Onsager principle in polymer dynamics

A Unified Model for Non-Fickian Diffusion and Anomalous Swelling of Glassy Polymer Gels

A sheet of glassy polymers placed in a solvent shows swelling behaviors quite different from that of soft polymers (rubbers and gels). (1) Non-Fickian diffusion (called case II diffusion): As solvent permeates into the sample, a sharp front is created between the swollen part and the glassy part, and it moves toward the center at constant speed. (2) Nonmonotonous swelling: The thickness of the sample first increases and then decreases toward the equilibrium value. Here we propose a theory to explain such anomalous behavior by extending the previous theory for swelling of soft gels. We regard the material as a continuum mixture of a glassy polymer network and solvent. We assume that the polymer network is a viscoelastic gel of glassy polymers, and its relaxation time depends strongly on solvent concentration. We show that this theory explains the above two characteristics of glassy polymers in a simple and unified framework. The theory predicts how the permeation speed of the solvent and the characteristic times of the swelling process depend on material parameters and experimental conditions, which can be checked experimentally.

A ternary mixture model with dynamic boundary conditions

The influence of short-range interactions between a multi-phase, multi-component mixture and a solid wall in confined geometries is crucial in life sciences and engineering. In this work, we extend the Cahn-Hilliard model with dynamic boundary conditions from a binary to a ternary mixture, employing the Onsager principle, which accounts for the cross-coupling between forces and fluxes in both the bulk and surface. Moreover, we have developed a linear, second-order and unconditionally energy-stable numerical scheme for solving the governing equations by utilizing the invariant energy quadratization method. This efficient solver allows us to explore the impacts of wall-mixture interactions and dynamic boundary conditions on phenomena like spontaneous phase separation, coarsening processes and the wettability of droplets on surfaces. We observe that wall-mixture interactions influence not only surface phenomena, such as droplet contact angles, but also patterns deep within the bulk. Additionally, the relaxation rates control the droplet spreading on surfaces. Furthermore, the cross-coupling relaxation rates in the bulk significantly affect coarsening patterns. Our work establishes a comprehensive framework for studying multi-component mixtures in confined geometries.

Physicochemical Mechanics and Nonequilibrium Chemical Thermodynamics

Equilibrium thermodynamics answers the question, "by how much?" Nonequilibrium thermodynamics answers the question "how fast?" The physicochemical mechanics approach presented in this article answers both of these questions. It also gives equilibrium laws and expressions for all major transport coefficients and their relations, which was previously impossible. For example, Onsager's reciprocal relations only tell us that symmetric transport coefficients are equal, and even for these, the value is often not known. Our new approach, applicable to non-isolated systems, leads to a new formulation of the second law of thermodynamics and agrees with entropy increase in spontaneous processes for isolated systems. Instead of entropy, it is based on a modified Lagrangian formulation which always increases during system evolution, even in the presence of external fields. This article will present numerous examples of physicochemical mechanics can be applied to various transport processes and their equilibriums, including thermodiffusion and different surface processes. It has been proven that the efficiency of a transport process with an actual steady-state flux (as opposed to a reversible process near equilibrium) is 50%. Finally, an analogy between physicochemical mechanics and some social processes is mentioned.

Accelerating the stimuli-responsive bending of a gel using mechanical constraints

Gel bends in response to external stimuli, which has important technical applications ranging from artificial muscle to drug delivery. Here, we predict a simple and effective method to accelerate the bending of gel using mechanical constraints. We propose an exact theory of the bending dynamics of gel, which gives analytical solutions for the time evolution of the gel curvature and the relaxation time with which the system approaches to its final equilibrium state. The theory shows that the relaxation time of a slender gel confined between two parallel and rigid plates is smaller than it of a free gel with no constraints, indicating that gel bends faster when swollen in the direction parallel to the two confined plates by adding more mechanical constraints. The advantages of this new method is no need to change the microstructure and components of gel itself as previous methods. This finding brings valuable approach in designing soft robotics and healthcare devices, and is subject to experimental test.

Gelatin Methacryloyl-Based Sponge with Designed Conical Microchannels for Rapidly Controlling Hemorrhage and Theoretical Verification

It remains a challenge to develop effective hemostatic products in battlefield rescue for noncompressible massive hemorrhage. Some previous research had concentrated on the modification of different materials to improve the hemostasis ability of sponges. Herein, to investigate the relationship between the taper of microchannels and hemostatic performance of porous sponges, gelatin methacryloyl-based sponges with designed conical microchannels and a disordered porous structure were prepared using the 3D printing method and freeze-drying technology. Experiments and theoretical model analysis demonstrated that the taper and distribution of microchannels in the sponge affected the water and blood absorption properties, as well as the expansion ability. In treatment of SD rat liver defect and SD rat liver perforation wound, GS-1 sponge with the taper (1/15) microchannels exhibited an excellent hemostatic effect with blood loss of 0.866 ± 0.093 g and a hemostasis time of 280 ± 10 s. Results showed that the hemostatic capacities of GelMA sponges were increased with the bottom diameter (taper) of conical microchannels. This is a potential strategy to develop designed taper sponges with designed taper microchannels for rapidly controlling hemorrhage.

Mechanism of temperature-induced asymmetric swelling and shrinking kinetics in self-healing hydrogels

Understanding the physical principle that governs the stimuli-induced swelling and shrinking kinetics of hydrogels is indispensable for their applications. Here, we show that the shrinking and swelling kinetics of self-healing hydrogels could be intrinsically asymmetric. The structure frustration, formed by the large difference in the heat and solvent diffusions, remarkably slows down the shrinking kinetics. The plateau modulus of viscoelastic gels is found to be a key parameter governing the formation of structure frustration and, in turn, the asymmetric swelling and shrinking kinetics. This work provides fundamental understandings on the temperature-triggered transient structure formation in self-healing hydrogels. Our findings will find broad use in diverse applications of self-healing hydrogels, where cooperative diffusion of water and gel network is involved. Our findings should also give insight into the molecular diffusion in biological systems that possess macromolecular crowding environments similar to self-healing hydrogels.

Variational methods and deep Ritz method for active elastic solids

Variational methods have been widely used in soft matter physics for both static and dynamic problems. These methods are mostly based on two variational principles: the variational principle of minimum free energy (MFEVP) and Onsager's variational principle (OVP). Our interests lie in the applications of these variational methods to active matter physics. In our former work [H. Wang, T. Qian and X. Xu, Soft Matter, 2021, 17, 3634-3653], we have explored the applications of OVP-based variational methods for the modeling of active matter dynamics. In the present work, we explore variational (or energy) methods that are based on MFEVP for static problems in active elastic solids. We show that MFEVP can be used not only to derive equilibrium equations, but also to develop approximate solution methods, such as the Ritz method, for active solid statics. Moreover, the power of the Ritz-type method can be further enhanced using deep learning methods if we use deep neural networks to construct the trial functions of the variational problems. We then apply these variational methods and the deep Ritz method to study the spontaneous bending and contraction of a thin active circular plate that is induced by internal asymmetric active contraction. The circular plate is found to be bent towards its contracting side. The study of such a simple toy system gives implications for understanding the morphogenesis of solid-like confluent cell monolayers. In addition, we introduce a so-called activogravity length to characterize the importance of gravitational forces relative to internal active contraction in driving the bending of the active plate. When the lateral plate dimension is larger than the activogravity length (about 100 micron), gravitational forces become important. Such gravitaxis behaviors at multicellular scales may play significant roles in the morphogenesis and in the up-down symmetry broken during tissue development.

Derivation of Two-Fluid Model Based on Onsager Principle

Using the Onsager variational principle, we study the dynamic coupling between the stress and the composition in a polymer solution. In the original derivation of the two-fluid model of Doi and Onuki the polymer stress was introduced a priori; therefore, a constitutive equation is required to close the equations. Based on our previous study of viscoelastic fluids with homogeneous composition, we start with a dumbbell model for the polymer, and derive all dynamic equations using the Onsager variational principle.

Capillary Rising in a Tube with Corners

We studied the dynamics of a fluid rising in a capillary tube with corners. In the cornered tube, unlike the circular tube, fluid rises with two parts, the bulk part where the entire cross-section is occupied by the fluid and the finger part where the cross-section is only partially filled. Using the Onsager principle, we derive coupled time-evolution equations for the two parts. We show the following: (a) At the early stage of rising, the dynamics is dominated by the bulk part and the fluid height h₀(t) shows the same behavior as that in the circular tube. (b) At the late stage, the bulk part stops rising but the finger part continues, following the scaling law h₁(t) ∼ t^1/3. We also show that, due to the coupling between the two parts, the equilibrium bulk height is smaller than the Jurin's height, which ignores the effect of the finger part.

Evaporation Dynamics of Sessile Droplets: The Intricate Coupling of Capillary, Evaporation, and Marangoni Flow

A single-component droplet placed on a completely wetting substrate shows a pseudostable apparent contact angle (θ_app) during evaporation. We propose a simple theory to explain the phenomenon accounting for the liquid evaporation and the internal flow induced by the capillary and Marangoni effects. The theory predicts that when evaporation starts, the contact angle approaches to θ_app in a short time τ_s, remains constant for most of the time of evaporation, and finally increases rapidly when the droplet size becomes very small. This explains the behavior observed for alkane droplets. Analytical expressions are given for the apparent contact angle θ_app and the relaxation time τ_s, which predict how they change when the evaporation rate, droplet size, and other experimental parameters such as thermal conductivity of the substrate are changed.

Transport coefficients of gel electrolytes: A molecular dynamics simulation study

The responses of gel electrolytes to stimuli make them useful in applications such as sensors and actuators. However, few studies have explored their transport properties from a molecular viewpoint. We studied the transport coefficients of gel electrolytes based on perfluorinated sulfonic acid using molecular dynamics simulations. The transport coefficients for electric and pressure fields, namely, the ionic conductivity, Darcy permeability, and cross coupling constant, were calculated based on Kubo’s linear response theory from the corresponding velocity correlation functions and mean square displacements. The effects of the water content of the gel electrolyte and those of the monovalent cationic species were also analyzed. The calculated transport coefficients qualitatively agree with the reported experimental results. The role of the cross coupling constants in determining the functional efficiency of gel electrolytes as pressure sensors or electroactive actuators is discussed.

Chemomechanical equilibrium at the interface between a simple elastic solid and its liquid phase

Applying diffusion coupled deformation theory, we investigate how the elastic properties of a solid body are modified when forced to keep its chemical potential aligned with that of its melt. The theory is implemented at the classical level of continuum mechanics, treating materials as simple continua defined by uniform constitutive relations. A phase boundary is a sharp dividing surface separating two continua in mechanical and chemical equilibrium. We closely follow the continuum theory of the swelling of elastomers (gels) but now applied to a simple two phase one-component system. The liquid is modeled by a local free energy density defining a chemical potential and hydrostatic pressure as usual. The model is extended to a solid by adding a non-linear shear elastic energy term with an effective modulus depending on density. Imposing chemomechanical equilibrium with the liquid reservoir reduces the bulk modulus of the solid to zero. The shear modulus remains finite. The stability of the hyper-compressible solid is investigated in a thought experiment. A mechanical load is applied to a rectangular bar under the constraint of fixed lateral dimensions. The linear elastic modulus for axial loading is evaluated and found to be larger than zero, implying that the bar, despite the zero bulk modulus, can support a weight placed on its upper surface. The weight is stabilized by the induced shear stress. The density dependence of the shear modulus is found to be a second order effect reducing the density of the stressed solid (chemostriction).

Temperature Dependence of Polymer Network Diffusion

The swelling dynamics of polymer gels are characterized by the (collective) diffusion coefficient D of the polymer network. Here, we measure the temperature dependence of D of polymer gels with controlled homogeneous network structures using dynamic light scattering. An evaluation of the diffusion coefficient at the gelation point D_{gel} and the increase therein as the gelation proceeds ΔD≡D-D_{gel} indicates that ΔD is a linear function of the absolute temperature with a significantly large negative constant term. This feature is formally identical to the recently discovered "negative energy elasticity" [Y. Yoshikawa et al. Phys. Rev. X 11, 011045 (2021)PRXHAE2160-330810.1103/PhysRevX.11.011045], demonstrating a nontrivial similarity between the statics and dynamics of polymer networks.

Recent Advances in Conservation-Dissipation Formalism for Irreversible Processes

The main purpose of this review is to summarize the recent advances of the Conservation–Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF’s physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker–Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, etc. Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.

The contact angle of an evaporating droplet of a binary solution on a super wetting surface

We study the dynamics of the contact angle of a droplet of a binary solution evaporating on a super wetting surface. Recent experiments have shown that although the equilibrium contact angle of such a droplet is zero, the contact angle can show complex time dependence before reaching the equilibrium value. We analyse such phenomena by extending our previous theory for the dynamics of an evaporating single component droplet to a double component droplet. We show that the time dependence of the contact angle can be quite complex. Typically, it first decreases slightly, and then increases and finally decreases again. Under certain conditions, we find that the contact angle remains constant over a certain period of time during evaporation. We study how the plateau or peak contact angle depends on the initial composition and the humidity. This theory explains the experimental results reported previously.

Onsager's variational principle in active soft matter

Onsagers variational principle (OVP) was originally proposed by Lars Onsager in 1931 [L. Onsager, Phys. Rev., 1931, 37, 405]. This fundamental principle provides a very powerful tool for formulating thermodynamically consistent models. It can also be employed to find approximate solutions, especially in the study of soft matter dynamics. In this work, OVP is extended and applied to the dynamic modeling of active soft matter such as suspensions of bacteria and aggregates of animal cells. We first extend the general formulation of OVP to active matter dynamics where active forces are included as external non-conservative forces. We then use OVP to analyze the directional motion of individual active units: a molecular motor walking on a stiff biofilament and a toy two-sphere microswimmer. Next we use OVP to formulate a diffuse-interface model for an active polar droplet on a solid substrate. In addition to the generalized hydrodynamic equations for active polar fluids in the bulk region, we have also derived thermodynamically consistent boundary conditions. Finally, we consider the dynamics of a thin active polar droplet under the lubrication approximation. We use OVP to derive a generalized thin film equation and then employ OVP as an approximation tool to find the spreading laws for the thin active polar droplet. By incorporating the activity of biological systems into OVP, we develop a general approach to construct thermodynamically consistent models for better understanding the emergent behaviors of individual animal cells and cell aggregates or tissues.