Direction of Spontaneous Processes in Non-Equilibrium Systems with Movable/Permeable Internal Walls.

We consider three different systems in a heat flow: an ideal gas, a van der Waals gas, and a binary mixture of ideal gases. We divide each system internally into two subsystems by a movable wall. We show that the direction of the motion of the wall, after release, under constant boundary conditions, is determined by the same inequality as in equilibrium thermodynamics dU-dQ≤0. The only difference between the equilibrium and non-equilibrium laws is the dependence of the net heat change, dQ, on the state parameters of the system. We show that the same inequality is valid when introducing the gravitational field in the case of both the ideal gas and the van der Waals gas in the heat flow. It remains true when we consider a thick wall permeable to gas particles and derive Archimedes' principle in the heat flow. Finally, we consider the Couette (shear) flow of the ideal gas. In this system, the direction of the motion of the internal wall follows from the inequality dE-dQ-dWs≤0, where dE is the infinitesimal change in total energy (internal plus kinetic) and dWs is the infinitesimal work exchanged with the environment due to the shear force imposed on the flowing gas. Ultimately, we synthesize all these cases within a general framework of the second law of non-equilibrium thermodynamics.

Steady-state thermodynamics of a system with heat and mass flow coupling.

Equilibrium thermodynamics describes the energy exchange of a body with its environment. Here, we describe the global energy exchange of an ideal gas in the Coutte flow in a thermodynamic-like manner. We derive a fundamental relation between internal energy as a function of parameters of state. We analyze a non-equilibrium transition in the system and postulate the extremum principle, which determines stable steady states in the system. The steady-state thermodynamic framework resembles equilibrium thermodynamics.

Fundamental Relation for Gas of Interacting Particles in a Heat Flow.

There is a long-standing question of whether it is possible to extend the formalism of equilibrium thermodynamics to the case of nonequilibrium systems in steady-states. We have made such an extension for an ideal gas in a heat flow. Here, we investigated whether such a description exists for the system with interactions: the van der Waals gas in a heat flow. We introduced a steady-state fundamental relation and the parameters of state, each associated with a single way of changing energy. The first law of nonequilibrium thermodynamics follows from these parameters. The internal energy U for the nonequilibrium states has the same form as in equilibrium thermodynamics. For the van der Waals gas, U(S*,V,N,a*,b*) is a function of only five parameters of state (irrespective of the number of parameters characterizing the boundary conditions): the effective entropy S*, volume V, number of particles N, and rescaled van der Waals parameters a*, b*. The state parameters, a*, b*, together with S*, determine the net heat exchange with the environment. The net heat differential does not have an integrating factor. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

Fundamental Relation for the Ideal Gas in the Gravitational Field and Heat Flow.

We formulate the first law of global thermodynamics for stationary states of the ideal gas in the gravitational field subjected to heat flow. We map the non-uniform system (described by profiles of the density and temperature) onto the uniform one and show that the total internal energy U(S*,V,N,L,M*) is the function of the following parameters of state: the non-equilibrium entropy S*, volume V, number of particles, N, height of the column L along the gravitational force, and renormalized mass of a particle M*. Each parameter corresponds to a different way of energy exchange with the environment. The parameter M* changes internal energy due to the shift of the centre of mass induced by the heat flux. We give analytical expressions for the non-equilibrium entropy S* and effective mass M*. When the heat flow goes to zero, S* approaches equilibrium entropy. Additionally, when the gravitational field vanishes, our fundamental relation reduces to the fundamental relation at equilibrium.

Parameters of State in the Global Thermodynamics of Binary Ideal Gas Mixtures in a Stationary Heat Flow.

In this paper, we formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy U(S*,V,N1,N2,f1*,f2*) is the function of the following parameters of state: a non-equilibrium entropy S*, volume V, number of particles of the first component, N1, number of particles of the second component N2 and the renormalized degrees of freedom. The parameters f1*,f2*, N1,N2 satisfy the relation (N1/(N1+N2))f1*/f1+(N2/(N1+N2))f2*/f2=1 (f1 and f2 are the degrees of freedom for each component respectively). Thus, only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy S* and new thermodynamic parameters of state f1*,f2* explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.

Storage of Energy in Constrained Non-Equilibrium Systems.

We study a quantity T defined as the energy U, stored in non-equilibrium steady states (NESS) over its value in equilibrium U 0 , Δ U = U - U 0 divided by the heat flow J U going out of the system. A recent study suggests that T is minimized in steady states (Phys.Rev.E.99, 042118 (2019)). We evaluate this hypothesis using an ideal gas system with three methods of energy delivery: from a uniformly distributed energy source, from an external heat flow through the surface, and from an external matter flow. By introducing internal constraints into the system, we determine T with and without constraints and find that T is the smallest for unconstrained NESS. We find that the form of the internal energy in the studied NESS follows U = U 0 ∗ f ( J U ) . In this context, we discuss natural variables for NESS, define the embedded energy (an analog of Helmholtz free energy for NESS), and provide its interpretation.

Chemical memory with states coded in light controlled oscillations of interacting Belousov-Zhabotinsky droplets.

The information storing potential of droplets, in which an oscillatory, photosensitive Belousov-Zhabotinsky (BZ) reaction proceeds, is investigated experimentally. We consider coupled oscillations in pairs and triplets of droplets. Droplets are surrounded by a solution of lipids in decane. Oscillations synchronize via diffusion of an activator through a lipid bilayer. The reaction in each droplet can be individually controlled by illumination with blue light through an optical fiber. We found that in pairs of BZ droplets, only the in-phase and the forcing oscillation modes are stable, however switching between these modes is not reliable. In triplets of droplets, switching between two different, stable rotational modes (clockwise and anticlockwise) can be easily implemented. Therefore, such a system is an excellent candidate for a light controlled, reliable, one bit chemical memory unit.

Cancer classification with a network of chemical oscillators.

We discuss chemical information processing considering dataset classifiers formed with a network of interacting droplets. Our arguments are based on computer simulations of droplets in which a photosensitive variant of the Belousov-Zhabotinsky (BZ) reaction proceeds. By applying optical control we can adjust the time evolution of individual droplets and prepare the network to perform a specific computational task. We demonstrate that chemical classifiers made of droplets can be designed in computer simulations based on evolutionary algorithms. The mutual information between the dataset and the observed time evolution of droplets in the network is taken as the fitness function in the optimization process. We show that a classifier of the Wisconsin Breast Cancer Dataset made of a relatively small number of droplets can distinguish between malignant and benign forms of cancer with an accuracy exceeding 97%. The reliability of the optimized chemical classifiers of this dataset as a function of optimization time, number of droplets involved in data processing and the method of extracting the output information is discussed.

Evolutionary Design of Classifiers Made of Droplets Containing a Nonlinear Chemical Medium.

Unconventional computing devices operating on nonlinear chemical media offer an interesting alternative to standard, semiconductor-based computers. In this work we study in-silico a chemical medium composed of communicating droplets that functions as a database classifier. The droplet network can be "programmed" by an externally provided illumination pattern. The complex relationship between the illumination pattern and the droplet behavior makes manual programming hard. We introduce an evolutionary algorithm that automatically finds the optimal illumination pattern for a given classification problem. Notably, our approach does not require us to prespecify the signals that represent the output classes of the classification problem, which is achieved by using a fitness function that measures the mutual information between chemical oscillation patterns and desired output classes. We illustrate the feasibility of our approach in computer simulations by evolving droplet classifiers for three machine learning datasets. We demonstrate that the same medium composed of 25 droplets located on a square lattice can be successfully used for different classification tasks by applying different illumination patterns as its externally supplied program.

Gold-oxoborate nanocomposite-coated orthodontic brackets gain antibacterial properties while remaining safe for eukaryotic cells.

The study's main objective is to limit bacterial biofilm formation on fixed orthodontic appliances. Bacterial biofilm formation on such devices (e.g., brackets) causes enamel demineralization, referred to as white spot lesions (WSL). WSL is significant health, social and economic problem. We provide a nanotechnology-based solution utilizing a nanocomposite of gold nanoparticles embedded in a polyoxoborate matrix (BOA: B-boron, O-oxygen, A-gold, Latin aurum). The nanocomposite is fully inorganic, and the coating protocol is straightforward, effective, and ecologically friendly (low waste and water-based). Prepared coatings are mechanically stable against brushing with a toothbrush (up to 100 min of brushing). Bacteria adhesion and antibacterial properties are tested against Streptococcus mutans-common bacteria in the oral cavity. BOA reduces the adhesion of bacteria by around 78%, that is, from around 7.99 × 105  ± 1.33 × 105  CFU per bracket to 1.69 × 105  ± 3.07 × 104  CFU per bracket of S. mutans detached from unmodified and modified brackets, respectively. Modified fixed orthodontic brackets remain safe for eukaryotic cells and meet ISO 10993-5:2009 requirements for medical devices. The gathered data show that BOA deposited on orthodontic appliances provides a viable preventive measure against bacteria colonization, which presents frequent and significant complications of orthodontic treatment.

Combining rotary wet-spinning biofabrication and electro-mechanical stimulation for thein vitroproduction of functional myo-substitutes.

In this work, we present an innovative, high-throughput rotary wet-spinning biofabrication method for manufacturing cellularized constructs composed of highly-aligned hydrogel fibers. The platform is supported by an innovative microfluidic printing head (MPH) bearing a crosslinking bath microtank with a co-axial nozzle placed at the bottom of it for the immediate gelation of extruded core/shell fibers. After a thorough characterization and optimization of the new MPH and the fiber deposition parameters, we demonstrate the suitability of the proposed system for thein vitroengineering of functional myo-substitutes. The samples produced through the described approach were first characterizedin vitroand then used as a substrate to ascertain the effects of electro-mechanical stimulation on myogenic maturation. Of note, we found a characteristic gene expression modulation of fast (MyH1), intermediate (MyH2), and slow (MyH7) twitching myosin heavy chain isoforms, depending on the applied stimulation protocol. This feature should be further investigated in the future to biofabricate engineered myo-substitutes with specific functionalities.

Internal energy in compressible Poiseuille flow.

We analyze a compressible Poiseuille flow of ideal gas in a plane channel. We provide the form of internal energy U for a nonequilibrium stationary state that includes viscous dissipation and pressure work. We demonstrate that U depends strongly on the ratio Δp/p_{0}, where Δp is the pressure difference between inlet and outlet and p_{0} is the outlet's pressure. In addition, U depends on two other variables: the channel aspect ratio and the parameter equivalent to Reynolds number. The stored internal energy, ΔU=U-U_{0}, is small compared to the internal energy U_{0} of the equilibrium state for a moderate range of values of Δp/p_{0}. However, ΔU can become large for big Δp or close to vacuum conditions at the outlet (p_{0}≈0Pa).

Dynamic Self-Assembly of Magnetic/Polymer Composites in Rotating Frames of Reference.

Small ferromagnetic particles suspended in a rotating viscous polymer and subjected to an external static magnetic field dynamically self-assemble into open-lattice, periodic structures. Depending on the orientation of the magnetic field with respect to the system's axis of rotation, these structures range from arrays of parallel plates to single, double, triple, or even quaternary helices. Dynamic self-assembly in this rotating frame of reference can be explained by an interplay between magnetic, dipole-dipole, viscous drag, and centripetal forces. Once formed, the dynamic aggregates can be made permanent by thermally curing the polymer matrix.

Non-Equilibrium Self-Assembly of Monocomponent and Multicomponent Tubular Structures in Rotating Fluids.

When suspended in a denser rotating fluid, lighter particles experience a cylindrically symmetric confining potential that drives their crystallization into either monocomponent or unprecedented binary tubular packing. These assemblies form around the fluid's axis of rotation, can be dynamically interconverted (upon accelerating or decelerating the fluid), can exhibit preferred chirality, and can be made permanent by solidifying the fluid. The assembly can be extended to fluids forming multiple concentric interfaces or to systems of bubbles forming both ordered and "gradient" structures within curable polymers.

Interference-like patterns of static magnetic fields imprinted into polymer/nanoparticle composites.

Interference of waves is important and used in many areas of science and technology but does not extend to static magnetic fields which lack the wave structure. On the other hand, magnetic fields can be spatially modulated using microstructured materials comprising magnetic and non-magnetic domains. Here, we show that when such spatial modulation is coupled to the dynamics of magnetic particles, it can give rise to interference-like patterns. These patterns are imprinted into thin polymer films by overlaying "stamps" presenting periodic arrays of magnetic and nonmagnetic regions. The structures that emerge from such a superposition are sensitive to any motions of the stamps, can depend on the history of these motions, can produce features significantly smaller than those in the stamps, and can be either planar or three-dimensional.

Microfluidic platform for reproducible self-assembly of chemically communicating droplet networks with predesigned number and type of the communicating compartments.

We report a microfluidic system for individually tailored generation and incubation of core-shell liquid structures with multiple cores that chemically communicate with each other via lipid membranes. We encapsulate an oscillating reaction-diffusion Belousov-Zhabotinsky (BZ) medium inside the aqueous droplets and study the propagation of chemical wave-fronts through the membranes. We further encapsulate the sets of interconnected BZ-droplets inside oil-lipid shells in order to i) chemically isolate the structures and ii) confine them via tunable capillary forces which leads to self-assembly of predesigned topologies. We observe that doublets (pairs) of droplets encapsulated in the shell exhibit oscillation patterns that evolve in time. We collect statistical data from tens of doublets all created under precisely controlled, almost identical conditions from which we conclude that the different types of transitions between the patterns depend on the relative volumes of the droplets within a chemically coupled pair. With this we show that the volume of the compartment is an important control parameter in designing chemical networks, a feature previously appreciated only by theory. Our system not only allows for new insights into the dynamics of geometrically complex and interacting chemical systems but is also suitable for generating autonomous chemically interconnected microstructures with possible future use, e.g., as smart biosensors or drug-release capsules.

Understanding Networks of Computing Chemical Droplet Neurons Based on Information Flow.

In this paper, we present general methods that can be used to explore the information processing potential of a medium composed of oscillating (self-exciting) droplets. Networks of Belousov-Zhabotinsky (BZ) droplets seem especially interesting as chemical reaction-diffusion computers because their time evolution is qualitatively similar to neural network activity. Moreover, such networks can be self-generated in microfluidic reactors. However, it is hard to track and to understand the function performed by a medium composed of droplets due to its complex dynamics. Corresponding to recurrent neural networks, the flow of excitations in a network of droplets is not limited to a single direction and spreads throughout the whole medium. In this work, we analyze the operation performed by droplet systems by monitoring the information flow. This is achieved by measuring mutual information and time delayed mutual information of the discretized time evolution of individual droplets. To link the model with reality, we use experimental results to estimate the parameters of droplet interactions. We exemplarily investigate an evolutionary generated droplet structure that operates as a NOR gate. The presented methods can be applied to networks composed of at least hundreds of droplets.