Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality

We consider the evolution of interfaces in binary mixtures permeating strongly heterogeneous systems such as porous media. To this end, we first review available thermodynamic formulations for binary mixtures based on \emph{general reversible-irreversible couplings} and the associated mathematical attempts to formulate a \emph{non-equilibrium variational principle} in which these non-equilibrium couplings can be identified as minimizers. Based on this, we investigate two microscopic binary mixture formulations fully resolving heterogeneous/perforated domains: (a) a flux-driven immiscible fluid formulation without fluid flow; (b) a momentum-driven formulation for quasi-static and incompressible velocity fields. In both cases we state two novel, reliably upscaled equations for binary mixtures/multiphase fluids in strongly heterogeneous systems by systematically taking thermodynamic features such as free energies into account as well as the system's heterogeneity defined on the microscale such as geometry and materials (e.g. wetting properties). In the context of (a), we unravel a \emph{universality} with respect to the coarsening rate due to its independence of the system's heterogeneity, i.e. the well-known ${\cal O}(t^{1/3})$-behaviour for homogeneous systems holds also for perforated domains. Finally, the versatility of phase field equations and their \emph{thermodynamic foundation} relying on free energies, make the collected recent developments here highly promising for scientific, engineering and industrial applications for which we provide an example for lithium batteries

New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials

We consider the Poisson-Nernst-Planck system which is well-accepted for describing dilute electrolytes as well as transport of charged species in homogeneous environments. Here, we study these equations in porous media whose electric permittivities show a contrast compared to the electric permittivity of the electrolyte phase. Our main result is the derivation of convenient low-dimensional equations, that is, of effective macroscopic porous media Poisson-Nernst-Planck equations, which reliably describe ionic transport. The contrast in the electric permittivities between liquid and solid phase and the heterogeneity of the porous medium induce strongly oscillating electric potentials (fields). In order to account for this special physical scenario, we introduce a modified asymptotic multiple-scale expansion which takes advantage of the nonlinearly coupled structure of the ionic transport equations. This allows for a systematic upscaling resulting in a new effective porous medium formulation which shows a new transport term on the macroscale. Solvability of all arising equations is rigorously verified. This emergence of a new transport term indicates promising physical insights into the influence of the microscale material properties on the macroscale. Hence, systematic upscaling strategies provide a source and a prospective tool to capitalize intrinsic scale effects for scientific, engineering, and industrial applications

A new mode reduction strategy for the generalized Kuramoto–Sivashinsky equation

Consider the generalized Kuramoto–Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction–diffusion systems, to interface motion of viscous film flows. Our aim is to develop a systematic and rigorous low-dimensional representation of the gKS equation. For this purpose, we approximate it by a renormalization group equation which is qualitatively characterized by rigorous error bounds. This formulation allows for a new stochastic mode reduction guaranteeing optimality in the sense of maximal information entropy. Herewith, noise is systematically added to the reduced gKS equation and gives a rigorous and analytical explanation for its origin. These new results would allow one to reliably perform low-dimensional numerical computations by accounting for the neglected degrees of freedom in a systematic way. Moreover, the presented reduction strategy might also be useful in other applications where classical mode reduction approaches fail or are too complicated to be implemented

High-yield production of a super-soluble miniature spidroin for biomimetic high-performance materials

The mechanical properties of artificial spider silks are approaching a stage where commercial applications become realistic. However, the yields of recombinant silk proteins that can be used to produce fibers with good mechanical properties are typically very low and many purification and spinning protocols still require the use of urea, hexafluoroisopropanol, and/or methanol. Thus, improved production and spinning methods with a minimal environmental impact are needed. We have previously developed a miniature spider silk protein that is characterized by high solubility in aqueous buffers and spinnability in biomimetic set-ups. In this study, we developed a production protocol that resulted in an expression level of >20 g target protein per liter in an Escherichia coli fedbatch culture, and subsequent purification under native conditions yielded 14.5 g/l. This corresponds to a nearly six-fold increase in expression levels, and a 10-fold increase in yield after purification compared to reports for recombinant spider silk proteins. Biomimetic spinning using only aqueous buffers resulted in fibers with a toughness modulus of 74 MJ/m(3), which is the highest reported for biomimetically as-spun artificial silk fibers. Thus, the process described herein represents a milestone for the economic production of biomimetic silk fibers for industrial applications

Impact of physio-chemical spinning conditions on the mechanical properties of biomimetic spider silk fibers

Artificial spider silk has emerged as a biobased fiber that could replace some petroleum-based materials that are on the market today. Recent progress made it possible to produce the recombinant spider silk protein NT2RepCT at levels that would make the commercialization of fibers spun from this protein economically feasible. However, for most applications, the mechanical properties of the artificial silk fibers need to be improved. This could potentially be achieved by redesigning the spidroin, and/or by changing spinning conditions. Here, we show that several spinning parameters have a significant impact on the fibers’ mechanical properties by tensile testing more than 1000 fibers produced under 92 different conditions. The most important factors that contribute to increasing the tensile strength are fast reeling speeds and/or employing post-spin stretching. Stretching in combination with optimized spinning conditions results in fibers with a strength of >250 MPa, which is the highest reported value for fibers spun using natively folded recombinant spidroins that polymerize in response to shear forces and lowered pH

Prospect redux

The remote estimation of leaf biochemical content from spaceborne platforms has been the subject of many studies aimed at better understanding of terrestrial ecosystem functioning. The major ecological processes involved in exchange of matter and energy, like photosynthesis, primary production, evaportranspiration, respiration, and decomposition can be related to plant properties e.g., chlorophyll, water, protein, cellulose and lignin contents. As leaves represent the most important plant surfaces interacting with solar energy, a top priority has been to relate optical properties to biochemical constituents. Two different approaches have been considered: first, statistical correlations between the leaf reflectance (or transmittance) and biochemical content, and second, physically based models of leaf scattering and absorption developed using the laws of optics. Recently reviewed by Verdebout et al., the development of models of leaf optical properties has resulted in better understanding of the interaction of light with plant leaves. Present radiative transfer models mainly use chlorophyll and/or water contents as input parameters to calculate leaf reflectance. Inversion of these models allows to retrieve these constituents from spectrophotometric measurements. Conel et al. recently proposed a two-stream Kubelka-Munk model to analyze the influence of protein, cellulose, lignin, and starch on leaf reflectance, but in fact, the estimation of leaf biochemistry from remote sensing is still an open question. In order to clarify it, a laboratory experiment associating visible/infrared spectra of plan leaves both with physical measurements and biochemical analyses was conducted at the Joint Research Center during the summer of 1993. This unique data set has been used to upgrade the PROSPECT model, by including leaf biochemistry

An Image-Analysis-Based Method for the Prediction of Recombinant Protein Fiber Tensile Strength

Silk fibers derived from the cocoon of silk moths and the wide range of silks produced by spiders exhibit an array of features, such as extraordinary tensile strength, elasticity, and adhesive properties. The functional features and mechanical properties can be derived from the structural composition and organization of the silk fibers. Artificial recombinant protein fibers based on engineered spider silk proteins have been successfully made previously and represent a promising way towards the large-scale production of fibers with predesigned features. However, for the production and use of protein fibers, there is a need for reliable objective quality control procedures that could be automated and that do not destroy the fibers in the process. Furthermore, there is still a lack of understanding the specifics of how the structural composition and organization relate to the ultimate function of silk-like fibers. In this study, we develop a new method for the categorization of protein fibers that enabled a highly accurate prediction of fiber tensile strength. Based on the use of a common light microscope equipped with polarizers together with image analysis for the precise determination of fiber morphology and optical properties, this represents an easy-to-use, objective non-destructive quality control process for protein fiber manufacturing and provides further insights into the link between the supramolecular organization and mechanical functionality of protein fibers

Impact of physio-chemical spinning conditions on the mechanical properties of biomimetic spider silk fibers

Artificial spider silk has emerged as a biobased fiber that could replace some petroleum-based materials that are on the market today. Recent progress made it possible to produce the recombinant spider silk protein NT2RepCT at levels that would make the commercialization of fibers spun from this protein economically feasible. However, for most applications, the mechanical properties of the artificial silk fibers need to be improved. This could potentially be achieved by redesigning the spidroin, and/or by changing spinning conditions. Here, we show that several spinning parameters have a significant impact on the fibers' mechanical properties by tensile testing more than 1000 fibers produced under 92 different conditions. The most important factors that contribute to increasing the tensile strength are fast reeling speeds and/or employing post-spin stretching. Stretching in combination with optimized spinning conditions results in fibers with a strength of >250 MPa, which is the highest reported value for fibers spun using natively folded recombinant spidroins that polymerize in response to shear forces and lowered pH.The mechanical properties of spider silk are known to be dependent on spinning conditions. Here, the tensile behavior of over 1000 biomimetic spider silk fibers spun under 92 different conditions are tested, resulting in a yield strength of more than 250 MPa

Nonlinear forecasting of the generalised Kuramoto-Sivashinsky equation

We study the emergence of pattern formation and chaotic dynamics in the one-dimensional (1D) generalized Kuramoto-Sivashinsky (gKS) equation by means of a time-series analysis, in particular a nonlinear forecasting method which is based on concepts from chaos theory and appropriate statistical methods. We analyze two types of temporal signals, a local one and a global one, finding in both cases that the dynamical state of the gKS solution undergoes a transition from high dimensional chaos to periodic pulsed oscillations through low dimensional deterministic chaos with increasing the control parameter of the system. Our results demonstrate that the proposed nonlinear forecasting methodology allows to elucidate the dynamics of the system in terms of its predictability properties