Interfacial rheology of linearly growing polyelectrolyte multilayers at the water-air interface: from liquid to solid viscoelasticity.

Despite the long history of investigations of polyelectrolyte multilayer formation on solid or liquid surfaces, important questions remain open concerning the construction of the first set of layers. These are generally deposited on a first anchoring layer of different chemistry, influencing their construction and properties. We propose here an in-depth investigation of the formation of NaPSS/PAH multilayers at the air/water interface in the absence of a chemically different anchoring layer, profiting from the surface activity of NaPSS. To analyse the mechanical properties of the different layers, we combine recently established analysis techniques of an inflating/deflating bubble exploiting simultaneous shape and pressure measurement: bubble shape elastometry, general stress decomposition and capillary meniscus dynanometry. We complement these measurements by interfacial shear rheology. The obtained results allow us to confirm, first of all, the strength of the aforementioned techniques to characterize complex interfaces with non-linear viscoelastic properties. Furthermore, their sensitivity allows us to show that the multilayer properties are highly sensitive to the temporal and mechanical conditions under which they are constructed and manipulated. We nevertheless identify a robust trend showing a clear transition from a liquid-like viscoelastic membrane to a solid-like viscoelastic membrane after the deposition of 5 layers. We interpret this as the number of layers required to create a fully connected multilayer, which is consistent with previous results obtained on solid or liquid interfaces.

Elastometry of Complex Fluid Pendant Capsules.

Oil/water interfaces are ubiquitous in nature. Opposing polarities at these interfaces attract surface-active molecules, which can seed complex viscoelastic or even solid interfacial structure. Biorelevant proteins such as hydrophobin, polymers such as PNIPAM, and the asphaltenes in crude oil (CRO) are examples of some systems where such layers can occur. When a pendant drop of CRO is aged in brine, it can form an interfacial elastic membrane of asphaltenes so stiff that it wrinkles and crumples upon retraction. Most of the work studying CRO/brine interfaces focuses on the viscoelastic liquid regime, leaving a wide range of fully solidified, elastic interfaces largely unexplored. In this work, we quantitatively measure elasticity in all phases of drop retraction. In early retraction, the interface shows a fluid viscoelasticity measurable using a Gibbs isotherm or dilatational rheology. Further retraction causes a phase transition to a 2D elastic solid with nonisotropic, nonhomogeneous surface stresses. In this regime, we use new techniques in the elastic membrane theory to fit for the elasticities of these solid capsules. These elastic measurements can help us develop a deeper understanding not only of CRO interfaces but also of the myriad fluid systems with solid interfacial layers.

Enhancing robustness, precision, and speed of traction force microscopy with machine learning.

Traction patterns of adherent cells provide important information on their interaction with the environment, cell migration, or tissue patterns and morphogenesis. Traction force microscopy is a method aimed at revealing these traction patterns for adherent cells on engineered substrates with known constitutive elastic properties from deformation information obtained from substrate images. Conventionally, the substrate deformation information is processed by numerical algorithms of varying complexity to give the corresponding traction field via solution of an ill-posed inverse elastic problem. We explore the capabilities of a deep convolutional neural network as a computationally more efficient and robust approach to solve this inversion problem. We develop a general purpose training process based on collections of circular force patches as synthetic training data, which can be subjected to different noise levels for additional robustness. The performance and the robustness of our approach against noise is systematically characterized for synthetic data, artificial cell models, and real cell images, which are subjected to different noise levels. A comparison with state-of-the-art Bayesian Fourier transform traction cytometry reveals the precision, robustness, and speed improvements achieved by our approach, leading to an acceleration of traction force microscopy methods in practical applications.

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.

Pendant drop tensiometry: A machine learning approach.

Modern pendant drop tensiometry relies on the numerical solution of the Young-Laplace equation and allows us to determine the surface tension from a single picture of a pendant drop with high precision. Most of these techniques solve the Young-Laplace equation many times over to find the material parameters that provide a fit to a supplied image of a real droplet. Here, we introduce a machine learning approach to solve this problem in a computationally more efficient way. We train a deep neural network to determine the surface tension of a given droplet shape using a large training set of numerically generated droplet shapes. We show that the deep learning approach is superior to the current state of the art shape fitting approach in speed and precision, in particular if shapes in the training set reflect the sensitivity of the droplet shape with respect to surface tension. In order to derive such an optimized training set, we clarify the role of the Worthington number as a quality indicator in conventional shape fitting and in the machine learning approach. Our approach demonstrates the capabilities of deep neural networks in the material parameter determination from rheological deformation experiments, in general.