A Second Order Fully-discrete Linear Energy Stable Scheme for a Binary Compressible Viscous Fluid Model

We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flow mixtures derived from the generalized Onsager Principle. The hydrodynamic model not only possesses the variational structure, but also warrants the mass, linear momentum conservation as well as energy dissipation. We first reformulate the model in an equivalent form using the energy quadratization method and then discretize the reformulated model to obtain a semi-discrete partial differential equation system using the Crank-Nicolson method in time. The numerical scheme so derived preserves the mass conservation and energy dissipation law at the semi-discrete level. Then, we discretize the semi-discrete PDE system on a staggered grid in space to arrive at a fully discrete scheme using the 2nd order finite difference method, which respects a discrete energy dissipation law. We prove the unique solvability of the linear system resulting from the fully discrete scheme. Mesh refinements and two numerical examples on phase separation due to the spinodal decomposition in two polymeric fluids and interface evolution in the gas-liquid mixture are presented to show the convergence property and the usefulness of the new scheme in applications

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 that accounts for cross-coupling between forces and fluxes in both bulk and surface. Moreover, we have developed a linear, second-order, and unconditionally energy stable numerical scheme for solving the governing equations, utilizing the Invariant Energy Quadratization (IEQ) 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

Thermodynamically Consistent Hydrodynamic Phase Field Models and Numerical Approximation for Multi-Component Compressible Viscous Fluid Mixtures

Material systems comprising of multi-component, some of which are compressible, are ubiquitous in nature and industrial applications. In the compressible fluid flow, the material compressibility comes from two sources. One is the material compressibility itself and another is the mass-generating source. For example, the compressibility in the binary fluid flows of non-hydrocarbon (e.g. Carbon dioxide) and hydrocarbons encountered in the enhanced oil recovery (EOR) process, comes from the compressibility of the gas-liquid mixture itself. Another example of the mixture of compressible fluids is growing tissue, in which cell proliferation and cell migration make the material volume changes so that it cannot be described as incompressible. We present a systematic derivation of thermodynamically consistent hydrodynamic phase field models for compressible viscous fluid mixtures using the generalized Onsager principle along with the one fluid multi-component formulation. By maintaining momentum conservation while enforcing mass conservation at different levels, we obtain two compressible models. When the fluid components in the mixture are incompressible, we show that one compressible model reduces to the quasi-incompressible model via a Lagrange multiplier approach. Several different approaches to arriving at the quasi-incompressible model are discussed. Then, we conduct a linear stability analysis on all the binary models derived in the thesis and show the differences of the models in near equilibrium dynamics. We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible flows of fluid mixtures derived from the generalized Onsager Principle. v The hydrodynamic model not only possesses the variational structure, but also warrants the mass, linear momentum conservation as well as energy dissipation. We first reformulate the model in an equivalent form using the energy quadratization method and then discretize the reformulated model to obtain a semi-discrete partial differential equation system using the Crank-Nicolson method in time. The numerical scheme so derived preserves the mass conservation and energy dissipation law at the semi-discrete level. Then, we discretize the semi-discrete PDE system on a staggered grid in space to arrive at a fully discrete scheme using the 2nd order finite difference method, which respects a discrete energy dissipation law. We prove the unique solvability of the linear system resulting from the fully discrete scheme. Mesh refinements are presented to show the convergence property of the new scheme. In the compressible polymer mixtures, we first construct a Flory-Huggins type of free energy and explore the phase separation phenomena due to spinodal decomposition. We investigate the phase separation with and without hydrodynamics, respectively. It tells us that hydrodynamics indeed changes local densities, the path of phase evolution and even the final energy steady states of fluid mixtures. This is alarming, indicating that hydrodynamic effects are instrumental in determining the correct spatial phase diagram for the binary fluid mixture. Finally, we study the interface dynamics and investigate the mass adsorption phenomena of one component at the interface, to show the performance of our model and the numerical scheme in simulating hydrodynamics of the hydrocarbon mixture

Bio-inspired Design and Fabrication of Super-Strong and Multifunctional Carbon Nanotube Composites

Carbon nanotubes (CNTs) are ideal scaffolds to design and architect high-performance composites at high CNT volume fractions. In these composites, the CNT alignment determines the level of aggregation and the structure morphology, and thus the load transfer efficiency between neighboring CNTs. Here, we discuss two major solutions to produce high-volume fraction CNT composites, namely the layer-by-layer stacking of aligned CNT sheets and the stretching of entangled CNT webs (networks). As inspired by the growth procedure of natural composites, the aggregation of CNTs can be well controlled during the assembling process. As a result, the CNTs can be highly packed, aligned, and importantly unaggregated, with the impregnated polymers acting as interfacial adhesion or mortars to build up the composite structure. The CNT/bismaleimide composites can yield a super-high tensile strength up to 6.27–6.94 GPa and a modulus up to 315 GPa

Chemically Active Wetting

Wetting of liquid droplets on passive surfaces is ubiquitous in our daily lives, and the governing physical laws are well-understood. When surfaces become active, however, the governing laws of wetting remain elusive. Here we propose chemically active wetting as a new class of active systems where the surface is active due to a binding process that is maintained away from equilibrium. We derive the corresponding non-equilibrium thermodynamic theory and show that active binding fundamentally changes the wetting behavior, leading to steady, non-equilibrium states with droplet shapes reminiscent of a pancake or a mushroom. The origin of such anomalous shapes can be explained by mapping to electrostatics, where pairs of binding sinks and sources correspond to electrostatic dipoles along the triple line. This is an example of a more general analogy, where localized chemical activity gives rise to a multipole field of the chemical potential. The underlying physics is relevant for cells, where droplet-forming proteins can bind to membranes accompanied by the turnover of biological fuels

Architectural Design of a Blockchain-Enabled, Federated Learning Platform for Algorithmic Fairness in Predictive Health Care: Design Science Study

Background: Developing effective and generalizable predictive models is critical for disease prediction and clinical decision-making, often requiring diverse samples to mitigate population bias and address algorithmic fairness. However, a major challenge is to retrieve learning models across multiple institutions without bringing in local biases and inequity, while preserving individual patients\u27 privacy at each site. Objective: This study aims to understand the issues of bias and fairness in the machine learning process used in the predictive health care domain. We proposed a software architecture that integrates federated learning and blockchain to improve fairness, while maintaining acceptable prediction accuracy and minimizing overhead costs. Methods: We improved existing federated learning platforms by integrating blockchain through an iterative design approach. We used the design science research method, which involves 2 design cycles (federated learning for bias mitigation and decentralized architecture). The design involves a bias-mitigation process within the blockchain-empowered federated learning framework based on a novel architecture. Under this architecture, multiple medical institutions can jointly train predictive models using their privacy-protected data effectively and efficiently and ultimately achieve fairness in decision-making in the health care domain. Results: We designed and implemented our solution using the Aplos smart contract, microservices, Rahasak blockchain, and Apache Cassandra-based distributed storage. By conducting 20,000 local model training iterations and 1000 federated model training iterations across 5 simulated medical centers as peers in the Rahasak blockchain network, we demonstrated how our solution with an improved fairness mechanism can enhance the accuracy of predictive diagnosis. Conclusions: Our study identified the technical challenges of prediction biases faced by existing predictive models in the health care domain. To overcome these challenges, we presented an innovative design solution using federated learning and blockchain, along with the adoption of a unique distributed architecture for a fairness-aware system. We have illustrated how this design can address privacy, security, prediction accuracy, and scalability challenges, ultimately improving fairness and equity in the predictive health care domain

Thermodynamics of wetting, prewetting and surface phase transitions with surface binding

In living cells, protein-rich condensates can wet the cell membrane and surfaces of membrane-bound organelles. Interestingly, many phase-separating proteins also bind to membranes leading to a molecular layer of bound molecules. Here we investigate how binding to membranes affects wetting, prewetting and surface phase transitions. We derive a thermodynamic theory for a three-dimensional bulk in the presence of a two-dimensional, flat membrane. At phase coexistence, we find that membrane binding facilitates complete wetting and thus lowers the wetting angle. Moreover, below the saturation concentration, binding facilitates the formation of a thick layer at the membrane and thereby shifts the prewetting phase transition far below the saturation concentration. The distinction between bound and unbound molecules near the surface leads to a large variety of surface states and complex surface phase diagrams with a rich topology of phase transitions. Our work suggests that surface phase transitions combined with molecular binding represent a versatile mechanism to control the formation of protein-rich domains at intra-cellular surfaces

Theory of Wetting Dynamics with Surface Binding

Biomolecules, such as proteins and RNAs, can phase separate in the cytoplasm of cells to form biological condensates. Such condensates are liquid-like droplets that can wet biological surfaces such as membranes. Many molecules that can participate in phase separation can also reversibly bind to membrane surfaces. When a droplet wets such a surface, these molecules can diffuse both inside the droplet or in the bound state on the surface. How the interplay between surface binding and surface diffusion affects the wetting kinetics is not well understood. Here, we derive the governing equations using non-equilibrium thermodynamics by relating the diffusive fluxes and forces at the surface coupled to the bulk. We use our theory to study the spreading kinetics in the presence of surface binding and find that binding speeds up wetting by nucleating a droplet inside the surface. Our results are relevant both to artificial systems and to condensates in cells. They suggest that the wetting of droplets in living cells could be regulated by two-dimensional droplets in the surface-bound layer changing the binding affinity to biological surfaces