann angle, and wetting contact angles. As such, LIS are not only "slippery" parallel to the surface, but they are also "sticky" perpendicular to the surface.

Control of Superselectivity by Crowding in Three-Dimensional Hosts.

Motivated by the fine compositional control observed in membraneless droplet organelles in cells, we investigate how a sharp binding-unbinding transition can occur between multivalent client molecules and receptors embedded in a porous three-dimensional structure. In contrast to similar superselective binding previously observed at surfaces, we have identified that a key effect in a three-dimensional environment is that the presence of inert crowding agents can significantly enhance or even introduce superselectivity. In essence, molecular crowding initially suppresses binding via an entropic penalty, but the clients can then more easily form many bonds simultaneously. We demonstrate the robustness of the superselective behavior with respect to client valency, linker length, and binding interactions in Monte Carlo simulations of an archetypal lattice polymer model.

Predicting Hemiwicking Dynamics on Textured Substrates.

The ability to predict liquid transport rates on textured surfaces is key to the design and optimization of devices and processes such as oil recovery, coatings, reaction-separation, high-throughput screening, and thermal management. In this work we develop a fully analytical model to predict the propagation coefficients for liquids hemiwicking through micropillar arrays. This is carried out by balancing the capillary driving force and a viscous resistive force and solving the Navier-Stokes equation for representative channels. The model is validated against a large data set of experimental hemiwicking coefficients harvested from the literature and measured in-house using high-speed imaging. The theoretical predictions show excellent agreement with the measured values and improved accuracy compared to previously proposed models. Furthermore, using lattice Boltzmann (LB) simulations, we demonstrate that the present model is applicable over a broad range of geometries. The scaling of velocity with texture geometry, implicit in our model, is compared against experimental data, where good agreement is observed for most practical systems. The analytical expression presented here offers a tool for developing design guidelines for surface chemistry and microstructure selection for liquid propagation on textured surfaces.

Self-propelled droplet transport on shaped-liquid surfaces.

The transport of small amounts of liquids on solid surfaces is fundamental for microfluidics applications. Technologies allowing control of droplets of liquid on flat surfaces generally involve the generation of a wettability contrast. This approach is however limited by the resistance to motion caused by the direct contact between the droplet and the solid. We show here that this resistance can be drastically reduced by preventing direct contact with the help of dual-length scale micro-structures and the concept of "liquid-surfaces". These new surfaces allow the gentle transport of droplets along defined paths and with fine control of their speed. Moreover, their high adhesion permits the capture of impacting droplets, opening new possibilities in applications such as fog harvesting and heat transfer.

Phase transitions on non-uniformly curved surfaces: coupling between phase and location.

For particles confined to two dimensions, any curvature of the surface affects the structural, kinetic and thermodynamic properties of the system. If the curvature is non-uniform, an even richer range of behaviours can emerge. Using a combination of bespoke Monte Carlo, molecular dynamics and basin-hopping methods, we show that the stable states of attractive colloids confined to non-uniformly curved surfaces are distinguished not only by the phase of matter but also by their location on the surface. Consequently, the transitions between these states involve cooperative migration of the entire colloidal assembly. We demonstrate these phenomena on toroidal and sinusoidal surfaces for model colloids with different ranges of interactions as described by the Morse potential. In all cases, the behaviour can be rationalised in terms of three universal considerations: cluster perimeter, stress, and the packing of next-nearest neighbours.

Factors controlling the pinning force of liquid droplets on liquid infused surfaces.

Liquid infused surfaces with partially wetting lubricants have recently been exploited for numerous intriguing applications, such as for droplet manipulation, droplet collection and spontaneous motion. When partially wetting lubricants are used, the pinning force is a key factor that can strongly affect droplet mobility. Here, we derive an analytical prediction for contact angle hysteresis in the limit where the meniscus size is much smaller than the droplet, and numerically study how it is controlled by the solid fraction, the lubricant wetting angles, and the various fluid surface tensions. We further relate the contact angle hysteresis and the pinning force experienced by a droplet on a liquid infused surface, and our predictions for the critical sliding angles are consistent with existing experimental observations. Finally, we discuss why a droplet on a liquid infused surface with partially wetting lubricants typically experiences stronger pinning compared to a droplet on a classical superhydrophobic surface.

Unrestrained ESCRT-III drives micronuclear catastrophe and chromosome fragmentation.

The ESCRT-III membrane fission machinery maintains the integrity of the nuclear envelope. Although primary nuclei resealing takes minutes, micronuclear envelope ruptures seem to be irreversible. Instead, micronuclear ruptures result in catastrophic membrane collapse and are associated with chromosome fragmentation and chromothripsis, complex chromosome rearrangements thought to be a major driving force in cancer development. Here we use a combination of live microscopy and electron tomography, as well as computer simulations, to uncover the mechanism underlying micronuclear collapse. We show that, due to their small size, micronuclei inherently lack the capacity of primary nuclei to restrict the accumulation of CHMP7-LEMD2, a compartmentalization sensor that detects loss of nuclear integrity. This causes unrestrained ESCRT-III accumulation, which drives extensive membrane deformation, DNA damage and chromosome fragmentation. Thus, the nuclear-integrity surveillance machinery is a double-edged sword, as its sensitivity ensures rapid repair at primary nuclei while causing unrestrained activity at ruptured micronuclei, with catastrophic consequences for genome stability.

Critical Pressure Asymmetry in the Enclosed Fluid Diode.

Joint physically and chemically pattered surfaces can provide efficient and passive manipulation of fluid flow. The ability of many of these surfaces to allow only unidirectional flow means they are often termed fluid diodes. Synthetic analogues of these are enabling technologies from sustainable water collection via fog harvesting to improved wound dressings. One key fluid diode geometry features a pore sandwiched between two absorbent substrates-an important design for applications that require liquid capture while preventing back-flow. However, the enclosed pore is particularly challenging to design as an effective fluid diode due to the need for both a low Laplace pressure for liquid entering the pore and a high Laplace pressure to liquid leaving. Here, we calculate the Laplace pressure for fluid traveling in both directions on a range of conical pore designs with a chemical gradient. We show that this chemical gradient is in general required to achieve the largest critical pressure differences between incoming and outgoing liquids. Finally, we discuss the optimization strategy to maximize this critical pressure asymmetry.

Effect of Ageing on the Structure and Properties of Model Liquid-Infused Surfaces.

Liquid-infused surfaces (LISs) exhibit unique properties that make them ideal candidates for a wide range of applications, from antifouling and anti-icing coatings to self-healing surfaces and controlled wetting. However, when exposed to realistic environmental conditions, LISs tend to age and progressively lose their desirable properties, potentially compromising their application. The associated ageing mechanisms are still poorly understood, and results reflecting real-life applications are scarce. Here, we track the ageing of a model LIS composed of glass surfaces functionalized with hydrophobic nanoparticles and infused with silicone oil. The LISs are fully submerged in aqueous solutions and exposed to acoustic pressure waves for set time intervals. The ageing is monitored by periodic measurements of the LIS's wetting properties. We also track the changes to the LIS's nanoscale structure. We find that the LISs rapidly lose their slippery properties because of a combination of oil loss, smoothing of the nanoporous functional layer, and substrate degradation when directly exposed to the solution. The oil loss is consistent with water microdroplets entering the oil layer and displacing oil away from the surface. These mechanisms are general and could play a role in the ageing of most LISs.