Fluid dynamics alters liquid-liquid phase separation in confined aqueous two-phase systems

Electrokinetics at liquid-liquid interfaces: Physical models and transport mechanisms

The electrification effects and electrokinetic flow phenomena at immiscible liquid-liquid interfaces have been a subject of scientific inquiry for over a century. Unlike solid-liquid interfaces, liquid-liquid interfaces exhibit not only multiphysical and cross-scale characteristics but also diffuse soft properties, including finite thickness, fluidity, ion adsorbability, and permeability, which introduces diverse interfacial charging mechanisms and conductive dielectric properties, imparting unique characteristics to electrokinetic multiphase flow systems. Electrokinetic multiphase hydrodynamics (EKmHD), grounded in electrochemistry and colloid and interface science, has experienced renewed interest in recent years. This is particularly evident in systems such as the interface between two immiscible electrolyte solutions (ITIES) in electrochemistry, self-propelling droplets in physicochemical hydrodynamics, and digital microfluidics in electromechanics. The multiphase diffuse soft nature of charged liquid-liquid interfaces introduces novel physical scales and theoretical dimensions, positioning EKmHD as a potential foundation for a new interdisciplinary field rather than merely a cross-disciplinary area. This review highlights the need for an integrated research approach that combines interfacial charging mechanisms with electrokinetic flows, alongside a cross-scale modeling framework for interfacial multiphysical transport. It systematically organizes the characteristics of liquid-liquid interfaces from the perspectives of charging mechanisms and electrokinetic behaviors, with particular emphasis on spontaneous partition- and adsorption-induced charging at the interface, and the strong coupling between multiphase diffuse soft interface flow and ion transport. Furthermore, the paper comprehensively summarizes the transport mechanisms of electrokinetic multiphase flows concerning interfacial ion transport and fluid flow, while refining the corresponding dominant dimensionless parameters. Additionally, it systematically consolidates current understanding of typical electrokinetic multiphase flow scenarios, with special focus on potential future research directions. These include the electrokinetic double-sided coupling effects in ITIES systems, solidification and nonlinear effects in droplet/bubble electrophoresis, the validity of the leaky dielectric model, electrokinetic instabilities of jets and ion-selective soft interfaces, and the active and passive control of two-phase electrokinetic wetting dynamics and displacement.

Physics-informed deep learning for stochastic particle dynamics estimation

Single-particle tracking has enabled quantitative studies of complex systems, providing nanometer localization precision and millisecond temporal resolution in heterogeneous environments. However, at micro- or nanometer scales, probe dynamics become inherently stochastic due to Brownian motion and complex interactions, leading to varied diffusion behaviors. Typically, analysis of such trajectory data involves certain moving-window operation and assumes the existence of some pseudo-steady states, particularly when evaluating predefined parameters or specific types of diffusion modes. Here, we introduce the stochastic particle-informed neural network (SPINN), a physics-informed deep learning framework that integrates stochastic differential equations to model and infer particle diffusion dynamics. The SPINN autonomously explores parameter spaces and distinguishes between deterministic and stochastic components with single-frame resolution. Using the anomalous diffusion dataset, we validated SPINN's ability to reduce frame-to-frame variability while preserving key statistical correlations, allowing for accurate characterization of different stochastic processes. When applied to the diffusion of single gold nanorods in hydrogels, the SPINN revealed enhanced microrheological properties during hydrogel gelation and uncovered interfacial dynamics during dextran/tetra-PEG liquid-liquid phase separation. By improving the temporal resolution of stochastic dynamics, the SPINN facilitates the estimation and prediction of complex diffusion behaviors, offering insights into underlying physical mechanisms at mesoscopic scales.

Thermophilic Behavior of Heat-Dissociative Coacervate Droplets

In exploring the genesis of life, liquid-liquid phase-separated coacervate droplets have been proposed as primitive protocells. Within the hydrothermal hypothesis, these droplets would emerge from molecule-rich hot fluids and thus be subjected to temperature gradients. Investigating their thermophoretic behavior can provide insights into protocell footprints in thermal landscapes, advancing our understanding of life's origins. Here, we report the thermophilic behavior of heat-dissociative droplets, contrary to the intuition that heat-associative condensates would prefer hotter areas. This aspect implies the preferential presence of heat-dissociative primordial condensates near hydrothermal environments, facilitating molecular incorporation and biochemical syntheses. Additionally, our investigations reveal similarities between thermophoretic and electrophoretic motions, dictated by molecular redistribution within droplets due to their fluid nature, which necessitates revising current electrophoresis frameworks for surface charge characterization. Our study elucidates how coacervate droplets navigate thermal and electric fields, reveals their thermal-landscape-dependent molecular characteristics, and bridges foundational theories of early life: the hydrothermal and condensate-as-protocell hypotheses.

A reaction network model of microscale liquid-liquid phase separation reveals effects of spatial dimension

Proteins can form droplets via liquid-liquid phase separation (LLPS) in cells. Recent experiments demonstrate that LLPS is qualitatively different on two-dimensional (2D) surfaces compared to three-dimensional (3D) solutions. In this paper, we use mathematical modeling to investigate the causes of the discrepancies between LLPS in 2D and 3D. We model the number of proteins and droplets inducing LLPS by continuous-time Markov chains and use chemical reaction network theory to analyze the model. To reflect the influence of space dimension, droplet formation and dissociation rates are determined using the first hitting times of diffusing proteins. We first show that our stochastic model reproduces the appropriate phase diagram and is consistent with the relevant thermodynamic constraints. After further analyzing the model, we find that it predicts that the space dimension induces qualitatively different features of LLPS, which are consistent with recent experiments. While it has been claimed that the differences between 2D and 3D LLPS stem mainly from different diffusion coefficients, our analysis is independent of the diffusion coefficients of the proteins since we use the stationary model behavior. Our results thus give new hypotheses about how space dimension affects LLPS.

Liquid-liquid phase transition as a basis for novel materials for skin repair and regeneration

Inorganic materials are of increasing interest not only for bone repair but also for other applications in regenerative medicine. In this study, the combined effects of energy-providing, regeneratively active inorganic polyphosphate (polyP) and also morphogenetically active pearl powder on wound healing were investigated. Aragonite, the mineralic constituent of pearl nacre and thermodynamically unstable form of crystalline calcium carbonate, was found to be converted into a soluble state in the presence of a Ca2+-containing wound exudate, particularly upon addition of sodium polyP (Na-polyP), driven by the transfer of Ca2+ ions from aragonite to polyP, leading to liquid-liquid phase separation to form an aqueous Ca-polyP coacervate. This process is further enhanced in the presence of Ca-polyP nanoparticles (Ca-polyP-NP). Kinetic studies revealed that the coacervation of polyP and nacre aragonite in wound exudate is a very rapid process that results in the formation of a stronger gel with a porous structure compared to polyP alone. Coacervate formation, enabled by phase transition of crystalline aragonite in the presence of Na-polyP/Ca-polyP-NP and wound exudate, could also be demonstrated in a hydroxyethyl cellulose-based hydrogel used for wound treatment. Furthermore, it is shown that Na-polyP/Ca-polyP-NP together with nacre aragonite strongly enhances the proliferation of mesenchymal stem cells and promotes microtube formation in the in vitro angiogenesis assay with HUVEC endothelial cells. The latter effect was confirmed by gene expression studies, applying real-time polymerase chain reaction, using the biomarker genes VEGF (vascular endothelial growth factor) and hypoxia-inducible factor-1 α (HIF-1α). Division of Escherichia coli is suppressed when suspended in a matrix containing Na-polyP/Ca-polyP-NP and aragonite. The potential medical relevance of these findings is supported by an animal study on genetically engineered diabetic mice (db/db), which demonstrated a marked increase in granulation tissue and microvessel formation in regenerating experimental wounds treated with Ca-polyP-NP compared to controls. Co-administration of aragonite significantly accelerated the wound healing-promoting effect of polyP in db/db mice. Based on these results, we propose that the ability of polyP to form a mixed coacervate with aragonite, in addition to its energy (ATP)-generating function, can decisively contribute to the regenerative activity of this polymer in wound repair.

Highly sensitive Raman measurements of protein aqueous solutions using liquid-liquid phase separation

A highly sensitive method is proposed for obtaining the Raman spectra of low-concentration proteins and nucleic acids in an aqueous solution using liquid-liquid phase separation. This method uses water droplets formed by adding a large amount of polyethylene glycol into a biomolecular aqueous solution. Ordinary spontaneous Raman spectra are obtained with a high signal-to-noise ratio.