Nucleation and growth dynamics of ellipsoidal crystals in metastable liquids

Predictive Shapes of Ellipsoid PPDL-PTHF Copolymer Particles Prepared by the Phantom Stretching Technique

Ellipsoidal polymer particles can be prepared from spheres by unidirectional stretching at elevated temperatures, while the particles’ aspect ratios (AR) that result from this phantom stretching methodology are often not precisely predictable. Here, an elastic deformation model was exemplarily evaluated for ~50 µm spherical microparticles from PPDL-PTHF block copolymers. The prolate ellipsoidal particles, obtained by stretching in polyvinyl alcohol phantoms, differed in dimensions at identical relative phantoms elongations up to 150%, depending on the relative polymer composition and their systematically altered mechanical properties. Importantly, the resulting particle shapes within the studied range of AR up to ~4 matched the predictions of the elastic deformation model, which includes information of the elastic moduli of phantom and particle materials. These data suggest that the model may be applicable to predict the conditions needed to precisely prepare ellipsoids of desired AR and may be applicable to various deformable particle materials.

A review on the theory of stable dendritic growth

This review article summarizes the main outcomes following from recently developed theories of stable dendritic growth in undercooled one-component and binary melts. The nonlinear heat and mass transfer mechanisms that control the crystal growth process are connected with hydrodynamic flows (forced and natural convection), as well as with the non-local diffusion transport of dissolved impurities in the undercooled liquid phase. The main conclusions following from stability analysis, solvability and selection theories are presented. The sharp interface model and stability criteria for various crystallization conditions and crystalline symmetries met in actual practice are formulated and discussed. The review is also focused on the determination of the main process parameters-the tip velocity and diameter of dendritic crystals as functions of the melt undercooling, which define the structural states and transitions in materials science (e.g. monocrystalline-polycrystalline structures). Selection criteria of stable dendritic growth mode for conductive and convective heat and mass fluxes at the crystal surface are stitched together into a single criterion valid for an arbitrary undercooling. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Evaporation kinetics of a polydisperse ensemble of drops

A mathematical model of the evaporation of a polydisperse ensemble of drops, with allowance for a nonlinear 'diffusion' term in the kinetic equation for the population density distribution function, is developed. The model describes the interaction of a gas phase with vaporizing drops: it has great potential for application in condensed matter physics, thermophysics and engineering devices (e.g. spray drying, cooling, power engineering). The kinetics of heat transfer between phases is theoretically studied. An analytical solution to the integro-differential equations of the process of droplet evaporation is found in a parametric form. Analytical solutions in the presence and absence of the 'diffusion' term are compared. It is shown that the fluctuations in particle evaporation rates ('diffusion' term in the Fokker-Planck equation) play a decisive role in the evolutionary behaviour of a polydisperse ensemble of vaporizing liquid drops. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

The influence of non-stationarity and interphase curvature on the growth dynamics of spherical crystals in a metastable liquid

This manuscript is concerned with the theory of nucleation and evolution of a polydisperse ensemble of crystals in metastable liquids during the intermediate stage of a phase transformation process. A generalized growth rate of individual crystals is obtained with allowance for the effects of their non-stationary evolution in unsteady temperature (solute concentration) field and the phase transition temperature shift appearing due to the particle curvature (the Gibbs-Thomson effect) and atomic kinetics. A complete system of balance and kinetic equations determining the transient behaviour of the metastability degree and the particle-radius distribution function is analytically solved in a parametric form. The coefficient of mutual Brownian diffusion in the Fokker-Planck equation is considered in a generalized form defined by an Einstein relation. It is shown that the effects under consideration substantially change the desupercooling/desupersaturation dynamics and the transient behaviour of the particle-size distribution function. The asymptotic state of the distribution function (its 'tail'), which determines the relaxation dynamics of the concluding (Ostwald ripening) stage of a phase transformation process, is derived. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Ostwald ripening in the presence of simultaneous occurrence of various mass transfer mechanisms: an extension of the Lifshitz-Slyozov theory

The Ostwald ripening stage of a phase transformation process with allowance for synchronous operation of various mass transfer mechanisms (volume diffusion and diffusion along the block boundaries and dislocations) and the initial condition for the particle-radius distribution function is theoretically studied. The initial condition is taken from the analytical solution describing the intermediate stage of a phase transition process. The present theory focuses on relaxation dynamics from the beginning of the ripening process to its final asymptotic state, which is described by the previously constructed theories (Slezov VV. et al. 1978 J. Phys. Chem. Solids 39, 705-709. (doi:10.1016/0022-3697(78)90002-1) and Alexandrov & Alexandrova 2020 Phil. Trans. R. Soc. A 378, 20190247. (doi:10.1098/rsta.2019.0247)). An evolutionary behaviour of particle growth rates dependent on various mass transfer mechanisms and time is analytically described. The boundaries of the transition layer, which surround the blocking point, are found. The fundamental and relaxation contributions to the particle-radius distribution function are derived for the simultaneous occurrence of various mass transfer mechanisms. The left branch of this function is shifted to smaller particle radii whereas its right branch extends to the right of the blocking point as compared with the asymptotic universal distribution function. The theory under consideration well agrees with experimental data. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Transport phenomena in complex systems (part 1)

The issue, in two parts, is devoted to theoretical, computational and experimental studies of transport phenomena in various complex systems (in porous and composite media; systems with physical and chemical reactions and phase and structural transformations; in biological tissues and materials). Various types of these phenomena (heat and mass transfer; hydrodynamic and rheological effects; electromagnetic field propagation) are considered. Anomalous, relaxation and nonlinear transport, as well as transport induced by the impact of external fields and noise, is the focus of this issue. Modern methods of computational modelling, statistical physics and hydrodynamics, nonlinear dynamics and experimental methods are presented and discussed. Special attention is paid to transport phenomena in biological systems (such as haemodynamics in stenosed and thrombosed blood vessels magneto-induced heat generation and propagation in biological tissues, and anomalous transport in living cells) and to the development of a scientific background for progressive methods in cancer, heart attack and insult therapy (magnetic hyperthermia for cancer therapy, magnetically induced circulation flow in thrombosed blood vessels and non-contact determination of the local rate of blood flow in coronary arteries). The present issue includes works on the phenomenological study of transport processes, the derivation of a macroscopic governing equation on the basis of the analysis of a complicated internal reaction and the microscopic determination of macroscopic characteristics of the studied systems. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.