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).

Solidification of Polyurethane Model Foams via Catalyst Drainage from a Secondary Foam.

Due to their unique mechanical and thermal properties, polyurethane foams are widely used in multiple fields of applications, including cushioning, thermal insulation or biomedical engineering. However, the way polyurethane foams are usually manufactured - via chemical foaming - produces samples where blowing and gelling occurs at the same time, resulting in a morphology control achieved by trial and error processes. Here, we introduce a novel strategy to build model homogeneous polyurethane foams of controlled density with millimetric bubbles from liquid templates. We show that by producing a polyurethane foam via physical bubbling without a catalyst and gently depositing a secondary foam containing catalyst on the top of this first foam, we can take advantage of drainage mechanisms to trigger the solidification of the bottom foam. The characterisation of our samples performed by X-ray microtomography allows us to study quantitatively the structure of the final solid foam, at the global and at the local scale. Using the tomographic three-dimensional images of the foam architectures, we show that the superimposed foam technique introduced in this article is promising to produce foams with a good homogeneity along the vertical direction, with a density controlled by varying the concentration of catalyst in the secondary foam. This article is protected by copyright. All rights reserved.

Perturbing the catenoid: Stability and mechanical properties of nonaxisymmetric minimal surfaces.

Minimal surface problems arise naturally in many soft matter systems whose free energies are dominated by surface or interface energies. Of particular interest are the shapes, stability, and mechanical stresses of minimal surfaces spanning specific geometric boundaries. The "catenoid" is the best-known example where an analytical solution is known which describes the form and stability of a minimal surface held between two parallel, concentric circular frames. Here we extend this problem to nonaxisymmetric, parallel frame shapes of different orientations by developing a perturbation approach around the known catenoid solution. We show that the predictions of the perturbation theory are in good agreement with experiments on soap films and finite element simulations (Surface Evolver). Combining theory, experiment, and simulation, we analyze in depth how the shapes, stability, and mechanical properties of the minimal surfaces depend on the type and orientation of elliptic and three-leaf clover shaped frames. In the limit of perfectly aligned nonaxisymmetric frames, our predictions show excellent agreement with a recent theory established by Alimov et al. [Phys. Fluids 33, 052104 (2021)1070-663110.1063/5.0047461]. Moreover, we put in evidence the intriguing capacity of minimal surfaces between nonaxisymmetric frames to transmit a mechanical torque despite being completely liquid. These forces could be interesting to exploit for mechanical self-assembly of soft matter systems or as highly sensitive force captors.

Elastocapillary deformation of thin elastic ribbons in 2D foam columns.

The ability of liquid interfaces to shape slender elastic structures provides powerful strategies to control the architecture of mechanical self assemblies. However, elastocapillarity-driven intelligent design remains unexplored in more complex architected liquids - such as foams. Here we propose a model system which combines an assembly of bubbles and a slender elastic structure. Arrangements of soap bubbles in confined environments form well-defined periodic structures, dictated by Plateau's laws. We consider a 2D foam column formed in a container with square cross-section in which we introduce an elastomer ribbon, leading to architected structures whose geometry is guided by a competition between elasticity and capillarity. In this system, we quantify both experimentally and theoretically the equilibrium shapes, using X-ray micro-tomography and energy minimisation techniques. Beyond the understanding of the amplitude of the wavy elastic ribbon deformation, we provide a detailed analysis of the profile of the ribbon, and show that such a setup can be used to grant a shape to a UV-curable composite slender structure, as a foam-forming technique suitable to miniaturisation. In more general terms, this work provides a stepping stone towards an improved understanding of the interactions between liquid foams and slender structures.

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.

Counterrotation of magnetic beads in spinning fields.

A magnetic stirrer, an omnipresent device in the laboratory, generates a spinning magnetic dipolelike field that drives in a contactless manner the rotation of a ferromagnetic bead on top of it. We investigate here the surprisingly complex dynamics displayed by the spinning magnetic bead emerging from its dissipatively driven, coupled translation and rotation. A particularly stunning and counterintuitive phenomenon is the sudden inversion of the bead's rotational direction, from corotation to counterrotation, acting seemingly against the driving field, when the stirrer's frequency surpasses a critical value. The bead counterrotation effect, experimentally described by Chau et al. [J. Magn. Magn. Mater. 476, 376 (2019)JMMMDC0304-885310.1016/j.jmmm.2018.12.073], is here comprehensively studied, with numerical simulations and a theoretical approach complementing experimental observations.

Validation of Milner's visco-elastic theory of sintering for the generation of porous polymers with finely tuned morphology.

Sacrificial sphere templating has become a method of choice to generate macro-porous materials with well-defined, interconnected pores. For this purpose, the interstices of a sphere packing are filled with a solidifying matrix, from which the spheres are subsequently removed to obtain interconnected voids. In order to control the size of the interconnections, viscous sintering of the initial sphere template has proven a reliable approach. To predict how the interconnections evolve with different sintering parameters, such as time or temperature, Frenkel's model has been used with reasonable success over the last 70 years. However, numerous investigations have shown that the often complex flow behaviour of the spheres needs to be taken into account. To this end, S. Milner [arXiv:1907.05862] developed recently a theoretical model which improves on some key assumptions made in Frenkel's model, leading to a slightly different scaling. He also extended this new model to take into account the visco-elastic response of the spheres. Using an in-depth investigation of templates of paraffin spheres, we provide here the first systematic comparison with Milner's theory. Firstly, we show that his new scaling describes the experimental data slightly better than Frenkel's scaling. We then show that the visco-elastic version of his model provides a significantly improved description of the data over a wide parameter range. We finally use the obtained sphere templates to produce macro-porous polyurethanes with finely controlled pore and interconnection sizes. The general applicability of Milner's theory makes it transferable to a wide range of formulations, provided the flow properties of the sphere material can be quantified. It therefore provides a powerful tool to guide the creation of sphere packings and porous materials with finely controlled morphologies.

New conserved structural fields for supercooled liquids.

By considering Voronoi tessellations of the configurations of a fluid, we propose two new conserved fields, which provide structural information not fully accounted for by the usual 2-point density correlation functions. One of these fields is scalar and associated with the volume of the Voronoi cell, whereas the other one, termed the "geometric polarisation", is vectorial and related to the local anisotropy of the configurations. We study the static and dynamical properties of these fields in the supercooled regime of a model glass-forming liquid. We show that the geometric polarisation is statically correlated to the force field, but contrary to it develops a plateau regime when the temperature is lowered. This different relaxation is related to the cage effect in glass-forming liquids, which prevents a complete relaxation of the shape of the cage around particle on intermediate time scales.

Injected power fluctuations in one-dimensional dissipative systems: role of ballistic transport.

This paper is a generalization of the models considered in J. Stat. Phys. 128, 1365 (2007). Using an analogy with free fermions, we compute exactly the large deviation function (LDF) of the energy injected up to time t in a one-dimensional dissipative system of classical spins, where a drift is allowed. The dynamics are T=0 asymmetric Glauber dynamics driven out of rest by an injection mechanism, namely, a Poissonian flipping of one spin. The drift induces anisotropy in the system, making the model more comparable to experimental systems with dissipative structures. We discuss the physical content of the results, specifically the influence of the rate of the Poisson injection process and the magnitude of the drift on the properties of the LDF. We also compare the results of this spin model to simple phenomenological models of energy injection (Poisson or Bernoulli processes of domain wall injection). We show that many qualitative results of the spin model can be understood within this simplified framework.

Trotter derivation of algorithms for Brownian and dissipative particle dynamics.

This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to the proposal of Ermak and Buckholtz [J. Comput. Phys. 35, 169 (1980)] and not simply to the stochastic version of the velocity-Verlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same "weak order two" accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics. The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.

On a variational approach to the Soret coefficient.

In this paper, a variational approach to the Soret coefficient initiated by Kempers [J. Chem. Phys. 90, 6541 (1989)] is critically revisited. We show that the physical coherence of the whole procedure leads to a very peculiar choice of the type of constraint one can select to mimic the nonequilibrium stationary state. However, we demonstrate that its precise definition would require a statistical evaluation of the heat of transfer, or a variational approach based on more microscopic ingredients.