Optothermal grid activation of microflow with magnetic nanoparticle thermophoresis for microfluidics

We report focused light-induced activation of intense magnetic microconvection mediated by suspended magnetic nanoparticles in microscale two-dimensional optothermal grids. Fully anisotropic control of microflow and mass transport fluxes is achieved by engaging the magnetic field along one or the other preferred directions. The effect is based on the recently described thermal diffusion–magnetomechanical coupling in synthetic magnetic nanofluids. We expect that the new phenomenon can be applied as an efficient all-optical mixing strategy in integrated microfluidic devices. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Multiscale analysis of crystalline defect formation in rapid solidification of pure aluminium and aluminium–copper alloys

Rapid solidification leads to unique microstructural features, where a less studied topic is the formation of various crystalline defects, including high dislocation densities, as well as gradients and splitting of the crystalline orientation. As these defects critically affect the material’s mechanical properties and performance features, it is important to understand the defect formation mechanisms, and how they depend on the solidification conditions and alloying. To illuminate the formation mechanisms of the rapid solidification induced crystalline defects, we conduct a multiscale modelling analysis consisting of bond-order potential-based molecular dynamics (MD), phase field crystal-based amplitude expansion simulations, and sequentially coupled phase field–crystal plasticity simulations. The resulting dislocation densities are quantified and compared to past experiments. The atomistic approaches (MD, PFC) can be used to calibrate continuum level crystal plasticity models, and the framework adds mechanistic insights arising from the multiscale analysis. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Transport phenomena in complex systems (part 2)

This theme issue, in two parts, continues research studies of transport phenomena in complex media published in the first part (Alexandrov & Zubarev 2021 Phil. Trans. R. Soc. A 379 , 20200301. ( doi:10.1098/rsta.2020.0301 )). The issue is concerned with theoretical, numerical and experimental investigations of nonlinear transport phenomena in heterogeneous and metastable materials of different nature, including biological systems. The papers are devoted to the new effects arising in such systems (e.g. pattern and microstructure formation in materials, impacts of external processes on their properties and evolution and so on). State-of-the-art methods of numerical simulations, stochastic analysis, nonlinear physics and experimental studies are presented in the collection of issue papers. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Structure diagram and dynamics of formation of hexagonal boron nitride in phase-field crystal model

The phase-field crystal (PFC-model) is a powerful tool for modelling of the crystallization in colloidal and metallic systems. In the present work, the modified hyperbolic phase-field crystal model for binary systems is presented. This model takes into account slow and fast dynamics of moving interfaces for both concentration and relative atomic number density (which were taken as order parameters). The model also includes specific mobilities for each dynamical field and correlated noise terms. The dynamics of chemical segregation with origination of mixed pseudo-hexagonal binary phase (the so-called ‘triangle phase’) is used as a benchmark in two spatial dimensions for the developing model. Using the free energy functional and specific lattice vectors for hexagonal crystal, the structure diagram of co-existence of liquid and three-dimensional hexagonal phase for the binary PFC-model was carried out. Parameters of the crystal lattice correspond to the hexagonal boron nitride (BN) crystal, the values of which have been taken from the literature. The paper shows the qualitative agreement between the developed structure diagram of the PFC model and the previously known equilibrium diagram for BN constructed using thermodynamic functions. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Modelling of hemodynamics in bifurcation lesions of coronary arteries before and after myocardial revascularization

Modelling of patient-specific hemodynamics for a clinical case of severe coronary artery disease with the bifurcation stenosis was carried out with allowance for standard angiographic data obtained before and after successfully performed myocardial revascularization by stenting of two arteries. Based on a non-Newtonian fluid model and an original algorithm for fluid dynamics computation operated with a limited amount of initial data, key characteristics of blood flow were determined to analyse the features of coronary disease and the consequences of its treatment. The results of hemodynamic modelling near bifurcation sites are presented with an emphasis on physical, physiological and clinical phenomena to demonstrate the feasibility of the proposed approach. The main limitations and ways to minimize them are the subjects of discussion as well. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Modelling of liquid film migration in Al-Cu alloys

Microstructural evolution in the presence of liquid film migration (LFM) is simulated for Al-Cu alloys using a cellular automaton (CA) model. Simulations are performed for the microstructural evolution and concentration distribution in an Al-4 wt.%Cu alloy with initially equiaxed grain structures holding in a temperature gradient. A slight deviation from local equilibrium, estimated from experimental data, is considered to be the driving force for LFM. The direction of LFM is triggered by concentration fluctuations setting a concentration gradient as a further driving force. The simulation successfully reproduces the experimentally observed microstructures generated by LFM accompanied by a particle free zone behind the liquid film. The solid concentration in the particle free zone is found to be the equilibrium solid concentration. The simulated concentration profile across the migrating liquid film agrees well with experimental measurements. The simulated grain structure becomes coarser and highly elongated after holding in the temperature gradient. The results reveal that the increase in transversal grain width is mainly controlled by LFM, while the grain elongation in longitudinal direction is attributed to both LFM and temperature gradient zone melting. The solid concentration decreases from the initial (supersaturated) composition to the local equilibrium solid concentration corresponding to the local temperature. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Thermodynamic description of metastable fcc/liquid phase equilibria and solidification kinetics in Al-Cu alloys

The thermodynamic description of the fcc phase in the Al-Cu system has been revised, allowing for the prediction of metastable fcc/liquid phase equilibria to undercoolings of Δ T = 421 K below the eutectic temperature. Hypoeutectic Al-Cu alloys that are prone to pronounced microsegregation were solidified containerlessly in electromagnetic levitation. Solidus and liquidus concentrations were experimentally determined from highly undercooled samples employing energy-dispersive X-ray analysis. Solid concentrations at a rapidly propagating solid/liquid interface were additionally calculated using a sharp interface model that considers all undercoolings and is based on solvability theory. Modelling results (front velocity versus undercooling) were also corroborated by in situ observation with a high-speed camera. A newly established thermodynamic description of the fcc phase in Al-Cu is compatible with existing CALPHAD-type databases. Inconsistencies of previous descriptions such as a miscibility gap between Al-fcc and Cu-fcc on the Al-rich side, an unrealistic curvature of the solidus line in the same composition range or an azeotropic point near the melting point of Cu, are amended in the new description. The procedure to establish the description of phase equilibria at high undercoolings can be transferred to other alloy systems and is of a general nature. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Predicting concurrent structural mechanical mechanisms during microstructure evolution

The interdependence between structural mechanics and microstructure solidification has been widely observed experimentally as a factor leading to undesirable macroscopic properties and casting defects. Despite this, numerical modelling of microstructure solidification often neglects this interaction and is therefore unable to predict key mechanisms such as the development of misoriented grains. This paper presents a numerical method coupling a finite volume structural mechanics solver to a cellular automata solidification solver, where gravity or pressure-driven displacements alter the local orientation and thereby growth behaviour of the solidifying dendrites. Solutions obtained using this model are presented which show fundamental behaviours observed in experiments. The results show that small, localized deformations can lead to significant changes in the crystallographic orientation of a dendrite and ultimately affect the overall microstructure development. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Variability of complex oscillatory regimes in the stochastic model of cold-flame combustion of a hydrocarbon mixture

Processes of the cold-flame combustion of a mixture of two hydrocarbons are studied on the base of a three-dimensional nonlinear dynamical model. Bifurcation analysis of the deterministic model reveals mono- and bistability parameter zones with equilibrium and oscillatory attractors. For this model, effects of random disturbances in the bistability parameter zone are studied. We show that random forcing causes transitions between coexisting stable equilibria and limit cycles with the formation of complex stochastic mixed-mode oscillations. Properties of these oscillatory regimes are studied by means of statistics of interspike intervals. A phenomenon of anti-coherence resonance is discussed. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Dynamic magnetic birefringence in a viscoelastic ferrocolloid

A model is developed to describe the oscillations of optical anisotropy induced in a viscoelastic ferrocolloid (nanodispersion of magnetic particles) by an AC magnetic field. The viscoelasticity of the matrix (carrier medium) is assumed to obey the Jeffreys rheological scheme, whose advantage is that with the aid of just two viscous parameters and a single one for elasticity it enables one to vary the retarded mechanical response of the carrier from a weakly Maxwellian fluid to a medium with the rheology of a Kelvin gel. As the orientational motion of the particles driven by the AC field is always strongly affected by thermal motion, the occurring process is described with the aid of a kinetic (Fokker–Planck type) equation that combines diffusional and drift terms. On this basis, an exact evolution equation for the macroscopic optical anisotropy of a ferrocolloid is derived that is, however, just one link in an infinite chain of equations for statistical moments. The solution is obtained by applying effective field approximation: reducing the number of moment equations to their minimum and closing the chosen set. This solution is substituted to the scheme of a standard polarimetric set-up, and it is demonstrated how the peculiarities imparted by viscoelasticity should manifest themselves on the intensity of the light transmitted through the set up containing a ferrocolloid sample. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.